The early and late time acceleration of the Universe

Transcription

1 The early and late time acceleration of the Universe Tomo Takahashi (Saga University) March 7, 2016 New Generation Quantum Theory -Particle Physics, Cosmology, and University

2 The early and late time acceleration of the expansion of the Universe Tomo Takahashi (Saga University) March 7, 2016 New Generation Quantum Theory -Particle Physics, Cosmology, and University

3 Expansion of the Universe

4 Expansion of the Universe In 1929, Edwin Hubble discovered that distant galaxies move away from us. [ The recessional velocity is proportional to the distance to the galaxy: Hubble constant velocity (Hubble s law) distance to galaxies

5 Expansion of the Universe Its natural interpretation is that galaxies move away with each other. [ This observation indicates that the Universe is expanding.

6 Expansion of the Universe [

7 How can we describe the expansion of the Universe? The expansion of the Universe is the expansion of spacetime. We need to investigate the dynamics of the spacetime. Theory of general relativity can describe it. metric Energy momentum tensor Einstein equation: Information on the spacetime

8 Recent detection of gravitational waves On February 11, LIGO has announced that they detected gravitational waves from BH merger. [ [ The detection confirms the prediction of general relativity. The description of the evolution of the Universe also relies on general relativity.

9 How can we describe the expansion of the Universe? The Universe is homogeneous and isotropic. (The distribution of matter in the Universe is homogeneous and isotropic.) The metric (spacetime interval) can be given by Friedmann-Robertson-Walker metric (spacetime): [ ds 2 = dt 2 a(t) 2 dr 2 ] 1 Kr 2 + r2 dθ 2 + r 2 sin 2 θdφ 2 Scale factor (which describes the cosmic expansion) Comoving coordinates Curvature of the Universe K>0 K<0 K=0

10 Scale factor of the Universe The scale factor a(t) describes the expansion of the Universe. time expansion time t = t 1 t = t 2 a(t 1 ) Scale factor a(t 2 )

11 Friedmann equation Time evolution of the scale factor a(t) describes the expansion of the Universe. a(t) is given by solving the Einstein equation. The (differential) equation of a(t) is obtained by putting: FRW metric: ds 2 = dt 2 a(t) 2 [ dr 2 ] 1 Kr 2 + r2 dθ 2 + r 2 sin 2 θdφ 2 pressure Energy momentum tensor: (information of the components in the Universe) energy density into Einstein eq.

12 Friedmann equation Assuming a flat Universe, we obtain H 2 = ȧ a 2 = 8 G 3 where energy density ȧ = da dt We can also obtain the eq. of the acceleration: ä a = 4 G ( +3p) 3 pressure Once we specify the energy density and pressure, we can follow the evolution of the scale factor.

13 Components in the Universe Ordinary matter (baryon) Dark matter

14 Evolution of energy density of matter Energy density of baryon and dark matter: = mn Mass Number density Expansion of the Universe a 1 a 2 Energy density decreases as: (number density) (a 1 /a 2 ) 3 / a 3

15 Cosmic microwave background (CMB) There is yet another important component in the Universe. Photon (radiation) In 1965, Penzias and Wilson have discovered CMB. (Nobel prize in 1978.) (Microwaves are observed from all direction with the same intensity.)

16 Cosmic microwave background (CMB) In 1990s, COBE satellite confirmed that CMB is a black-body radiation with T0 = 2.7 K. (More precisely ) [Fixsen 2009] There exists (black-body) radiation in the Universe.

17 Evolution of energy density of radiation Energy density of radiation: (hν)x(number density) Expansion of the Universe a 1 a 2 Number density decreases as: (a 1 /a 2 ) 3 Wave length (energy) of radiation decreases as: (a 1 /a 2 ) / a 4

18 Components in the Universe Ordinary matter (baryon) Dark matter Radiation (photon, neutrino)

19 Evolution of energy density The Universe was very hot and dense in the early times. log(energy density) rad a 4 m a 3 past log(scale factor) present

20 Late time acceleration of the Universe (current)

21 Acceleration of the Universe The expansion of the Universe is determined by the components in the Universe. The acceleration of the cosmic expansion is given by 1 a d 2 a dt 2 = ä a = 4 G 3 ( +3p) If the Universe is dominated by baryon and dark matter p =0 ä<0 (decelerating) If the Universe is dominated by radiation (photon, neutrino) p = 3 ä<0 (decelerating) The cosmic expansion should be decelerating with these components.

22 Acceleration of the Universe However, in 1998, observations of type Ia supernovae revealed that the current expansion of the Universe is accelerating. ä>0

23 Observations of supernovae (SNe) By observing distant SNe, we can probe the cosmic expansion. (the Universe is expanding) observer [www-supernova.lbl.gov] Apparent magnitude m M = 5 log d L + 25 Absolute magnitude Luminosity distance

24 Observations of supernovae (SNe) By observing distant SNe, we can probe the cosmic expansion. (the Universe is expanding) observer [www-supernova.lbl.gov] Apparent magnitude m M = 5 log d L + 25 Absolute magnitude Luminosity distance If we know the absolute luminosity of the source, by observing apparent luminosity, we can know the distance to the source. Type Ia supernovae (SNeIa) can be used as the standard candle.

25 Observations of supernovae (SNe) By observing distant SNe, we can probe the cosmic expansion. (the Universe is expanding) observer [www-supernova.lbl.gov] Luminosity distance: 4πd 2 Lf = L d L = (1 + z) Apparent magnitude z 0 1 H(z ) dz H 2 = 8 G 3 m M = 5 log d L + 25 Absolute magnitude L Luminosity distance Apparent luminosity Absolute luminosity d L f

26 Observations of supernovae (SNe) By observing distant SNe, we can probe the cosmic expansion. (the Universe is expanding) observer [www-supernova.lbl.gov] Apparent magnitude m M = 5 log d L + 25 Absolute magnitude Luminosity distance The luminosity distance carries the information of the expansion of the Universe (time evolution of the scale factor). By observing SNe, we can probe the acceleration of the Universe.

27 Acceleration of the Universe Decelerating Universe Accelerating Universe (future) (past) [

28 Acceleration of the Universe In 1998, observations of type Ia supernovae revealed that the expansion of the Universe is accelerating. ä>0 However, known matter (baryon, dark matter, radiation) in the Universe cannot accelerate the expansion of the Universe. What accelerates the Universe??

29 Acceleration of the Universe The accelerating Universe implies: ä a = 4 G 3 ( +3p) p< 1 3 (component with a negative pressure) To explain the accelerated expansion of the Universe, we need a very weird component with p < -ρ/3. = dark energy

30 Candidates of dark energy Cosmological constant 1 R µ 2 g µ R + g µ =8 GT µ (Λ was originally introduced by Einstein to obtain a static Universe) This acts as a component with p = Scalar field (quintessence) ( Modification of gravity)

31 Candidates of dark energy In general, the nature of dark energy can be represented by the equation of state (EoS) parameter w. w p (examples) Cosmological constant: w = 1 (p = ) Quintessence: w> 1 = V ( ), (dependent on time) p = V ( ) By probing the EoS parameter with observations, we can have information on dark energy.

32 Constraints on dark energy Current constrain on w from Planck+BAO, SN, H0 (for constant w) w = (95% C.L.) [Planck collaboration, ] In many models of dark energy, the EoS parameter w depends on time. Analysis with time-varying EoS Planck+BSH Planck+WL Planck+BAO/RSD Planck+WL+BAO/RSD wa w(a) =w 0 +(1 a)w a 1 2 The nature of dark energy is still a mystery w 0 [Planck collaboration, ]

33 Components in the Universe Ordinary matter (baryon) Dark matter Radiation (photon, neutrino) Dark energy

34 Components in the Universe Ordinary matter (baryon) ~ 5 % Dark matter ~ 25 % Radiation (photon, neutrino) ~ % Dark energy ~ 70 %

35 Evolution of energy density log(energy density) Radiation dominated (RD) rad a 4 m a 3 Matter dominated (MD) Dark energy dominated DE constant Now log(scale factor)

36 Evolution of energy density log(energy density) Radiation dominated (RD) rad a 4 m a 3 Matter dominated (MD) Dark energy dominated the Universe is accelerated DE constant Now log(scale factor)

37 A brief history of the Universe [ very hot and dense plasma

38 A brief history of the Universe [ Recombination: e + p H + Free electrons have combined with proton to form atoms.

39 A brief history of the Universe [ Recombination: e + p H + Free electrons have combined with proton to form atoms. Photons can freely travel from this epoch. (the epoch of last scattering)

40 A brief history of the Universe [ CMB photons we observe today

41 Standard big bang cosmological model In the early era, the Universe is dominated by radiation. (The Universe was dense and hot in the early times.) The Universe has been expanding. [

42 Early time acceleration of the Universe

43 Problems in the standard big bang model Although the standard big bang model is very successful in explaining key observations, there are serious problems Horizon problem Flatness problem

44 Horizon problem What is the horizon? Nothing can travel faster than light. There should be a limit which the information can be reached in a finite time (= Horizon). Horizon t = t 0 t = t 1 c(t 1 t 0 )

45 Horizon problem CMB radiation is very isotropic. Temperature is the same within % precision. horizon However, no causal contact between these points at earlier time. Horizon problem

46 Inflation If the Universe experienced a very rapid accelerated expansion, the horizon problem can be solved. No causal contact A CMB CMB B (recombination) observer (today)

47 Inflation If the Universe experienced a very rapid accelerated expansion, the horizon problem can be solved. The universe expands very rapidly. Inside the horizon a e Ct A CMB CMB B (recombination) observer (today)

48 What drives inflation? Inflation is considered to be driven by a scalar field, called inflaton field. V ( ) (Example) The potential energy (vacuum energy) of the inflaton drives inflation. = const. 1 a da dt 2 = 1 3M 2 pl a / exp (Ct) (accelerated expansion)

49 What drives inflation? Inflation ends when the inflaton rolls down to the minimum of the potential and begins to oscillate. V ( ) oscillate around the minimum

50 What drives inflation? At some point, the inflaton decays into radiation and the Universe becomes radiation-dominated. V ( ) Inflaton decays into radiation (reheating)

51 Can we test the inflation? Inflation can solve the problems in the standard big bang model. But, how can we test the inflation? In fact, the inflation not only solves the problems, but also can give the origin of the structure of the Universe.

52 Structure in the Universe Distribution of galaxies [

53 Structure in the Universe Cosmic microwave background anisotropies Although CMB is almost isotropic, there exists slight deviations from the complete isotropy (at the level of O(0.001%)). [Planck:

54 Can we test the inflation? Inflation can solve the problems in the standard big bang model. But, how can we test the inflation? In fact, the inflation not only solves the problems, but also can give the origin of the structure of the Universe. Inflation can be tested by looking at the structure of the Universe.

55 Quantum fluctuations of the inflaton Quantum fluctuations of the inflaton can give the origin of density fluctuations. V ( ) Density fluctuations in the Universe Properties of fluctuations depend on the model of inflation. can be used as a test of inflation models For details, see Masahide Yamaguchi s talk.

56 History of the Universe The Universe has experienced two accelerated expansion in its history. [ Inflation (early time acceleration) Dark energy dominated (late time acceleration)

57 Summary The Universe experienced a very rapid expansion in the very early Universe, called inflation. (early time acceleration) The present Universe is also accelerating (due to dark energy, modified gravity, ) (late time acceleration) Precise mechanism of these accelerations are still unknown. Future observations are expected to reveal these accelerated eras.