Cenni di Cosmologia Cos’e’ la cosmologia scientifica

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

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

3 Cos’e’ la Cosmologia Cosmologia scientifica:
descrizione dell’Universo nel suo insieme a partire dalle leggi fisiche fondamentali (cosi’ come le conosciamo ora!!) e da osservazioni sperimentali 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 Non e’ semplicemente “Cosmogonia” ATTENZIONE ALLA SEPARAZIONE DA FILOSOFIA E RELIGIONE... E. Fiandrini

4 La nascita della Cosmologia Scientifica Moderna: Newton
Il seme per una nuova e razionale comprensione dell’universo 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: sempre attrattiva e additiva in modo istantaneo! determina l’evoluzione di qualsiasi oggetto -> quindi l’universo E. Fiandrini

5 Newton’s 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 [6.6710-11 N m2/kg2] 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 E. Fiandrini

7 Un universo statico non puo’ che essere
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.... E. Fiandrini

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

9 Newton’s Universe In order to avoid collapse infinite in time
homogeneous isotropic infinite size no center infinite in time has always been will always be  perfect cosmological principle 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? E. Fiandrini

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

12 How to solve Olber’s 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 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, ora segnale che si propaga con v=c v<c tempo a cui la luce e’ stata emessa Questa stella non la possiamo ancora vedere E. Fiandrini

14 Einstein’s 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 E. Fiandrini

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

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

18 Energy Newton: kinetic energy: Ekin= ½ m v2 v=0  Ekin= 0 Einstein: E =  m0 c2 v=0  E= m0 c2 “rest energy” Ekin = (-1) m0 c2 Example: energy required to accelerate 1kg of mass to v=0.87c  equivalent of 20 megatons of TNT =1/[1-(v/c)2]1/2 To have v=c for a particle of mass m  0,  =1  particle energy must be impossible to reach in a finite interval of time Particles without mass can move only at v=c because they dont have inertia E. Fiandrini

19 geometrical interval (x1,y1) y1 s2= y2 + x2 y y y2 (x2,y2) x x1
E. Fiandrini

20 Spacetime interval (x1,t1) ct1 s2= (ct)2 – x2 ct ct ct2
The – sign makes the space not euclidean! (x1,t1) ct1 s2= (ct)2 – x2 ct ct x ct2 (x2,t2) x x1 x2 E. Fiandrini

21 Future, past, and elsewhere
E. Fiandrini

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

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

24 Se l’universo 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! 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 E. Fiandrini

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

28 Effetto Doppler velocita’ V E. Fiandrini

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

30 Doppler effect Red-shift e velocita' sono la stessa cosa
Definizione di “red shift”: Se v<<c Si misura z e si ottiene v Red-shift e velocita' sono la stessa cosa E. Fiandrini

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

32 The redshift-distance relation
E. Fiandrini

33 The redshift-distance relation
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 = H0  d Hubble’s measurement of the constant H0: H0 = 500 km/s/Mpc today’s best fit value of the constant: H0 = 72 § 8 km/s/Mpc E. Fiandrini

35 Tutto sembra allontanarsi (IN MEDIA) da noi
Siamo per caso in un punto speciale dell’Universo? Crediamo di no: estensione del principio Copernicano al “Principio Cosmologico” ogni punto dell’universo e’ uguale a un altro e non esiste un centro Come si puo’ quindi spiegare l’espansione che osserviamo? 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’ nell’aria attorno al 1920 grazie ad una rivoluzione di tipo teorico... E. Fiandrini

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

38 Importantissimo:!!! 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 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) A. Einstein Presupposti matematici: “La geometria differenziale” le geometrie “non euclidee” (Gauss, Riemann, Lobacevsky, Ricci, Levi-Civita,...) E. Fiandrini

40 Mass curves space E. Fiandrini

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

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

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

45 Flat space    ++ = 180º E. Fiandrini

46 Curved space ++  180º E. Fiandrini

47 Flat space circumference = 2  radius E. Fiandrini

48 Curved space circumference  2  radius E. Fiandrini

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

50 Example: distance between two points at the surface of the Earth
Coordinate differences: ,  naïve, but false: correct: metric coefficients: f=R2, h= R2 cos2 E. Fiandrini

51 Spacetime Fourth coordinate: ct
time coordinate has different sign than spatial coordinates spacetime distance: , ,  : metric coefficients 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 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) 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 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 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 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 Einstein’s elevation to a celebrity. 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 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. Mercury’s 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 E. Fiandrini

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

61 Let’s apply Einstein’s equation to the Universe
What is the solution of Einstein’s 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) E. Fiandrini

62 Einstein’s proposal: cosmological constant 
There is a repulsive force in the universe vacuum exerts a pressure 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 … ? E. Fiandrini

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

64 R.G.: l’equazione di Einstein (sistema di 10 eq.)
costante di Newton Prima formulazione... (Metro, Orologi) “=“ (Energia, Materia) “Costante Cosmologica” Energia del Vuoto (????) aggiunta di Einstein in seconda battuta... 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 Einstein’s equation Hubble: observational evidence that the universe is indeed expanding Consequence: Universe started from a point  The Big Bang Model E. Fiandrini

66 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! ? E. Fiandrini

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

70 Torniamo all’analogia della superficie sferica
Griglia di coordinate “comoventi”: r,, la cui scala, cioe' unita' di misura, e' R(t) in queste coordinate le distanze rimangono uguali durante l’espansione Ci servono 3 coordinate per lo spazio: 1 raggio e 2 angoli (come la latitudine e la longitudine) E. Fiandrini

71 La “dinamica” dello spazio e del tempo
(cioe’ la loro evoluzione nel tempo) dipende dalla materia e dall’energia!  L’ ESPANSIONE DELLO SPAZIO TEMPO E’ PREVISTA ~AUTOMATICAMENTE SECONDO LA R.G.!!! 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!!! E. Fiandrini

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

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

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

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

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

77 tHubble: Hubble time. For H0 = 72 km/s/Mpc: tHubble ' 13.5 Gyr
How old is the universe? A galaxy at distance d recedes at velocity v=H0  d. When was the position of this galaxy identical to that of our galaxy? Answer: tHubble: Hubble time. For H0 = 72 km/s/Mpc: tHubble ' 13.5 Gyr E. Fiandrini

78 How big is the universe? We can’t 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: dHubble: Hubble radius. For H0 = 72 km/s/Mpc: dHubble = 4.2 Gpc 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 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=0 k<0 E. Fiandrini

81 La “metrica” dello spazio-tempo nella relativita’ generale
Sulla base dell’ipotesi di uniformita’ arriviamo a dire che viviamo in uno spazio tridimensionale curvo “ortogonale” ad una dimensione di tipo temporale coordinate sferiche “comoventi” fattore di scala dipende dal tempo: R = R(t) secondo la densita’ e la specie dell’ energia/materia E. Fiandrini

82 Ancora l’analogia 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) E. Fiandrini

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

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

85 Cosmological redshift
Examples: z=1  Rthen/Rnow = 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  Rthen/Rnow = 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 E. Fiandrini

86 Importantissimo:!!! 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 E. Fiandrini

87 La “Legge di Hubble” v=dR/dt v=H£R(t) Red-shift misurato:
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) E. Fiandrini

88 Evoluzione dinamica dell’Universo
Legge di Hubble: v=Hd Principio cosmologico Relatività generale a(t1) a(t2) Equazioni Friedmann-Lemaitre K=0 ) densità critica: Definendo: a(t) K>0 , <1 Universo aperto, espansione infinita K=0 , =1 Universo piatto, velocità si annulla K<0 , >1 Universo chiuso… BIG CRUNCH E. Fiandrini t

89 Einstein’s equations:
Equation of state: relation between pressure P and energy density c2: the Universe is like a perfect gas  = 0 for dust (no pressure)  = 1/3 for radiation (very hard pressure) Or: acceleration = Critical parameter 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 E. Fiandrini

91 Come varia il fattore di scala (R) nel tempo?
Inserendo la metrica di RW nelle equazioni di Einstatin nell'ipotesi dell’isotropia e omogeneita’ dell’Universo vale l’equazione di Friedman densita’ di materia/energia coefficiente di curvatura E. Fiandrini

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

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

94 I don’t change with time
Friedman Equation I don’t change with time 2 6 a≡R const, -kc2 /a2 3 rearrange Friedman Equation E. Fiandrini

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

96 Fluid / Conservation Equation
1st Law of Thermodynamics Reverseable 4 a≡R Einstein’s 5 E. Fiandrini

97 Fluid Equation a≡R 6 6 4 6 5 + into Fluid Equation *3/a3 7
E. Fiandrini 7

98 Acceleration / Differential Friedman Equation
7 Fluid Equation Friedman Equation a≡R 3 8 Acceleration Equation E. Fiandrini

99 Acceleration / Differential Friedman Equation
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 a≡R E. Fiandrini

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

101 Friedmann Equations for Expansion
a≡R Dark energy affects the expansion of the universe, described by the Friedmann equations of GR Beware most authors use c=1 and drop it. Compare with Newtonian analogs for expansion rate/critical density and gravity force law with no pressure Demystify, main new result for flat universe is pressure contribution to gravitational “mass” a = scale factor (a0 / a) is proportional to (1+z) = obs / em k = 0 for our flat Universe (k = -1 is open, k = +1 is closed)  = energy (mc2 for matter) density, p = pressure (can be < 0) Both pressure and energy density are gravitationally active in GR E. Fiandrini

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

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

104 What is the future of that galaxy ?
Critical velocity: escape speed v<vesc: galaxy eventually stops and falls back v>vesc: galaxy will move away forever E. Fiandrini

105 Let’s rewrite that a bit ...
<0  v<vesc: galaxy eventually stops and falls back >0  v>vesc: galaxy will move away forever E. Fiandrini

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

107 Let’s switch to general relativity
Friedmann equation same k as in the Robertson-Walker metric E. Fiandrini

108 Let’s switch to general relativity
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 E. Fiandrini

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

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

111 Can we predict the fate of Universe ?
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 don’t know precisely  >crit very unlikely E. Fiandrini

112 k>0 k=0 k<0 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’ l’illusione che k=0 procedendo lungo una stessa direzione... ...si ritorna al punto di partenza Definizione di spazio “chiuso” E. Fiandrini

114 How big is crit ? crit = 810-30 g/cm3  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 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 ? E. Fiandrini

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

117 So what’s the meaning of q0 ?
deceleration parameter q0 q0>0.5: deceleration is so strong that eventually the universe stops expanding and starts collapsing 0<q0<0.5: deceleration is too weak to stop expansion q0<0: universe is accelerating the expansion What’s the difference between q0, 0 and k ? k: curvature of the universe 0: mass content of the universe q0: kinematics of the universe E. Fiandrini

118 So let’s measure q0 ! 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. E. Fiandrini

119 So let’s measure q0 ! q0 = 0 q0 = 0.5 Data indicates: q0 < 0
 Expansion is accelerating fainter more distant 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! E. Fiandrini

121 Friedmann’s 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 k is the curvature constant k=0: flat space, flat universe k>0: spherical geometry, closed universe k<0: hyperbolic geometry, open universe 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 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 +  E. Fiandrini

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

125 Cosmology: the quest for 3 numbers
The Hubble constant H0 how fast is the universe expanding The density parameter 0 how much mass is in the universe The cosmological constant  the vacuum energy of the universe current observational situation: H0 = 72 § 8 km/s/Mpc 0 = 0.3 § 0.04; = 0.7 § 0.06  flat space E. Fiandrini

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

127 How old is the Universe? A galaxy at distance d recedes at velocity v=H0  d. When was the position of this galaxy identical to that of our galaxy? Answer: tHubble: Hubble time. For H0 = 65 km/s/Mpc: tHubble = 15 Gyr E. Fiandrini

128 The age of the Universe revisited
So far, we have assumed that the expansion velocity is not changing (q0=0, empty universe) How does this estimate change, if the expansion decelerates, i.e. q0>0 ? now An 0>0, =0 universe is younger than 15 Gyr E. Fiandrini

129 The age of the Universe revisited
So far, we only have considered decelerating universes How does this estimate change, if the expansion accelerates, i.e. q0<0 ? now An >0 universe can be older than 15 Gyr E. Fiandrini

130 The age of the Universe revisited
0=0, =0: tHubble =1/H0 = 15 Gyr 0=1, =0: tHubble =2/(3H0)= 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 decreases the age of the universe 0=0.3, =0.7: tHubble =0.96/H0 = 14.5 Gyr E. Fiandrini

131 Can we measure the age of the Universe ?
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 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 doesn’t 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  eternal expansion otherwise 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/tn There is an instant in the past where all the matter and energy were concentrated in a point...a singularity: the Big Bang 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 Einstein’s equation Space and time are created in the big bang 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. E. Fiandrini

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

137 Friedmann’s equation for >0, 0<1
Falls off like the cube of R Falls off like the square of R constant Expansion rate of the Universe At early epochs, the first term dominates the early universe appears to be almost flat At late epochs, the third term dominates the late universe appears to be exponentially expanding 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 exponentially expanding Isn’t it strange that we appear to live in that short period between those two extremes ? Flatness problem E. Fiandrini

139 The Expanding Universe
On large scales, galaxies are moving apart, with velocity proportional to distance. It’s not galaxies moving through space. Space is expanding, carrying the galaxies along! The galaxies themselves are not expanding! 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: Hubble’s law  Cosmic microwave background radiation  The origin of the elements Structure formation in the universe 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) E. Fiandrini

142 What are the consequences ?
In order to form hydrogen and helium at the right proportions, the following conditions are required: density:   10-5 g/cm-3 temperature: T  109 K Radiation from this epoch should be obser-vable as an isotropic background radiation Due to the expansion of the universe to   310-30 g/cm3, the temperature should have dropped to T  5 K (-268 C) Can we observe this radiation ? 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 couldn’t explain it  discovery of the background radiation Most significant cosmological observation since Hubble Nobel prize for physics 1978 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 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=T0(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 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 l’Universo aveva un eta’ di ~ anni: la distanza fra le stelle (come le conosciamo oggi) diviene ~nulla: Tutto l’universo e’ composto dal materiale di cui sono composte le stelle... Questo e’ l’inizio dell’Universo visibile come lo conosciamo adesso... E. Fiandrini

147 Situazione a T<300 000 anni
in quelle condizioni di densita’, tutto l’Universo 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 E. Fiandrini

148 Situazione a T~ anni con l’espansione dell’universo 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 pero’, a causa dello “stiramento” dello spazio la sua lunghezza d’onda aumenta (e l’energia diminuisce: si raffredda...) 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 E. Fiandrini

149 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. opaque trasparent E. Fiandrini

151 Black body radiation A hot a body is brighter than a cool one (LT4, Stefan-Boltzmann’s law) A hot body’s spectrum is bluer than that of a cool one (max1/T, Wien’s law) E. Fiandrini

152 The cosmic microwave background radiation (CMB)
Temperature of ±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 E. Fiandrini

153 Emissione di radiazione elettromagnetica da un corpo
Alla temperatura di 37 gradi centigradi (circa 310 gradi kelvin) l’emissione è concentrata nell’infrarosso E. Fiandrini

154 Should the CMB be perfectly smooth ?
No. Today’s 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. E. Fiandrini

155 Curiosita’: ~ l’1% dell’effetto “neve” nei TV e’ dato dal fondo
L’esistenza di questa radiazione primordiale e’ la prova diretta che l’Universo in qualche momento del passato era qualitativamente diverso da quello attuale. Permette di “fotografare” l’Universo quando aveva “soltanto” ~ anni... Tutt’oggi continuiamo ad imparare tantissimo dallo studio ad alta precisione di questa radiazione Curiosita’: ~ l’1% dell’effetto “neve” nei TV e’ dato dal fondo di radiazione cosmica 400 fotoni/cm3 CMB : Cosmic Microwave Background CBR: Cosmic Background Radiation 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 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 E. Fiandrini

158 Main results from COBE E. Fiandrini

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

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

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

165 Can we see the sound of the universe ?
Compressed gas heats up  temperature fluctuations 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 : lpeak=220o/ angle E. Fiandrini

167 The Music of the Universe
E. Fiandrini

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

169 Measuring the Curvature of the Universe Using the CMB
Recall: with supernovae, one measures q0 =½0 –  CMB fluctuations measure curvature  0 +  two equations for two variables  problem solved E. Fiandrini

170 Dark energy: we know is there, but have not idea of what it is
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 E. Fiandrini

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

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

173 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: Hubble’s law  Cosmic microwave background radiation  The origin of the elements Structure formation in the universe 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: Hubble’s law  Cosmic microwave background radiation The origin of the elements Structure formation in the universe 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) 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 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. E. Fiandrini

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

178 Ecco tutte le interazioni in breve....
(M=0 , S = 2) (M~90 GeV/c2 , S = 1) (M=0 , S = 1) (M=0 , S = 1) 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”?? 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 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 don’t the protons fly apart ? E. Fiandrini

181 Breve cronistoria dell’universo 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 dell’Universo per t<105 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 c’era prima? La domanda non ha senso. Come conseguenza della R.G., spazio e tempo non esistevano prima, non c’e’ stato un prima! (anche S. Agostino c’era arrivato...) E. Fiandrini

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

184 Formation of helium in the big bang
Hydrogen: 1 nucleon (proton) Helium: 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 E. Fiandrini

185 Transforming hydrogen into helium
Hot big bang: neutrons and protons Use a multi step procedure: p + n  2H p + 2H  3He n + 2H  3H 3He + 3He  4He + 2 p some side reactions: 3He + 3H  7Li 3He + 3He  7Be 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 7Li So how to form the more massive elements? There exist a meta-stable nucleus (8B*). If this nucleus is hit by another 4He during its lifetime, 12C and other elements can be formed E. Fiandrini

187 Mass gap/stability gap at A=5 and 8
Reaction chain: 4He + 4He  8B* 8B* + 4He  12C 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 7Li. Higher elements are formed in stars E. Fiandrini

188 Primordial nucleosynthesis
Consistent with abundance of H, He and Li Result: abundance of H,He and Li is consistent but: b ~0.04 while the tot content is 0.3 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 4He: equal number of protons and neutrons Assume that all neutrons grab a proton to form a 4He. The left over protons form hydrogen. E. Fiandrini

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

192 What happened when the universe was even younger?
Recall special relativity: E=mc2 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 E. Fiandrini

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

194 Examples T>1010 K: creation/annihilation of electron-positron pairs
T>1013 K: creation/annihilation of proton-antiproton pairs E. Fiandrini

195 A common theme ... For each reaction there is a temperature Tc:
For temperature larger than Tc, 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 Tc, pair creation freezes out, remaining pairs annihilate. E. Fiandrini

196 The thermal history of the Universe
E. Fiandrini

197 but temperature rises like (1+z) 2.7K < T < 10000K: matter era
t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = anni: Inizia l’era dominata dalla materia T= K 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 E. Fiandrini

198 t = 180 s: Nucleosintesi T=7.5 108 K
t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = anni: Inizia l’era dominata dalla materia T= K era della radiazione t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=1010 K As the temperature exceeds ~ 10000K, radiation starts dominating 10000K < T < 1010K: radiation era dominate particles (in order of decreasing contribution: photons, neutrinos, baryons dominant forces: electromagnetism, gravity E. Fiandrini

199 t = 180 s: Nucleosintesi T=7.5 108 K
t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = anni: Inizia l’era dominata dalla materia T= K era della radiazione t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=1010 K As the temperature exceeds ~ 1010K, creation of electron-positron pairs T > 1010K: equilibrium between electron-positron pair creation and annihilation T < 1010K: freeze-out. Remaining pairs annihilate E. Fiandrini

200 t = 180 s: Nucleosintesi T=7.5 108 K
t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = anni: Inizia l’era dominata dalla materia T= K era della radiazione t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=1010 K t ~ 10-4 s: Era “leptonica” t < 10-6 s: i quarks si combinano in p e n T=1013 K Hadron hannihilation: As the temperature exceeds ~ 1012K, creation of hadron-antihadron pairs (e.g. proton-antiproton) T > 1012K: equilibrium between hadron pair creation and annihilation T < 1012K: freeze-out. Remaining pairs annihilate E. Fiandrini

201 t = 180 s: Nucleosintesi T=7.5 108 K
Hadron era: 1012K < T < 1013K dominant particles (in order of decreasing contribution: baryons+antiparticles, mesons+antiparticles, electrons, positrons, photons, neutrinos, antineutrinos dominant forces: electromagnetism, strong nuclear, weak nuclear, gravity t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie t = anni: Proto-galassie Quark era:1013K < T < 1015K 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 t = anni: Disaccoppiamento materia-radiazione T=3000 K t = anni: Inizia l’era dominata dalla materia T= K era della radiazione t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=1010 K t ~ 10-4 s: Era “leptonica” t < 10-6 s: i quarks si combinano in p e n T=1013 K E. Fiandrini

202 t = 180 s: Nucleosintesi T=7.5 108 K
t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie Electroweak phase transition: As the temperature exceeds ~ 1015K, electromagnetism and weak nuclear force join to form the electroweak force T > 1015K: electroweak force T < 1015K: electromagnetism, weak nuclear force Limit of what we can test in particle accelerators. Nobel prizes 1979 (theory) and 1984 (experiment) t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = anni: Inizia l’era dominata dalla materia T= K era della radiazione t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=1010 K t ~ 10-4 s: Era “leptonica” t < 10-6 s: i quarks si combinano in p e n T=1013 K t ~ s: Separazione forza elettro-debole T=1015 K E. Fiandrini

203 t = 180 s: Nucleosintesi T=7.5 108 K
t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie 1015K < T < 1029K dominate particles (in order of decreasing contribution: quarks, antiquarks, electrons, positrons, photons, neutrinos, antineutrinos dominant forces: electroweak, strong nuclear, gravity t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = anni: Inizia l’era dominata dalla materia T= K era della radiazione t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=1010 K t ~ 10-4 s: Era “leptonica” t < 10-6 s: i quarks si combinano in p e n T=1013 K t ~ s: Separazione forza elettro-debole T=1015 K E. Fiandrini

204 t = 180 s: Nucleosintesi T=7.5 108 K
GUT phase transition: As the temperature exceeds ~ 1029K, electroweak force and strong nuclear force join to form the GUT (grand unified theories) T > 1029K: GUT T < 1029K: electroweak force, strong nuclear force relatively solid theoretical framework (but may be wrong), but pretty much no constraint by experiments t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K GUT era: 1029K < T < 1032K dominate particles (in order of decreasing contribution: Zillions of particles, most of them not detected yet dominant forces: GUT, gravity t = anni: Inizia l’era dominata dalla materia T= K era della radiazione t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=1010 K t ~ 10-4 s: Era “leptonica” t < 10-6 s: i quarks si combinano in p e n T=1013 K t ~ s: Separazione forza elettro-debole T=1015 K t < s: “Era della Grande Unificazione” T=1028 K E. Fiandrini

205 t = 180 s: Nucleosintesi T=7.5 108 K
t = anni: vita , noi, ora, T = 3 K era della materia t = 5 109: anni galassie Planck epoch: T > 1032K unification of GUT and gravity Particles: ??? Forces: TOE (theory of everything) The last frontier ... t = anni: Proto-galassie t = anni: Disaccoppiamento materia-radiazione T=3000 K t = anni: Inizia l’era dominata dalla materia T= K era della radiazione t = 180 s: Nucleosintesi T= K t = 1 s: Annichilazione elettroni-positroni T=1010 K t ~ 10-4 s: Era “leptonica” t < 10-6 s: i quarks si combinano in p e n T=1013 K t ~ s: Separazione forza elettro-debole T=1015 K t < s: “Era della Grande Unificazione” T=1028 K t = s: Tempo di PlancK: Limite della fisica moderna 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 GUT: grand unified theories (at T > 1029 K) electroweak force (at T > 1015 K) E. Fiandrini

207 T»100 GeV t»10-10 s E. Fiandrini

208 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: Hubble’s law  Cosmic microwave background radiation  The origin of the elements  Structure formation in the universe E. Fiandrini

209 Structure formation in the Big-Bang model
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210 The Hubble sequence of galaxies
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211 Younger galaxies should be smaller ...
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212 How good is the assumption of isotropy?
CMB: almost perfect but what about the closer neighborhood ? E. Fiandrini

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

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

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 E. Fiandrini

216 z=9.00 65 Mpc 50 million particle N-body simulation E. Fiandrini

217 z=4.00 65 Mpc 50 million particle N-body simulation E. Fiandrini

218 z=2.33 65 Mpc 50 million particle N-body simulation E. Fiandrini

219 z=1.00 65 Mpc 50 million particle N-body simulation E. Fiandrini

220 z=0.00 65 Mpc 50 million particle N-body simulation E. Fiandrini

221 Sommario della nuova cosmologia: si fonda su 3 fatti/osservazioni 1 postulato + 1 modello di riferimento su larga scala l’universo e’ lo stesso in tutte le direzioni (isotropia) 2) piu’ guardiamo indietro nel tempo (lontano da noi) piu’ l’universo 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 E. Fiandrini

222 Riassumendo: i successi del modello cosmologico standard (il Big Bang)
Spiegazione dell’esistenza del CMB Previsione quantitativa dell’abbondanza di elementi leggeri (idrogeno, deuterio, elio, litio) nell’universo in accordo con le misure spiegazione delle strutture su larga scala delle galassie in connessione con le piccole irregolarita’ del CMB Ma il modello standard non e’ piu’ sufficiente... E. Fiandrini

223 How can we measure mass ? Count all the mass we can “see”
tricky, some of the mass may be hidden … Using Kepler’s third law: measure the dynamics of a system and apply Kepler’s 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 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. E. Fiandrini

225 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] E. Fiandrini

227 Le scoperte piu’ recenti
C’e 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). La chiamiamo "materia oscura" Materia non oscura     Materia oscura E. Fiandrini

228 The Problem of Dark Matter
- Observed from gravitational interactions only! Observe galaxy rotation curve using Doppler shifts in 21 cm line from hyperfine splitting Galactic Rotation Curves A halo of non-luminous matter must be added to account for the observed radial speed Observed Expected from luminous mass Allen, Schmidt, Fabian (2002) 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 E. Fiandrini

229 Materia oscura E. Fiandrini

230 Let’s use some numbers ... A galaxy like the Milky Way or Andromeda has a total visible mass of about 61010 Msun. The rotation velocity is ~220 km/sec The radius about ~30 kpc Newton:  total mass: 3.31011 Msun  ~5 times more mass than visible E. Fiandrini

231 Dark Matter in Galaxy Clusters
Coma cluster 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 fBh3/2=0.0560.014 Combine with the BBN Wmatterh1/2=0.380.07 Agrees with SZ, virial Zwicky, Helv. Phys. Acta 6 (1933) 110  the most part of cluster gravitational mass is dark E. Fiandrini

232 Evidence of dark matter: X-ray clusters
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233 Evidence of dark matter: clusters of galaxies
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234 Evidence of dark matter: large scale flows
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235 Overall result: But lum = 0.001 and BBN =0.04 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 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. E. Fiandrini

237 90% dark matter ? These astronomers must be crazy !
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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 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 dell’universo. Forse è fatta di neutrini, o magari di altre forme materiali ancora più insolite... E. Fiandrini

240 I problemi non risolti dal modello cosmologico standard
Il problema della “piattezza” e dell’eta’ dell’universo I dati osservativi indicano una densita’ media dell’Universo vicinissima al “valore critico” (implica k~0) Bastava poca materia in piu’ per far “morire” (collassare) l’universo molto prima Il problema dell’orizzonte 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”? E. Fiandrini

241 I problemi non risolti dal modello cosmologico standard
Il problema della “piattezza” e dell’eta’ dell’universo I dati osservativi indicano una densita’ media dell’Universo vicinissima al “valore critico” (implica k~0) Bastava poca materia in piu’ per far “morire” (collassare) l’universo molto prima Il problema dell’orizzonte 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”? E. Fiandrini

242 Se D> c Tuniverso come possono A e B scambiarsi informazioni?
Il problema dell’orizzonte D A B Se D> c Tuniverso come possono A e B scambiarsi informazioni? E. Fiandrini

243 Un nuovo paradigma: L’ “Inflazione” (universo gonfiato)
A. Guth, 1980 L’ universo che vediamo puo’ venire da una porzione infinitesimamente piccola dell’universo 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... E. Fiandrini

244 Espansione “gonfiata”
Espansione “normale” Espansione “gonfiata” 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 nell’Universo 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 E. Fiandrini

246 2001: esp. “Boomerang” per la misura di alta precisione
delle irregolarita’ del CMB L’analisi delle variazioni di temperatura da’ informazioni sulla proporzione delle varie componenti dell’ universo Permette di ricostruire le dimensioni angolari con cui vediamo l’epoca del disaccoppiamento E. Fiandrini

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

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

249 Siamo in un universo speciale?
Molti indizi suggeriscono che delle condizioni dell’Universo anche solo infinitesimamente differenti avrebbero dato luogo ad un modo inospitale... L’espansione avrebbe potuto essere cosi’ veloce da non consentire la formazione di strutture. Un’espansione appena piu’ veloce non avrebbe permesso altri atomi oltre l’idrogeno 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... E. Fiandrini

250 2 risposte possibili: 1) La “Teoria del Tutto”
Una (futura) teoria della fisica spiega tutti gli aspetti dell’Universo, include queste che sembrano coincidenze Puo’ esistere la Teoria di Ogni Cosa? (TOC) 2) il Principo Antropico Se l’Universo non fosse cosi’ noi non ci saremmo... L’Universo e’ stato fatto per noi... ...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 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 E. Fiandrini

252 fine E. Fiandrini