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E. Fiandrini 1 Cenni di Cosmologia Cose la cosmologia scientifica Breve storia della nostra concezione delluniverso Le osservazioni e gli sviluppi fondamentali.

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Presentazione sul tema: "E. Fiandrini 1 Cenni di Cosmologia Cose la cosmologia scientifica Breve storia della nostra concezione delluniverso Le osservazioni e gli sviluppi fondamentali."— Transcript della presentazione:

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2 E. Fiandrini 1 Cenni di Cosmologia Cose la cosmologia scientifica Breve storia della nostra concezione delluniverso Le osservazioni e gli sviluppi fondamentali del XX secolo La relativita generale Infinatemente piccolo e Infinitamente grande Il modello standard delluniverso ai nostri giorni Possibili evoluzioni del nostro modo di concepire luniverso

3 E. Fiandrini 2 Cominciamo...dalla fine The Nobel Prize in Physics 2006Nobel Prize "for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation" John C. Mather George F. Smoot

4 E. Fiandrini 3 Cose la Cosmologia Cosmologia scientifica: descrizione dellUniverso nel suo insieme a partire dalle leggi fisiche fondamentali (cosi come le conosciamo ora!!) e da osservazioni sperimentali Non e semplicemente Cosmogonia Terreno nel quale si mette alla provala nostra comprensione della fisica: dove mettiamo in relazione infinitamente piccolo e infinitamente grande: non coincide con Astrofisica e Astronomia ATTENZIONE ALLA SEPARAZIONE DA FILOSOFIA E RELIGIONE...

5 E. Fiandrini 4 La nascita della Cosmologia Scientifica Moderna: Newton Il seme per una nuova e razionale comprensione delluniverso esistevano gia prima di Newton. A lui va il merito di aver inquadrato questa rivoluzione cognitiva in un quadro (modello) teorico (matematico) di immenso potere predittivo: La gravitazione come forza universale: determina levoluzione di qualsiasi oggetto -> quindi luniverso sempre attrattiva e additiva in modo istantaneo!

6 E. Fiandrini 5 Newtons law of gravity M: mass of one object [e.g. Earth] m: mass of the other object [e.g. apple, Moon] r: distance between the two objects F: Force with which the two objects are attracting each other G: gravitational constant [ N m 2 /kg 2 ]

7 E. Fiandrini 6 Newton II + law of gravity equivalence principle Acceleration does not depend on m, the mass of the object. All objects fall at the same rate. Left hand side: m inertia of the object Right hand side: m gravitational attraction of object equivalence of inertial and gravitating mass

8 E. Fiandrini 7 Newton e i suoi contemporanei (e i posteri fino al 1920 o quasi) pensano all Universo come una entita Statica Un universo statico non puo che essere infinitamente esteso (e omogeno, uniforme)! Problema 1: Attenzione: in un universo infinito, se la forza e instantanea basta un piccolo squilibrio in un punto per creare un grande sconvolgimento....

9 E. Fiandrini 8 A toy universe According to Newton, what is going to happen ? The model Universe is going to collapse under its own gravity boundary constant density (homogeneous)

10 E. Fiandrini 9 Newtons Universe In order to avoid collapse –homogeneous –isotropic –infinite size –no center infinite in time –has always been –will always be perfect cosmological principle perfect cosmological principle

11 E. Fiandrini 10 Questa visione apparentemente soddisfacente (universo senza confini e senza un inizio) viene pero messa in crisi anche da un altro problema: Il Paradosso di Olbers Perche di notte il cielo e nero?

12 E. Fiandrini 11 In universo omogeneo infinito e statico da qualunque parte si guardi locchio incontrera una stella. La compensazione e perfetta!: Tutto il cielo dovrebbe essere luminoso come la superficie del Sole!! Luminosita in funzione della distanza D: Numero di stelle in una buccia sferica a distanza D: costante...e infinite buccie infinita luminosita'!

13 E. Fiandrini 12 How to solve Olbers paradox ? The speed of light is finite Universe is finite Universe has finite age The distribution of stars throughout space is not uniform The wavelength of radiation increases with time. Note: for the big bang model, all these conditions are satisfied

14 E. Fiandrini 13 Oggi conosciamo la soluzione: -la velocita della luce e finita - Quello che vediamo sono immagini lontane che appartengono ad un Universo piu giovane. -Le stelle (e quindi le galassie) hanno una loro evoluzione: esiste un tempo in cui non brillavano... t x noi, oratempo a cui la luce e stata emessa segnale che si propaga con v=c v

15 E. Fiandrini 14 Einsteins new relativity Galileo: –The laws of mechanics are the same in all inertial frames of reference –time and space are the same in all inertial frames of reference Einstein: –The laws of physics are the same in all inertial frames of reference –the speed of light in the vacuum is the same in all inertial frames of reference

16 E. Fiandrini 15 Minkowskis spacetime Time intervals, lengths, and simultaneity is relative and depend on the relative velocity of the observer. velocity connects time and space Lets stop separating space and time, lets rather talk about spacetime spacetime is 4 dimensional, 3 spatial + 1 time dimension but is space and time really the same thing ?

17 E. Fiandrini 16 Faster than speed of light ? c t x

18 E. Fiandrini 17 A comment on superluminal speed The key issue is that no information can be transmitted faster than the speed of light. This does not exclude or forbid the existence of apparent superluminal velocities.

19 E. Fiandrini 18 Energy Newton: –kinetic energy: E kin = ½ m v 2 – v=0 E kin = 0 Einstein: –E = m 0 c 2 –v=0 E= m 0 c 2 rest energy –E kin = ( -1) m 0 c 2 Example: energy required to accelerate 1kg of mass to v=0.87c equivalent of 20 megatons of TNT To have v=c for a particle of mass m 0, =1 particle energy must be 1... impossible to reach in a finite interval of time Particles without mass can move only at v=c because they dont have inertia 1/[1-(v/c) 2 ] 1/2

20 E. Fiandrini 19 geometrical interval y x (x 1,y 1 ) (x 2,y 2 ) y y2y2 x1x1 x2x2 x s 2 = y 2 + x 2 y1y1

21 E. Fiandrini 20 Spacetime interval c t x (x 1,t 1 ) (x 2,t 2 ) c t c t 2 x1x1 x2x2 x s 2 = (c t) 2 – x 2 c t 1 The – sign makes the space not euclidean!

22 E. Fiandrini 21 Future, past, and elsewhere Future Past elsewhere s 2 >0 s 2 <0 t

23 E. Fiandrini 22 Principle of causality Cause must always precede the effect A must not influence D and vice versa nothing can move faster than speed of light A D Some see A happen first, some see D happen first C B All observers agree that B is in the past of A and C is in the future t

24 E. Fiandrini 23 d t Poiche' la luce viaggia a velocita' finita, guardare lontano significa andare indietro nella vita dell'Universo

25 E. Fiandrini 24 Se luniverso non e statico e in particolare, se stelle e galassie si sono formate in un qualche periodo del passato e se prima di quel periodo le condizioni erano tali che non esisteva materia luminosa, allora la luce proveniente da distanze sempre piu grandi e decrescente L Universo come noi lo conosciamo ha avuto un inizio nel lontano passato? SI!

26 E. Fiandrini 25 Nuovi sviluppi osservativi nei primi 20 anni del 1900 Edwin Hubble contribuisce alla scoperta di nuove lontane galassie e alla misurazione della loro distanza Mette in relazione la distanza con un fatto gia conosciuto: il red-shift delle righe spettrali

27 E. Fiandrini 26 Doppler effect (for sound) The pitch of an approaching car is higher than that of a car moving away.

28 E. Fiandrini 27 Doppler effect (for light) The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the red.

29 E. Fiandrini 28 velocita V Effetto Doppler

30 E. Fiandrini 29 Doppler effect red shift blue shift The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the red.

31 E. Fiandrini 30 Doppler effect Si misura z e si ottiene v Se v<

32 E. Fiandrini 31 Legge di Hubble: lo spostamento verso il rosso dipende dalla distanza

33 E. Fiandrini 32 The redshift-distance relation

34 E. Fiandrini 33 The redshift-distance relation

35 E. Fiandrini 34 Key results Most galaxies are moving away from us The recession speed v is larger for more distant galaxies. The relation between recess velocity v and distance d fulfills a linear relation: v = H 0 d Hubbles measurement of the constant H 0 : H 0 = 500 km/s/Mpc todays best fit value of the constant: H 0 = 72 § 8 km/s/Mpc

36 E. Fiandrini 35 Tutto sembra allontanarsi (IN MEDIA) da noi Siamo per caso in un punto speciale dellUniverso? Crediamo di no: estensione del principio Copernicano al Principio Cosmologico Come si puo quindi spiegare lespansione che osserviamo? ogni punto delluniverso e uguale a un altro e non esiste un centro

37 E. Fiandrini 36 Analogia con una superficie BiDimensionale: macchie sulla superficie di un palloncino che si gonfia Ogni macchia vede le altre allontanarsi: non esiste nessun centro! Ma e un vero movimento fisico? La risposta era gia nellaria attorno al 1920 grazie ad una rivoluzione di tipo teorico...

38 E. Fiandrini 37 Expanding Space Analogy: A loaf of raisin bread where the dough is rising and expanding, taking the raisins with it.

39 E. Fiandrini 38 La velocita con cui si espande R (velocita di recessione) puo anche essere maggiore di c! La limitazione a c vale solo per corpi materiali e raggi luminosi Importantissimo:!!!

40 E. Fiandrini 39 Nuovi sviluppi teorici nei primi 20 anni del 1900 Dalla Relativita Ristretta alla Relativita Generale : (tutti i riferimenti in caduta libera sono equivalenti) Presupposti matematici: La geometria differenziale le geometrie non euclidee (Gauss, Riemann, Lobacevsky, Ricci, Levi-Civita,...) A. Einstein

41 E. Fiandrini 40 Mass curves space

42 E. Fiandrini 41 General relativity Mass tells space how to curve Space tells mass how to move

43 E. Fiandrini 42 Some effects predicted by the theory of general relativity gravity bends light gravitational redshift gravitational time dilation gravitational length contraction

44 E. Fiandrini 43 Least action principle light travels on a path that minimizes the distance between two points for flat space: straight line a path that minimizes the distance between two points is called a geodesic Examples for geodesics –plane: straight line –sphere: great circle

45 E. Fiandrini 44 What is the shortest way to Europe?

46 E. Fiandrini 45 Flat space + + = 180º

47 E. Fiandrini 46 Curved space º

48 E. Fiandrini 47 Flat space circumference = 2 radius

49 E. Fiandrini 48 Curved space circumference 2 radius

50 E. Fiandrini 49 The metric equation Distance between two points (flat euclidean space) Distance between two points (curved space) f, g, h: metric coefficients

51 E. Fiandrini 50 Example: distance between two points at the surface of the Earth Coordinate differences:, naïve, but false: correct: metric coefficients: f=R 2, h= R 2 cos 2 metric coefficients: f=R 2, h= R 2 cos 2

52 E. Fiandrini 51 Spacetime Fourth coordinate: ct time coordinate has different sign than spatial coordinates spacetime distance:,, : metric coefficients,, : metric coefficients

53 E. Fiandrini 52 Why does space curvature result in attraction ? In uno spazio curvo, due particelle si muovono lungo le geodetiche tra due punti La curvatura dello spazio porta le geodetiche a ridurre la loro distanza quando si muovono NELLO spazio curvo: un osservatore NELLO spazio vede le particelle attrarsi Non esistono "forze", il moto e' determinato dalla curvatura dello spazio: le particelle seguono la linea piu' breve fra due punti

54 E. Fiandrini 53 The entire Universe in one line Geometry of spacetime (Einstein tensor) Distribution of mass and energy in the universe (stress-energy tensor)

55 E. Fiandrini 54 The entire Universe in one line The solutions of Einstein's equations provide the metric of the space-time and the motion of the particles in the space- time a in self-consistent way The space and time are part of the solution of the equations, not the simply the background where the events occur

56 E. Fiandrini 55 Why is general relativity (GR) difficult ? conceptually difficult (relativity of space and time, curvature of spacetime) set of 10 coupled partial differential equations non linear (solutions do not superpose) space and time are part of the solution exact solution known only for a very few simple cases exact solution known only for a very few simple cases

57 E. Fiandrini 56 First test: bending of light Star light should be bend as it passes through the gravitational field of the Sun, i.e., it should be possible to see a star behind the Sun

58 E. Fiandrini 57 First test: bending of light Star light should be bend as it passes through the gravitational field of the Sun, i.e., it should be possible to see a star behind the Sun General relativity predicts an angle of 1.75, twice as big as that predicted by Newtonian gravity measured by Arthur Eddington in Key event for Einsteins elevation to a celebrity.

59 E. Fiandrini 58 Test 2: Perihelion shift of Mercury Planets do not move on perfect ellipses, but ellipses are precessing. This effect is due to the gravitational force exerted by the other planets

60 E. Fiandrini 59 Test 2: Perihelion shift of Mercury Planets do not move on perfect ellipses, but ellipses are precessing. This effects is caused by the perturbing effect of the other planets gravitational field. Mercurys precession amounts to 5600 per century, but only 5557 can be explained by Newtonian gravity, leaves a discrepancy of 43 per century. General relativity predicts exactly this additional precession

61 E. Fiandrini 60 The expanding universe: How is it curved?

62 E. Fiandrini 61 Lets apply Einsteins equation to the Universe What is the solution of Einsteins equation for a homogeneous, isotropic mass distribution, ie the Universe? –As in Newtonian dynamics, gravity is always attractive –a homogeneous, isotropic and initially static universe is going to collapse under its own gravity –Alternative: expanding universe (Friedmann)

63 E. Fiandrini 62 Einsteins proposal: cosmological constant Einsteins proposal: cosmological constant There is a repulsive force in the universe vacuum exerts a pressure vacuum exerts a pressure empty space is curved rather than flat empty space is curved rather than flat The repulsive force compensates the attractive gravity static universe is possible but: such a universe turns out to be unstable: one can set up a static universe, but it simply does not remain static it must expand or shrink Einstein: greatest blunder of his life, but is it really … ?

64 E. Fiandrini 63 La costante cosmologica Essa dava luogo a un effetto antigravitazionale (gravità repulsiva) Riusciva ad arrestare il collasso dellUniverso Ciò rendeva la visione di Einstein compatibile con lidea generale di un Universo statico ed eterno

65 E. Fiandrini 64 R.G.: lequazione di Einstein (sistema di 10 eq.) (Metro, Orologi) = (Energia, Materia) Prima formulazione... aggiunta di Einstein in seconda battuta... costante di Newton Costante Cosmologica Energia del Vuoto (????)

66 E. Fiandrini 65 The great synthesis (1930) Meeting by Einstein, Hubble and Lemaître –Einstein: theory of general relativity –Friedmann and Lemaître: expanding universe as a solution to Einsteins equation –Hubble: observational evidence that the universe is indeed expanding Consequence: –Universe started from a point The Big Bang Model

67 E. Fiandrini 66

68 E. Fiandrini 67 The Necessity of a Big Bang If galaxies are moving away from each other with a speed proportional to distance, there must have been a beginning, when everything was concentrated in one single point: The Big Bang! ?

69 E. Fiandrini 68 A metric of an expanding Universe Recall: flat space better: using spherical coordinates (r,, )

70 E. Fiandrini 69 A metric of an expanding Universe But, this was for a static space. How does this expression change if we consider an expanding space ? R(t) is the so-called scale factor

71 E. Fiandrini 70 Griglia di coordinate comoventi: r,, la cui scala, cioe' unita' di misura, e' R(t) in queste coordinate le distanze rimangono uguali durante lespansione Torniamo allanalogia della superficie sferica Ci servono 3 coordinate per lo spazio: 1 raggio e 2 angoli (come la latitudine e la longitudine)

72 E. Fiandrini 71 Non sono gli oggetti che si muovono, ma e il metro (la scala delle distanze) che si modifica... E non e solo un effetto virtuale!!! La dinamica dello spazio e del tempo (cioe la loro evoluzione nel tempo) dipende dalla materia e dallenergia! L ESPANSIONE DELLO SPAZIO TEMPO E PREVISTA ~AUTOMATICAMENTE SECONDO LA R.G.!!!

73 E. Fiandrini 72 Example: static universe R(t) t

74 E. Fiandrini 73 Example: expanding at a constant rate R(t) t

75 E. Fiandrini 74 Example: expansion is slowing down R(t) t

76 E. Fiandrini 75 Example: expansion is accelerating R(t) t

77 E. Fiandrini 76 Example: collapsing R(t) t

78 E. Fiandrini 77 How old is the universe? A galaxy at distance d recedes at velocity v=H 0 d. When was the position of this galaxy identical to that of our galaxy? Answer: t Hubble : Hubble time. For H 0 = 72 km/s/Mpc: t Hubble ' 13.5 Gyr

79 E. Fiandrini 78 How big is the universe? We cant tell. We can only see (and are affected by) that part of the universe that is closer than the distance that light can travel in a time corresponding to the age of the Universe But we can estimate, how big the observable universe is: d Hubble : Hubble radius. For H 0 = 72 km/s/Mpc: d Hubble = 4.2 Gpc

80 E. Fiandrini 79 A metric of an expanding Universe But, so far, we only considered a flat space. What, if there is curvature ? k is the curvature constant –k=0: flat space –k>0: spherical geometry –k<0: hyperbolic geometry

81 E. Fiandrini 80 A metric of an expanding Universe But, so far, we only considered a flat space. What, if there is curvature ? k is the curvature constant –k=0: flat space –k>0: spherical geometry –k<0: hyperbolic geometry k>0 k<0k=0

82 E. Fiandrini 81 La metrica dello spazio-tempo nella relativita generale Sulla base dellipotesi di uniformita arriviamo a dire che viviamo in uno spazio tridimensionale curvo ortogonale ad una dimensione di tipo temporale fattore di scala coordinate sferiche comoventi dipende dal tempo: R = R(t) secondo la densita e la specie dell energia/materia

83 E. Fiandrini 82 Ancora lanalogia BiDimensionale (attenzione!!!...) Adesso possiamo capire meglio la legge di Hubble: la lunghezza d'onda della luce si sposta verso il rosso perche' lo spazio-tempo vuoto si espande, ie cambia il fattore di scala R(t)

84 E. Fiandrini 83 Cosmological redshift While a photon travels from a distance source to an observer on Earth, the Universe expands in size from R then to R now. Not only the Universe itself expands, but also the wavelength of the photon.

85 E. Fiandrini 84 Cosmological redshift General definition of redshift: for cosmological redshift:

86 E. Fiandrini 85 Cosmological redshift Examples: –z=1 R then /R now = 0.5 at z=1, the universe had 50% of its present day size emitted blue light (400 nm) is shifted all the way through the optical spectrum and is received as red light (800 nm) –z=4 R then /R now = 0.2 at z=4, the universe had 20% of its present day size emitted blue light (400 nm) is shifted deep into the infrared and is received at 2000 nm –most distant astrophysical object discovered so far: z=5.8

87 E. Fiandrini 86 La velocita con cui si espande R (velocita di recessione) puo anche essere maggiore di c! La limitazione a c vale solo per corpi materiali e raggi luminosi Importantissimo:!!!

88 E. Fiandrini 87 La Legge di Hubble fattore di espansione: v=dR/dt v=H£R(t) Red-shift misurato: z=( r - e )/ e = r / e -1 Effetto Doppler: r = e (1+v/c)

89 E. Fiandrini 88 Evoluzione dinamica dellUniverso 1.K>0, <1 Universo aperto, espansione infinita 2.K=0, =1 Universo piatto, velocità si annulla 3.K 1 Universo chiuso… BIG CRUNCH a(t) t 1.Legge di Hubble: v=Hd 2.Principio cosmologico 3.Relatività generale a(t 1 ) a(t 2 ) Equazioni Friedmann-Lemaitre K=0 ) densità critica: Definendo:

90 E. Fiandrini 89 Equation of state: relation between pressure P and energy density c 2 : the Universe is like a perfect gas = 0 for dust (no pressure) = 1/3 for radiation (very hard pressure) Or: acceleration = Einsteins equations: Critical parameter

91 E. Fiandrini 90 Can we calculate R(t)? We have to solve the Einstein equations but it is possible to make analogies with a classical gravitation at the cost of loosing the real meaning of the parameters in the equations

92 E. Fiandrini 91 Come varia il fattore di scala (R) nel tempo? Inserendo la metrica di RW nelle equazioni di Einstatin nell'ipotesi dellisotropia e omogeneita dellUniverso vale lequazione di Friedman densita di materia/energia coefficiente di curvatura

93 E. Fiandrini 92 Friedman Equation Birkhoffs Theorum which states that the gravitational field within a spherical hole embedded within an otherwise infinite medium is zero

94 E. Fiandrini 93 Friedman Equation Thus in a homogenous Universe we can ignore the matter outside a small sphere m r Grav. Pot. Kin. Energy. Conservation of Energy Mass in sphere 2 1

95 E. Fiandrini 94 Friedman Equation 2 6 I dont change with time /a 2 rearrange const, -kc 2 Friedman Equation 3 aRaR

96 E. Fiandrini 95 Nearly-Newtonian Cosmology Friedman Equation Fluid Equation Fluid Equation Acceleration Equation L'universo su scala cosmologica puo' essere considerato un gas perfetto

97 E. Fiandrini 96 Fluid / Conservation Equation 1st Law of Thermodynamics Reverseable Einsteins 4 5 aRaR

98 E. Fiandrini 97 Fluid Equation into *3/a 3 Fluid Equation 7 aRaR

99 E. Fiandrini 98 Acceleration / Differential Friedman Equation Friedman Equation 3 7 Fluid Equation Acceleration Equation 8 aRaR

100 E. Fiandrini 99 We derived the acceleration equation from the Friedman and fluid equations The acceleration equation has no new physics Thus only 2 of those 3 are independent The acceleration equation is interesting as it is independent of k Acceleration / Differential Friedman Equation aRaR

101 E. Fiandrini 100 Equation of State Equation of state relates P and Equation of state relates P and Some simple equations of state we can consider Matter, dust, galaxies Radiation Cosmological Constant 1 2 3

102 E. Fiandrini 101 Friedmann Equations for Expansion a = scale factor (a 0 / a) is proportional to (1+z) = obs / em k = 0 for our flat Universe (k = -1 is open, k = +1 is closed) = energy (mc 2 for matter) density, p = pressure (can be < 0) = energy (mc 2 for matter) density, p = pressure (can be < 0) Both pressure and energy density are gravitationally active in GR aRaR

103 E. Fiandrini 102 Newton analogy Hubble Radius distant galaxy F outside = 0 A distant galaxy is subjected only to gravitational force inside the distance from center. The mass outside does not coontribute

104 E. Fiandrini 103 Newton analogy The galaxy is subjected to gravitational force of the mass inside the radius

105 E. Fiandrini 104 What is the future of that galaxy ? Critical velocity: escape speed vv esc : galaxy will move away forever

106 E. Fiandrini 105 Lets rewrite that a bit... <0 v0 v>v esc : galaxy will move away forever >0 v>v esc : galaxy will move away forever

107 E. Fiandrini 106 Homogeneous sphere of density : so for the velocity: but what is ? Lets rewrite that a bit... The energy of "free" galaxy, that is the energy of the galaxy at 1 from mass distribution

108 E. Fiandrini 107 Friedmann equation same k as in the Robertson-Walker metric Lets switch to general relativity

109 E. Fiandrini 108 Friedmann equation k is the curvature constant –k=0: flat space, forever expanding –k>0: spherical geometry, eventually recollapsing –k<0: hyperbolic geometry, forever expanding Lets switch to general relativity

110 E. Fiandrini 109 Il nostro universo continuera ad espandersi?... oppure si fermera? o collassera su se stesso? Densita critica Le osservazioni attuali sembrano indicare che ~ 1: implicherebbe k ~ 0... Lequazione di Friedman si puo anche scrivere cosi: (ci torniamo dopo...)

111 E. Fiandrini 110 Can we predict the fate of the Universe ? Friedmann equation: k=0:

112 E. Fiandrini 111 If the density of the Universe – = crit : flat space, forever expanding – > crit : spherical geometry, recollapsing – < crit : hyperbolic geometry, forever expanding so what is the density of the universe? –We dont know precisely – > crit very unlikely Can we predict the fate of Universe ?

113 E. Fiandrini 112 k>0 k<0k=0

114 E. Fiandrini 113 Spazio a curvatura positiva (esempio bidimensionale!!) Su una superficie curva la somma degli angoli di un triangolo non e 180 gradi per K>0 la somma e >180 per K<0 la somma e <180 Pero su una porzione molto piccola e difficile capirlo: da lillusione che k=0 procedendo lungo una stessa direzione......si ritorna al punto di partenza Definizione di spazio chiuso

115 E. Fiandrini 114 How big is crit ? crit = g/cm 3 1 atom per 200 liter crit = g/cm 3 1 atom per 200 liter density parameter 0 – 0 =1: flat space, forever expanding (open) – 0 >1: spherical geometry, recollapsing (closed) – 0 <1: hyperbolic geometry, forever expanding

116 E. Fiandrini 115 How can we measure 0 ? Count all the mass we can see –tricky, some of the mass may be hidden … Measure the rate at which the expansion of the universe is slowing down –a more massive universe will slow down faster Measure the geometry of the universe –is it spherical, hyperbolic or flat ?

117 E. Fiandrini 116 The Universe does not expand at constant speed acceleration Acceleration according to Newton: acceleration parameter

118 E. Fiandrini 117 So whats the meaning of q 0 ? deceleration parameter q 0 –q 0 >0.5:deceleration is so strong that eventually the universe stops expanding and starts collapsing –0

119 E. Fiandrini 118 So lets measure q 0 ! How do we do that? –Measure the rate of expansion at different times, i.e. measure and compare the expansion based on nearby galaxies and based on high redshift galaxies Gravity is slowing down expansion expansion rate should be higher at high redshift.

120 E. Fiandrini 119 So lets measure q 0 ! q 0 = 0 q 0 = 0.5 more distant fainter Data indicates: q 0 < 0 Expansion Expansion is accelerating

121 E. Fiandrini 120 Science discovery of the year 1998 The expansion of the universe is accelerating !!! But gravity is always attractive, so it only can decelerate Revival of the cosmological constant to get a "repulsive" gravity for acceleration! Revival of the cosmological constant to get a "repulsive" gravity for acceleration!

122 E. Fiandrini 121 k is the curvature constant –k=0: flat space, flat universe –k>0: spherical geometry, closed universe –k<0: hyperbolic geometry, open universe Friedmanns equation for >0 k is the curvature constant –k=0: flat space –k>0: spherical geometry –k<0: hyperbolic geometry but for sufficiently large a spherically curved universe may expand forever

123 E. Fiandrini 122 Deceleration parameter q for >0 Acceleration according to Newton: deceleration parameter with If there is a cosmological constant, then it contributes to the energy/matter content of the universe

124 E. Fiandrini 123 Is the fate of the Universe well determined ? deceleration: –½ 0 – > 0: decelerating –½ 0 – < 0: accelerating curvature – 0 + = 1: flat – 0 + < 1: hyperbolic – 0 + > 1: spherical two equations for two variables well posed problem The total content of the energy/matter in the Universe is tot = o +

125 E. Fiandrini 124 k=+1 =0 >0 The fate of the Universe for >0

126 E. Fiandrini 125 Cosmology: the quest for 3 numbers The Hubble constant H 0 how fast is the universe expanding how fast is the universe expanding The density parameter 0 how much mass is in the universe how much mass is in the universe The cosmological constant The cosmological constant the vacuum energy of the universe the vacuum energy of the universe current observational situation: H 0 = 72 § 8 km/s/MpcH 0 = 72 § 8 km/s/Mpc 0 = 0.3 § 0.04; = 0.7 § 0.06 flat space 0 = 0.3 § 0.04; = 0.7 § 0.06 flat space

127 E. Fiandrini 126 The big-bang model: The life of a Universe

128 E. Fiandrini 127 How old is the Universe? A galaxy at distance d recedes at velocity v=H 0 d. When was the position of this galaxy identical to that of our galaxy? Answer: t Hubble : Hubble time. For H 0 = 65 km/s/Mpc: t Hubble = 15 Gyr

129 E. Fiandrini 128 The age of the Universe revisited So far, we have assumed that the expansion velocity is not changing ( q 0 =0, empty universe) How does this estimate change, if the expansion decelerates, i.e. q 0 >0 ? An 0 >0, =0 universe is younger than 15 Gyr now

130 E. Fiandrini 129 now So far, we only have considered decelerating universes How does this estimate change, if the expansion accelerates, i.e. q 0 <0 ? The age of the Universe revisited An >0 universe can be older than 15 Gyr

131 E. Fiandrini =0, =0: t Hubble =1/H 0 = 15 Gyr 0 =0, =0: t Hubble =1/H 0 = 15 Gyr 0 =1, =0: t Hubble =2/(3H 0 )= 10 Gyr 0 =1, =0: t Hubble =2/(3H 0 )= 10 Gyr open universes with 0< 0 <1, =0 are between 10 and 15 Gyr old closed universes with 0 >1, =0 are less than 10 Gyr old >0 increases, 0 increases, <0 decreases the age of the universe 0 =0.3, =0.7: t Hubble =0.96/H 0 = 14.5 Gyr 0 =0.3, =0.7: t Hubble =0.96/H 0 = 14.5 Gyr The age of the Universe revisited

132 E. Fiandrini 131 not directly but we can constrain the age of the Universe. It must not be younger than the oldest star in the Universe. How do we measure the age of stars? –radioactive dating –stellar evolution models Result: age of the oldest star ~12-14 Gyr 0 >~1 strongly disfavored 0 >~1 strongly disfavored Can we measure the age of the Universe ?

133 E. Fiandrini 132 The life of a universe – key facts Unless is sufficiently large (which is inconsistent with observations) all cosmological models start with a big bang. An universe doesnt change its geometry. A flat universe has always been and will always be flat, a spherical universe is always spherical and so on. Two basic solutions: –eventual collapse for large 0 or negative –eventual collapse for large 0 or negative –eternal expansion otherwise

134 E. Fiandrini 133 Unless is sufficiently large (which is inconsistent with observations) all cosmological models start with a big bang: the density of the Universe, treated as a perfect gas, is / 1/t n There is an instant in the past where all the matter and energy were concentrated in a point...a singularity: the Big Bang

135 E. Fiandrini 134 Some common misconceptions The picture that the Universe expands into a preexisting space like an explosion The question what was before the big bang? Remember: spacetime is part of the solution to Einsteins equation Space and time are created in the big bang

136 E. Fiandrini 135 So is the big crunch the same as the big bang run in reverse ? No. The Universe has meanwhile formed stars, black holes, galaxies etc. Second law of thermodynamics: The entropy (disorder) of a system at best stays the same but usually increases with time, in any process. There is no perpetual motion machine. Second law of thermodynamics defines an arrow of time.

137 E. Fiandrini 136 At early epochs, the first term dominates the early universe appears to be almost flat the early universe appears to be almost flat At late epochs, the second term dominates the late universe appears to be almost empty the late universe appears to be almost empty Friedmanns equation for =0, 0 <1 Expansion rate of the Universe Falls off like the cube of R Falls off like the square of R

138 E. Fiandrini 137 At early epochs, the first term dominates the early universe appears to be almost flat the early universe appears to be almost flat At late epochs, the third term dominates the late universe appears to be exponentially expanding the late universe appears to be exponentially expanding Friedmanns equation for >0, 0 0, 0 <1 Expansion rate of the Universe Falls off like the cube of R Falls off like the square of R constant

139 E. Fiandrini 138 A puzzling detail =0: for most of its age, the universe looks either to be flat or to be empty =0: for most of its age, the universe looks either to be flat or to be empty >0: for most of its age, the universe looks either to be flat or to be exponentially expanding >0: for most of its age, the universe looks either to be flat or to be exponentially expanding Isnt it strange that we appear to live in that short period between those two extremes ? Flatness problem Flatness problem

140 E. Fiandrini 139 The Expanding Universe On large scales, galaxies are moving apart, with velocity proportional to distance. Its not galaxies moving through space. Space is expanding, carrying the galaxies along! The galaxies themselves are not expanding!

141 E. Fiandrini 140 General acceptance of the big bang model Until mid 60ies: big bang model very controversial, many alternative models After mid 60ies: little doubt on validity of the big bang model Four pillars on which the big bang theory is resting: –Hubbles law –Hubbles law –Cosmic microwave background radiation –Cosmic microwave background radiation –The origin of the elements –Structure formation in the universe

142 E. Fiandrini 141 Georgy Gamov ( ) If the universe is expanding, then there has been a big bang Therefore, the early universe must have been very dense and hot Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948) –success: predicted that helium abundance is 25% –failure: could not reproduce elements more massive than lithium and beryllium ( formed in stars)

143 E. Fiandrini 142 What are the consequences ? In order to form hydrogen and helium at the right proportions, the following conditions are required: –density: g/cm -3 –temperature:T 10 9 K Radiation from this epoch should be obser- vable as an isotropic background radiation Due to the expansion of the universe to g/cm 3, the temperature should have dropped to T 5 K (-268 C) Can we observe this radiation ?

144 E. Fiandrini 143 Penzias and Wilson 1965 Working at Bell labs Used a satellite dish to measure radio emission of the Milky Way They found some extra noise in the receiver, but couldnt explain it discovery of the background radiation Most significant cosmological observation since Hubble Nobel prize for physics 1978

145 E. Fiandrini 144 When does a gas become opaque? A gas appears opaque (e.g. fog) if light is efficiently scattered by the atoms/molecules of the gas The three important factors are thus –the density of the gas (denser more particles more scattering) –the efficiency with which each individual particle can scatter light –wavelength of the light

146 E. Fiandrini 145 The transition from a transparent to an opaque universe At z=0 the universe is fairly transparent At higher z, the universe becomes denser ( = 0 (1+z) 3 ) and hotter (T=T 0 (1+z)) At z=1100, the universe is so dense that its temperature exceeds 3000K. In a fairly sharp transition, the universe becomes completely ionized and opaque to visible light. (last scattering surface) At z=1100, the universe is ~ yrs old

147 E. Fiandrini 146 Proviamo a guardare indietro nel tempo... -le distanze diminuiscono, tutto diventa piu denso, anche la densita di energia aumenta... -Il primo evento drammatico che incontriamo andando all indietro e successo quando lUniverso aveva un eta di ~ anni: la distanza fra le stelle (come le conosciamo oggi) diviene ~nulla: Tutto luniverso e composto dal materiale di cui sono composte le stelle... -Questo e linizio dellUniverso visibile come lo conosciamo adesso...

148 E. Fiandrini 147 Situazione a T< anni in quelle condizioni di densita, tutto lUniverso aveva la temperatura della superficie di una stella (>3000 K): non esistono atomi neutri etanta luce (fotoni) in interazione con la materia carica elettricamente La luce e intrappolata! non puo arrivarci nessun raggio luminoso da epoche per cui T< anni... (altre particelle in principio possono: i neutrini per esempio) Si ha equilibrio tra radiazione e materia spettro di corpo nero

149 E. Fiandrini 148 pero, a causa dello stiramento dello spazio la sua lunghezza donda aumenta (e lenergia diminuisce: si raffredda...) Situazione a T~ anni con lespansione delluniverso T diventa <3000 K, gli elettroni si legano ai protoni per formare atomi neutri di H non c'e' piu' interazione luce-materia: I fotoni cominciano a propagarsi liberamente (materia poco densa) e devono continuare tuttora: Disaccoppiamento radiazione-materia La radiazione prima intrappolata e' ora libera di propagarsi nello spazio e giungere fino a noi ci si aspetta che esista una radiazione uniforme che "riempe" tutto l'universo

150 E. Fiandrini 149

151 E. Fiandrini 150 Looking Back Towards the Early Universe The more distant the objects we observe, the further back into the past of the universe we are looking. trasparent opaque

152 E. Fiandrini 151 Black body radiation A hot a body is brighter than a cool one (L T 4, Stefan-Boltzmanns law) A hot bodys spectrum is bluer than that of a cool one ( max 1/T, Wiens law)

153 E. Fiandrini 152 The cosmic microwave background radiation (CMB) Temperature of 2.728±0.004 K isotropic to 1 part in perfect black body 1990ies: CMB is one of the major tools to study cosmology Note: ~1% of the noise in your TV is from the big bang

154 E. Fiandrini 153 Emissione di radiazione elettromagnetica da un corpo Alla temperatura di 37 gradi centigradi (circa 310 gradi kelvin) lemissione è concentrata nellinfrarosso

155 E. Fiandrini 154 Should the CMB be perfectly smooth ? No. Todays Universe is homogeneous and isotropic on the largest scales, but there is a fair amount of structure on small scales, such as galaxies, clusters of galaxies etc.

156 E. Fiandrini 155 Lesistenza di questa radiazione primordiale e la prova diretta che lUniverso in qualche momento del passato era qualitativamente diverso da quello attuale. Permette di fotografare lUniverso quando aveva soltanto ~ anni... Tuttoggi continuiamo ad imparare tantissimo dallo studio ad alta precisione di questa radiazione Curiosita: ~ l1% delleffetto neve nei TV e dato dal fondo di radiazione cosmica CMB : Cosmic Microwave Background CBR: Cosmic Background Radiation 400 fotoni/cm 3

157 E. Fiandrini 156 Should the CMB be perfectly smooth ? We expect some wriggles in the CMB radiation, corresponding to the seeds from which later on galaxies grow

158 E. Fiandrini 157 The Cosmic Background Explorer (COBE) Main objectives: To accurately measure the temperature of the CMB To find the expected fluctuations in the CMB

159 E. Fiandrini 158 Main results from COBE

160 E. Fiandrini 159 More results from the CMB The Earth is moving with respect to the CMB Doppler shift –Earths motion around the Sun –Suns motion around the Galaxy –Motion of the Galaxy with respect to other galaxies (large scale flows)

161 E. Fiandrini 160 More results from the CMB The Earth is moving with respect to the CMB Doppler shift The emission of the Galaxy

162 E. Fiandrini 161 More results from the CMB The Earth is moving with respect to the CMB Doppler shift The emission of the Galaxy Fluctuations in the CMB

163 E. Fiandrini 162 Where do the CMB fluctuations come from ? Wrinkles: some regions have a slightly higher gravity, some a slightly lower (potential wells) Matter falls into potential wells

164 E. Fiandrini 163 Where do the CMB fluctuations come from ? Wrinkles: some regions have a slightly higher gravity, some a slightly lower (potential wells) Matter falls into potential wells

165 E. Fiandrini 164 Competition between gravity (pull in) and pressure (push out) oscillations The Sound of the Universe What happens to the infalling gas?

166 E. Fiandrini 165 Can we see the sound of the universe ? Compressed gas heats up temperature fluctuations

167 E. Fiandrini 166 Measuring the Curvature of the Universe Using the CMB Sound waves universe is a resonator lowest pitch: fundamental mode resonates fundamental mode: distance sound can travel over the age of the universe z=1100) it depends on : l peak =220 o / fundamental mode: distance sound can travel over the age of the universe z=1100) it depends on : l peak =220 o / angle

168 E. Fiandrini 167 The Music of the Universe

169 E. Fiandrini 168 Measuring the Curvature of the Universe Using the CMB

170 E. Fiandrini 169 Measuring the Curvature of the Universe Using the CMB Recall: with supernovae, one measures q 0 =½ 0 – Recall: with supernovae, one measures q 0 =½ 0 – CMB fluctuations measure curvature 0 + CMB fluctuations measure curvature 0 + two equations for two variables problem solved

171 E. Fiandrini 170 The universe content The results: The Universe is flat: tot =1§ 0.1 »30% is matter 70% is cosmological constant, the so- called "dark energy" Dark energy: we know is there, but have not idea of what it is

172 E. Fiandrini 171 Se ne conclude che: 1.LUniverso è dominato da una forma sconosciuta di energia 2.La maggioranza della MATERIA è OSCURA 3.La maggioranza della materia oscura (DM) è diversa da quella ordinaria Contributi ad da: 1.Materia ) m 2.Radiazione ) r 3.Energia del vuoto ) Quali sono le stime attuali? Stima dei parametri cosmologici TOT =1.02§0.2 r »O(10 -5 ) =0.73§0.04 m =0.27§0.04 lum <0.006 B =0.044§0.004 ??

173 E. Fiandrini 172 The early Universe: Cooking the helium in the Universe - the Big Bang nucleosynthesis

174 E. Fiandrini 173 Until mid 60ies: big bang model very controversial, many alternative models After mid 60ies: little doubt on validity of the big bang model Four pillars on which the big bang theory is resting: –Hubbles law –Hubbles law –Cosmic microwave background radiation –The origin of the elements –Structure formation in the universe General acceptance of the big bang model Until mid 60ies: big bang model very controversial, many alternative models After mid 60ies: little doubt on validity of the big bang model Four pillars on which the big bang theory is resting: –Hubbles law –Hubbles law –Cosmic microwave background radiation –Cosmic microwave background radiation –The origin of the elements –Structure formation in the universe

175 E. Fiandrini 174 Georgy Gamov ( ) If the universe is expanding, then there has been a big bang Therefore, the early universe must have been very dense and hot Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948) –success: predicted that helium abundance is 25% –failure: could not reproduce elements more massive than lithium and beryllium ( formed in stars)

176 E. Fiandrini 175 Particle and nuclear physics Particle physics joins cosmology In the hot and dense young Universe high energy particles have enough energy to undergo to processes governed by elementary particle physics (quantum) laws as T 1

177 E. Fiandrini 176 La nostra attuale comprensione delle interazioni fondamentali delle particlle elementari e riassunta da quello che chiamiamo: esso descrive sia la materia che tutte le forze che la governano. La sua bellezza sta nella capacità di spiegare centinaia di particelle e interazioni complesse con poche particelle e interazioni (forze) fondamentali.

178 E. Fiandrini tipi di costituenti: 2) 3 tipi di costituenti: a)quarks (6 x 3 x 2) b)elettroni, neutrini e simili (leptoni) (6 x 2) c)particelle mediatrici delle forze: gravitoni, fotoni, gluoni, bosoni (13) 4 tipi di forze (ma in via di unificazione) 1) 4 tipi di forze (ma in via di unificazione) 1)nucleare forte 2)nucleare debole 3)elettromagnetica 4)gravitazionale particelle + antiparticelle elettrodebole In tale modello:

179 E. Fiandrini 178 Ecco tutte le interazioni in breve.... L aspetto entusiasmante della moderna visione e che camminiamo nella direzione di una descrizione unificata delle forze Siamo gia in grado di parlare di forza elettro-debole invece che di debole ed elettro-magnetica separatamente!!! Arriveremo mai alla Grande Unificazione?? (M=0, S = 2) (M~90 GeV/c 2, S = 1) (M=0, S = 1)

180 E. Fiandrini 179 The structure of matter Atoms are mostly empty space Atoms consist of protons (+), neutrons (o) and electrons (-) protons and neutrons form the atomic nucleus # of protons deter- mines the element electrons in the outskirts determine chemistry Protoni, neutroni quarks

181 E. Fiandrini 180 The structure of matter Neutrons and protons are very similar, but –Protons are electrically charged, neutrons are not –Neutrons have a slightly higher mass Electrons are much less massive than nucleons most of the mass of an atom is in its nucleus If charges of the same sign repel, and the nucleus is made of protons, why dont the protons fly apart ?

182 E. Fiandrini 181 Breve cronistoria delluniverso alla luce della nostra conoscenza attuale delle forze e della materia: il modello cosmologico standard - Il modello standard della fisica ci permettono di estrapolare la descrizione dellUniverso per t<10 5 anni -Fino a quando la densita e tale che le particelle di cui e costituita la materia perdono la loro identita... -Fino a ~ il Tempo 0 (il Big Bang) ma non proprio... Questo esercizio pero di puo fare con incertezze tanto maggiori tanto piu ci avviciniamo a t=0! Cosa cera prima? La domanda non ha senso. Come conseguenza della R.G., spazio e tempo non esistevano prima, non ce stato un prima! (anche S. Agostino cera arrivato...)

183 E. Fiandrini 182 Abundance of elements Hydrogen and helium most abundant gap around Li, Be, B Where do they come from?

184 E. Fiandrini 183 Thermal history of the universe When the universe was younger than yrs, it was so hot that neutral atoms separated into nuclei and electrons. It was too hot to bind atomic nuclei and electrons to atoms by the electromagnetic force When the universe was younger than ~1 sec, it was so hot that atom nuclei separated into neutrons and protons. It was too hot to bind protons and neutrons to atomic nuclei by the strong nuclear force

185 E. Fiandrini 184 Formation of helium in the big bang Hydrogen: 1 nucleon (proton) Helium: 4 nucleons (2 protons, 2 neutrons) In order to from helium from hydrogen one has to –bring 2 protons and 2 neutrons close together, so the strong nuclear force can act and hold them together –close together: Coulomb repulsion has to be overcome high velocities high temperatures but: 4 body collisions are highly unlikely

186 E. Fiandrini 185 Transforming hydrogen into helium Hot big bang: neutrons and protons Use a multi step procedure: – p + n 2 H – p + 2 H 3 He – n + 2 H 3 H – 3 He + 3 He 4 He + 2 p some side reactions: – 3 He + 3 H 7 Li – 3 He + 3 He 7 Be

187 E. Fiandrini 186 Mass gap/stability gap at A=5 and 8 There is no stable atomic nucleus with 5 or with 8 nucleons Reaction chain stops at 7 Li So how to form the more massive elements? There exist a meta-stable nucleus ( 8 B*). If this nucleus is hit by another 4 He during its lifetime, 12 C and other elements can be formed

188 E. Fiandrini 187 Mass gap/stability gap at A=5 and 8 Reaction chain: – 4 He + 4 He 8 B* – 8 B* + 4 He 12 C so-called 3-body reaction in order to have 3-body reactions, high particle densities are required –densities are not high enough in the big-bang –but they are in the center of evolved stars Conclusion: big bang synthesizes elements up to 7 Li. Higher elements are formed in stars

189 E. Fiandrini 188 Primordial nucleosynthesis Result: abundance of H,He and Li is consistent but: b ~0.04 while the tot content is 0.3 Consistent with abundance of H, He and Li

190 E. Fiandrini 189 Can we understand why 25% He? Before the universe cooled sufficiently to allow nucleons to assemble into helium, the neutron to proton ratio was 1:7 4 He: equal number of protons and neutrons Assume that all neutrons grab a proton to form a 4 He. The left over protons form hydrogen.

191 E. Fiandrini 190 Can we understand why 25% He? Abundance of hydrogen Abundance of helium: = 0.25 but why is n n /n p = 1/7 ?

192 E. Fiandrini 191 Less than 1 second after the Big Bang, the reactions shown maintain the neutron:proton ratio in thermal equilibrium. About 1 second after the Big Bang, the temperature is slightly less than the neutron-proton mass difference, these weak reactions become slower than the expansion rate of the Universe, and the neutron:proton ratio freezes out at about 1:7

193 E. Fiandrini 192 What happened when the universe was even younger? Recall special relativity: E=mc 2 If the thermal energy exceeds twice the rest mass energy of a particle, particle-antiparticle pairs can be created Pair creation Matter: protons, neutrons, electrons neutrinos Antimatter: antiprotons, antineutrons, positrons, antineutrino

194 E. Fiandrini 193 Pair creation Antiparticle: same mass as particle, but opposite charge. Antimatter has positive mass !!!!!! e+e+e+e+ e-e-e-e- The inverse process is called annihilation

195 E. Fiandrini 194 Examples T>10 10 K: creation/annihilation of electron- positron pairs T>10 13 K: creation/annihilation of proton- antiproton pairs

196 E. Fiandrini 195 A common theme... For each reaction there is a temperature T c : –For temperature larger than T c, there is a continuous transformation between photons into particle-antiparticle pairs and vice versa –This state is called thermal equilibrium –If the temperature drops below the threshold temperature T c, pair creation freezes out, remaining pairs annihilate.

197 E. Fiandrini 196 The thermal history of the Universe

198 E. Fiandrini 197 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K era della materia The energy of matter is nowadays ~10000 times higher than that of radiation but temperature rises like (1+z) 2.7K < T < 10000K: matter era dominate particles (in order of decreasing contribution: –baryons, photons, neutrinos dominant forces: –gravity

199 E. Fiandrini 198 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=10 10 K era della radiazione era della materia As the temperature exceeds ~ 10000K, radiation starts dominating 10000K < T < K: radiation era dominate particles (in order of decreasing contribution: –photons, neutrinos, baryons dominant forces: –electromagnetism, gravity

200 E. Fiandrini 199 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=10 10 K era della radiazione era della materia As the temperature exceeds ~ K, creation of electron-positron pairs –T > K: equilibrium between electron-positron pair creation and annihilation –T < K: freeze-out. Remaining pairs annihilate

201 E. Fiandrini 200 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=10 10 K t ~ s: Era leptonica t < s: i quarks si combinano in p e n T=10 13 K era della radiazione era della materia Hadron hannihilation: As the temperature exceeds ~ K, creation of hadron-antihadron pairs (e.g. proton-antiproton) –T > K: equilibrium between hadron pair creation and annihilation –T < K: freeze-out. Remaining pairs annihilate

202 E. Fiandrini 201 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=10 10 K t ~ s: Era leptonica t < s: i quarks si combinano in p e n T=10 13 K era della radiazione era della materia Hadron era: K < T < K dominant particles (in order of decreasing contribution: –baryons+antiparticles, mesons+antiparticles, electrons, positrons, photons, neutrinos, antineutrinos dominant forces: –electromagnetism, strong nuclear, weak nuclear, gravity Quark era:10 13 K < T < K hadrons (baryons, mesons) break into quarks dominate particles (in order of decreasing contribution: –quarks, antiquarks, e- e+, photons, neutrinos, antineutrinos dominant forces: –electromagnetism, strong nuclear, weak nuclear, gravity

203 E. Fiandrini 202 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=10 10 K t ~ s: Separazione forza elettro-debole T=10 15 K t ~ s: Era leptonica t < s: i quarks si combinano in p e n T=10 13 K era della radiazione era della materia Electroweak phase transition: As the temperature exceeds ~ K, electromagnetism and weak nuclear force join to form the electroweak force –T > K: electroweak force –T < K: electromagnetism, weak nuclear force Limit of what we can test in particle accelerators. Nobel prizes 1979 (theory) and 1984 (experiment)

204 E. Fiandrini 203 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=10 10 K t ~ s: Separazione forza elettro-debole T=10 15 K t ~ s: Era leptonica t < s: i quarks si combinano in p e n T=10 13 K era della radiazione era della materia K < T < K dominate particles (in order of decreasing contribution: –quarks, antiquarks, electrons, positrons, photons, neutrinos, antineutrinos dominant forces: –electroweak, strong nuclear, gravity

205 E. Fiandrini 204 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=10 10 K t ~ s: Separazione forza elettro-debole T=10 15 K t ~ s: Era leptonica t < s: i quarks si combinano in p e n T=10 13 K era della radiazione t < s: Era della Grande Unificazione T=10 28 K era della materia GUT phase transition: As the temperature exceeds ~ K, electroweak force and strong nuclear force join to form the GUT (grand unified theories) –T > K: GUT –T < K: electroweak force, strong nuclear force relatively solid theoretical framework (but may be wrong), but pretty much no constraint by experiments GUT era: K < T < K dominate particles (in order of decreasing contribution: –Zillions of particles, most of them not detected yet dominant forces: –GUT, gravity

206 E. Fiandrini 205 t = anni: vita, noi, ora, T = 3 K t = : anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = 10 4 anni: Inizia lera dominata dalla materia T= K t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=10 10 K t = s: Tempo di PlancK: Limite della fisica moderna t ~ s: Separazione forza elettro-debole T=10 15 K t ~ s: Era leptonica t < s: i quarks si combinano in p e n T=10 13 K era della radiazione t < s: Era della Grande Unificazione T=10 28 K era della materia Planck epoch: T > K unification of GUT and gravity Particles: –??? Forces: –TOE (theory of everything) The last frontier...

207 E. Fiandrini 206 The four forces of nature Gravity –weak, long ranged electromagnetism –intermediate, long ranged weak nuclear force –weak, short ranged strong nuclear force –strong, short ranged electroweak force (at T > K) GUT: grand unified theories (at T > K)

208 E. Fiandrini 207 T»100 GeV t» s

209 E. Fiandrini 208 Until mid 60ies: big bang model very controversial, many alternative models After mid 60ies: little doubt on validity of the big bang model Four pillars on which the big bang theory is resting: –Hubbles law –Hubbles law –Cosmic microwave background radiation –Cosmic microwave background radiation –The origin of the elements –The origin of the elements –Structure formation in the universe General acceptance of the big bang model

210 E. Fiandrini 209 Structure formation in the Big- Bang model

211 E. Fiandrini 210 The Hubble sequence of galaxies

212 E. Fiandrini 211 Younger galaxies should be smaller...

213 E. Fiandrini 212 How good is the assumption of isotropy? CMB: almost perfect but what about the closer neighborhood ?

214 E. Fiandrini 213 How good is the assumption of isotropy? CMB: almost perfect but what about the closer neighborhood ? The great wall

215 E. Fiandrini 214 Galaxies are not randomly distributed but correlated Network of structures (filaments, sheets, walls) cosmic web The spatial distribution of galaxies Courtesy: Huan Lin

216 E. Fiandrini 215 How does structure form ? Wrinkles in the CMB: regions of higher and lower temperature Those regions correspond to density fluctuations, regions of slightly higher/lower density than average Gravitational instability –higher density more mass in a given volume –more mass stronger gravitational attraction –stronger gravitational attraction mass is pulled in even higher density

217 E. Fiandrini 216 z= Mpc 50 million particle N-body simulation

218 E. Fiandrini 217 z= Mpc 50 million particle N-body simulation

219 E. Fiandrini 218 z= Mpc 50 million particle N-body simulation

220 E. Fiandrini 219 z= Mpc 50 million particle N-body simulation

221 E. Fiandrini 220 z= Mpc 50 million particle N-body simulation

222 E. Fiandrini 221 Sommario della nuova cosmologia: si fonda su 3 fatti/osservazioni 1 postulato + 1 modello di riferimento 1)su larga scala luniverso e lo stesso in tutte le direzioni (isotropia) 2) piu guardiamo indietro nel tempo (lontano da noi) piu luniverso appare diverso dal nostro: in particolare era molto caldo (CMB) 3) tanto piu un oggetto e lontano, tanto piu sembra allontanarsi velocemente da noi (legge di Hubble) Congettura: la porzione di universo in cui noi siamo non ha nulla di speciale (Principio Cosmologico) Modello di riferimento: La Relativita Generale

223 E. Fiandrini 222 Riassumendo: i successi del modello cosmologico standard (il Big Bang) 1)Spiegazione dellesistenza del CMB 2)Previsione quantitativa dellabbondanza di elementi leggeri (idrogeno, deuterio, elio, litio) nelluniverso in accordo con le misure 3)spiegazione delle strutture su larga scala delle galassie in connessione con le piccole irregolarita del CMB Ma il modello standard non e piu sufficiente...

224 E. Fiandrini 223 How can we measure mass ? Count all the mass we can see –tricky, some of the mass may be hidden … Using Keplers third law: measure the dynamics of a system and apply Keplers law to infer the mass –for hot systems (elliptical galaxies, clusters of galaxies): measure the velocity dispersion (random velocity) of the constituents –for cold systems (disk galaxies): measure the velocity at which stars orbit

225 E. Fiandrini 224 Counting all the mass... Obstacle: we want mass, but we see light Procedure: –count all the stars you see and multiply them with there luminosity total visible luminosity –correct for dust absorption total luminosity –convert luminosity into mass using a mass-to- light ratio –The sun has =1 by definition.

226 E. Fiandrini 225

227 E. Fiandrini 226 Visible mass in the Universe: Implications: less than the nucleosynthesis constraint of bary =0.04 in baryons consistent Most of the baryons in the universe (~75%) do not shine [are too dim to be detected] –gas and dust –stellar remnants (white dwarfs, neutron stars, black holes) –brown dwarfs [failed stars]

228 E. Fiandrini 227 Le scoperte piu recenti Ce un nuovo tipo di materia che non conosciamo: Dall'analisi degli effetti gravitazionali, si puo stabilire che esiste anche un tipo di materia che noi non possiamo vedere (non prodice luce), anzi la maggior parte dell'universo sembra non sia dello stesso tipo di materia di cui sono fatte le stelle (protoni-neutroni-elettroni). Materia non oscura Materia oscura La chiamiamo "materia oscura"

229 E. Fiandrini 228 The Problem of Dark Matter - Observed from gravitational interactions only! Galactic Rotation Curves Allen, Schmidt, Fabian (2002) Observe galaxy rotation curve using Doppler shifts in 21 cm line from hyperfine splitting Virtually all galaxies have a dark halo Luminous matter cannot account for the observed rotation curves There must be a dark a nearly spherical halo Expected from luminous mass Observed A halo of non-luminous matter must be added to account for the observed radial speed

230 E. Fiandrini 229 Materia oscura Materia oscura

231 E. Fiandrini 230 Lets use some numbers... A galaxy like the Milky Way or Andromeda has a total visible mass of about M sun. The rotation velocity is ~220 km/sec The radius about ~30 kpc Newton: total mass: M sun ~5 times more mass than visible

232 E. Fiandrini 231 Dark Matter in Galaxy Clusters Galaxies form clusters bound in a gravitational well Hydrogen gas in the well get heated, emit X-ray Can determine baryon fraction of the cluster f B h 3/2 = Combine with the BBN matter h 1/2 = matter h 1/2 = Agrees with SZ, virial Zwicky, Helv. Phys. Acta 6 (1933) 110 Coma cluster the most part of cluster gravitational mass is dark

233 E. Fiandrini 232 Evidence of dark matter: X-ray clusters

234 E. Fiandrini 233 Evidence of dark matter: clusters of galaxies

235 E. Fiandrini 234 Evidence of dark matter: large scale flows

236 E. Fiandrini 235 Overall result: Implications: most of the mass in the Universe is dark most of it is even of non-baryonic origin the perfect Copernican principle –The Earth is not at the center of the solar system –The Sun is not at the center of the Milky Way –The Milky Way is not at the center of the Universe –We may not even be made from the most abundant type of matter in the Universe But lum = and BBN =0.04

237 E. Fiandrini 236 ~90% of the mass in the Universe is of some sort of invisible (dark) matter, probably even of quite different nature than the stuff we are made of.

238 E. Fiandrini % dark matter ? These astronomers must be crazy !

239 E. Fiandrini 238 Is the claim that dark matter exist really so embarrassing ? When Leverrier was proposing in the 1840s that there maybe an 8th planet in the solar system, Neptune, a planet that can explain the irregularities of Uranus orbit, this planet was also dark matter But it was a clear prediction that eventually could be tested observationally The discovery of Neptune by Galle was one of the finest moments of science

240 E. Fiandrini 239 Occorre cambiare il Modello Standard delle particelle! Tra le nuove proposte una delle idee piu promettenti e quella della unificazione di tutte le forze nel quadro della SuperSimmetria Ad ogni particella che conosciamo ne corrisponde una ombra (e viceversa) molto pesante... ad ogni quark corrisponde uno s-quark (s sta per shadow) ad ogni leptone corrisponde uno s-leptone Ad ogni bosone mediatore...one corrisponde un...ino Es.: fotone fotino Una delle particelle della supersimmetria, il "neutralino" potrebbe essere quella che compone la massa mancante delluniverso. Forse è fatta di neutrini, o magari di altre forme materiali ancora più insolite...

241 E. Fiandrini 240 I problemi non risolti dal modello cosmologico standard Il problema della piattezza e delleta delluniverso Come e possibile realizzare la stupefacente uniformita del fondo di radiazione? Come si possono parlare fra loro delle zone di universo che non sono in connessione causale? I dati osservativi indicano una densita media dellUniverso vicinissima al valore critico (implica k~0) Bastava poca materia in piu per far morire (collassare) luniverso molto prima Il problema dellorizzonte

242 E. Fiandrini 241 I problemi non risolti dal modello cosmologico standard Il problema della piattezza e delleta delluniverso Come e possibile realizzare la stupefacente uniformita del fondo di radiazione? Come si possono parlare fra loro delle zone di universo che non sono in connessione causale? I dati osservativi indicano una densita media dellUniverso vicinissima al valore critico (implica k~0) Bastava poca materia in piu per far morire (collassare) luniverso molto prima Il problema dellorizzonte

243 E. Fiandrini 242 Il problema dellorizzonte Se D> c T universo come possono A e B scambiarsi informazioni? D A B

244 E. Fiandrini 243 Un nuovo paradigma: L Inflazione (universo gonfiato) A. Guth, 1980 L universo che vediamo puo venire da una porzione infinitesimamente piccola delluniverso primordiale che si e espansa per un breve periodo a velocita molto superiore a quella della luce (possibile anche in Relativita !) Meccanismo (molto complesso): prima della formazione di quarks e leptoni, si crea uno stato speciale (falso vuoto) che fornisce una enorme accelerazione...

245 E. Fiandrini 244 Espansione normale Espansione gonfiata

246 E. Fiandrini 245 Se la porzione iniziale e molto piccola, la luce aveva fatto a tempo a mettere in comunicazione regioni che ora sono fuori connessione Inoltre in questo modo la quantita di materia nellUniverso accessibile non dipende dalla quantita iniziale e tende verso il valore speciale misurato.! La piattezza viene fuori naturalmente L Universo puo naturalmente essere vicinissimo alle condizioni di perenne espansione

247 E. Fiandrini : esp. Boomerang per la misura di alta precisione delle irregolarita del CMB Permette di ricostruire le dimensioni angolari con cui vediamo lepoca del disaccoppiamento Lanalisi delle variazioni di temperatura da informazioni sulla proporzione delle varie componenti dell universo

248 E. Fiandrini 247 Le misure di Boomerang sono in perfetto accordo con la Teoria dellInflazione! Lo spazio e piatto quindi Euclideo! Il suo destino dipende solo dal rapporto fra materia ordinaria, materia oscura e energia oscura (del vuoto) Confermate e migliorate da WMAP

249 E. Fiandrini 248 Lo stupefacente quadro della composizione dellUniverso alla luce delle misure attuali La maggior parte dellUniverso e fatto di qualcosa di cui non sappiamo nulla e che ancora non capiamo!!!

250 E. Fiandrini 249 Siamo in un universo speciale ? Molti indizi suggeriscono che delle condizioni dellUniverso anche solo infinitesimamente differenti avrebbero dato luogo ad un modo inospitale... Lespansione avrebbe potuto essere cosi veloce da non consentire la formazione di strutture. Unespansione appena piu veloce non avrebbe permesso altri atomi oltre lidrogeno Una forza gravitazionale appena piu forte (o debole) avrebbe generato stelle totalmente diverse. Una forze elettro-magnetica appena diversa avrebbe prodotto atomi troppo piccoli o troppo grandi...

251 E. Fiandrini risposte possibili: 1) La Teoria del Tutto 2) il Principo Antropico Una (futura) teoria della fisica spiega tutti gli aspetti dellUniverso, include queste che sembrano coincidenze Puo esistere la Teoria di Ogni Cosa? (TOC) a)Se lUniverso non fosse cosi noi non ci saremmo... b)LUniverso e stato fatto per noi... c)...esistono INFINITI UNIVERSI, con leggi fisiche diverse. Solo in quella (infinitesima) parte di Universi in cui le condizioni lo consentono, la vita e possibile... il Multiverso

252 E. Fiandrini 251 Verso una teoria super-unificata Certamente la fisica si muove in questa direzione Progressi recenti: la teoria delle stringhe a molte dimensioni E possibile arrivare ad una descrizione unificata delle forze in uno spazio a 11 dimensioni: Il nostro spazio-tempo a 4 dimensioni e una membrana di questo spazio piu ampio Le altre dimensioni non sono facilmente osservabili perche arrotolate su loro stesse: Ma sono possibili segnali da futuri esperimenti su acceleratori

253 E. Fiandrini 252 fine


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