The cosmological context

Transcription

1 The cosmological context P. Binétruy AstroParticule et Cosmologie, Paris STE-Quest, ESTEC, 2013, May 22

2 Outline The Universe after Planck Where quantum physics meets gravity: the vacuum energy problem Dark energy models Violations of the fundamental symmetries

3 The Universe after Planck

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5 After cleaning the foregrounds

6 The Universe according to WMAP

7 The early Universe is an ionized plasma : photons interact strongly with the plasma and are absorbed before propagating: the Universe is dark. At t yrs i.e. kt 0.26 ev i.e. z 1100, electrons combine with protons to form neutral hydrogen: photons can travel large distances. The universe becomes transparent to light. Which light? ionized plasma us last scattering surface

8 Planck black body distribution at 2.7 K T(z) = T o (1+z) John Mather 2006 Physics Nobel Prize

9 1 1 1 Acoustic oscillations of the tightly coupled baryon-photon fluid within the «causal horizon» box (at time of recombination) leads to the famous distribution of acoustic peaks

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11 What do we learn? information about recombination and the evolution of the Universe since 5% 26.5% 68.5%

12 CMB lensing allows to reconstruct the large scale structures z 2

13 even more importantly, information about the very early Universe Last Scattering Surface (recombination) causal horizon All history of the Universe between Big Bang and years after

14 A word of caution: our observation of the Universe is very limited slice is observed only at given time

15 A word of caution: our observation of the Universe is very limited t t= us slice is observed only at given time 0 r

16 A word of caution: our observation of the Universe is very limited t t= us slice is observed only at given time 0 r

17 Planck results have taught us that the source of fluctuations is almost of a scale-free gaussian nature Power spectrum: P δρ/ρ (k) k n s-1 n s 1 This is best described effectively by the theory of inflation

18 Inflation scenario proposed first in the context of the phase transition associated with grand unification (Guth, 81) V 0 Fluctuations in CMB predicted at the level observed by the COBE satellite : V 0 = ε 1/ GeV ε slowroll parameter : 21/08/04 Astroparticle and cosmology 2ε=(M P V /V) 2 «1 ICHEP04

19 If a vacuum energy V 0 dominates the energy density, the Universe has the geometry of de Sitter space time. V 0 quantum fluctuations are scale-free n s = 1 Harrison-Zeldovich spectrum But there must be an end to inflation : an instability should be built in V 0 n s < 1 Planck: n s = ±0.0070

20 Two theoretical developments after the first inflation models: chaotic inflation: more natural initial conditions V M Pl 4 initial M Pl realistic models: multi-scalar field inflation φ Linde lead to sources of non-gaussianity (3-point function, etc )

21 Two theoretical developments after the first inflation models: chaotic inflation: more natural initial conditions V M Pl 4 realistic models: multi-scalar field inflation lead to sources of non-gaussianity (3-point function, etc ) φ

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26 How to go beyond? Key word is gravitation: the Universe is powered by gravity Search for primordial gravitational waves: CMB polarisation Search for possible alternatives to inflation Search for alternatives to general relativity

27 Where quantum physics meets gravity: the vacuum energy prob

28 Vacuum energy E 4 E 3 E 2 Classically, only differences of energy can be measured (e.g. Casimir effect). E 1 E 0 ground state = vacuum The absolute energy E 0 cannot be measured experimentally

29 No longer true in a gravitational context! Einstein equations: R µν - R g µν /2 = 8πG T µν geometry energy Hence geometry may provide a way to measure absolute energies i.e. vacuum energy: R µν - R g µν /2 = 8πG T µν + 8πG < T µν > vacuum energy similar to the cosmological term introduced by Einstein : R µν - R g µν /2 = 8πG T µν + λ g µν λ l Λ -2

30 Can we measure λ i.e. the associated scale l Λ? Einstein equations Friedmann equation c = 1 H 2 = ( 8 πg ρ + λ ) /3 - k/a 2 H =. a/a ρ Λ = λ / 8πG ρ c = 3 H 0 2 / 8πG ρ k = -3k / 8πGa 0 2 ρ c = ρ + ρ Λ + ρ k Ω Λ ρ Λ / ρ c = (H 0-1 / l Λ ) 2 / l Λ H 0-1 ~ m A very natural value for an astrophysicist: H 0-1 is the size of the visible Universe (our causal «horizon»)!

31 Introduce the quantum theory i.e. ħ Planck length l P = 8πG N ħ/c 3 = 8.1x10-35 m Planck l P ~10-34 m m P ~10 27 ev λ l Λ ~10 26 m m Λ ~10-33 ev

32 Can we measure λ i.e. the associated scale l Λ? Einstein equations Friedmann equation H 2 = ( 8 πg ρ + λ ) /3 - k/a 2 H =. a/a c = 1 ρ Λ = λ / 8 πg ρ c = 3 H 0 2 / 8 πg Ω Λ ρ Λ / ρ c = (H 0-1 / l Λ ) 2 / 3 ~ 0.7 A very natural value for an astrophysicist! l Λ ~ H 0-1 ~ m A very unnatural value for a Universe which presumably started as a quantum state!

33 Indeed, if we compute the vacuum energy, we obtain typically ρ Λ ~ m P 4 ~ ρ observed ħ=c=1 There should be a cancellation mechanism of most of the vacuum energy, Or there is a selection principle for our own Universe to have a much lower vacuum energy than expected. string vacuum inflation

34 Note that, if we write UV cut-off IR cut-off Cosmological constant problem : where the two ends meet

35 10-3 ev UV cut-off IR cut-off Cosmological constant problem : where the two ends meet

36 Central question : why now? why is our Universe so large, so old?

37 Are there more general ways than a cosmological constant to account for the acceleration of the expansion? Einstein equations: R µν - R g µν /2 = 8πG T µν geometry matter-energy modify gravity add new effects or a new form of energy Friedmann equation : H 2 = 8 πg ρ /3 - k/a 2 modified Friedmann equation new contributions to the Friedmann equation

38 Are the two cases so different?

39 Take for illustration the simplest model using a scalar field Quintessence V ε=(m P V /V) 2 /2«1 slowroll condition m P w = p ϕ /ρ ϕ =. ϕ 2 /2- V(ϕ). ϕ 2 /2+ V(ϕ) > -1 ϕ

40 A generic problem ϕ has to be very light : m ϕ ~ H 0 ~ ev ε=(m P V /V) 2 /2«1 slow roll V m P ϕ ϕ exchange between particles provides a long range force similar to gravity: ϕ has to be extremely weakly coupled to ordinary matter (more weakly than gravity!) NEW GRAVITATIONAL-TYPE INTERACTION

41 Scalar field nonconstancy of fundamental csts time-dependent COUPLED TO ultralight m ~ H 0 ~ ev violations of the equivalence principle RADIATION AND MATTER: quarks and charged leptons neutrinos dark matter

42 A simple example Wetterich, 02 1 ϕ quintessence field L kin = k 2 µ ϕ µ ϕ 2 Fermion masses: m f (ϕ) graviton Quintessence charge : β f m Pl m f m f k ϕ Damour, Esposito-Farèse, 92 m f ϕ m f G V N = - N m 2 f (1+ β f2 ) r Acceleration in the Earth gravitational field : G N M E m 2 a f = [ Pl lnm 1 + ( E lnm )( f ) ] r 2 k 2 ϕ ϕ M E Earth mass

43 For two test bodies with same mass M but different composition M a 1 a 2 M M = N i m n + Z i m H + B i ε m H = m p + m e B i = N i + Z i N = N 1 -N 2, 2 a 1 -a 2 η = ( N + Z + B ) a 1 +a 2 m Pl 2 k 2 lnm E ϕ m n m H ε ϕ ϕ ϕ N m n + Z m H + B ε = 0 m Pl 2 lnm E ϕ m H ln(m η = ( Z H /m n ) + B ε ln(ε /m n ) k 2 M M ϕ ϕ lnm E /B E ϕ ~ ~ lnm n /m Pl ϕ

44 In most cases, difficult to reconcile with existing limits: C. Will, Living Rev. Relativity, 2006

45 Modification of gravity

46 Extended gravity The Einstein action S = -g R can be generalized into S = -g f(r) Perform a redefinition of the metric g (E) µν = 2 df/dr g µν and write Then φ ( 6/2) ln [2 df/dr ]

47 Brane world models: induced gravity à la DGP Dvali, Gabdadze, Porrattii 5D For distances r > r c one recovers the 5-dim 1/r 3 behavior: r r c = M Pl 2 / 2 M 5 3 Gravity leakage into the 5th dimension 4D

48 Cosmology Deffayet, Dvali, Gabadadze acceleration

49 This looks like a genuine modification of gravity. However, define the scalar field π (x,t) = - H x (H/H+H) t 2 + bt + c 4r c 4r c Then the generalized Friedmann equation can be recast into: 6 π - 4r c 2 ( µ ν π) 2 + 4r c 2 ( π) 2 = - T µ µ = ρ -3p Hence this can be described by an effective scalar field (a brane-bending mode) genearlized to the notion of galileon field Nicolis, Rattazzi, Trincherini, Deffayet, Tsujikawa,, Trodden.

50 Note two problems in this approach: one solved (Vainshtein mechanism) Mass M r M = 2G N M Schwarzsch. radius non perturbative regime r m = (m g r M ) 1/5 /m g perturbative regime: expansion in powers of G N one unsolved: presence of a ghost

51 More about the couplings of dark energy

52 Fundamental tests probe the most crucial part of dark energy models : the coupling of dark energy to any form of matter Why is it so important? crucial tests of the most «realistic» models of dark energy often connected to the «Why now?» question Some examples

53 Mass varying neutrino scenarios Hung; Gu, Wang, Zhang, Fardon, Nelson, Weiner, Amendola, Baldi, Wetterich; Consider a neutrino with mass depending on scalar field φ: m ν (φ) Effective potential : V eff (φ) = V(φ) + n ν m ν (φ) Dark energy is the coupled fluid neutrino-scalar: ρ DE = ρ φ + ρ ν (φ) But neutrinos have a tendancy to cluster (extra force due to φ exchange)! Coupled dark energy Anderson, Carroll; Casas, Garcia-Bellido, Carroll; Farrar, Peebles; Amendola; Comelli, Pietroni, Riotto; ϕ-dependent mass for the dark matter particle χ: M χ (ϕ) = M 0 exp(-λϕ) If the scalar potential is V(ϕ) = V 0 exp(βϕ), there is an attractor corresponding to ρ ϕ ~ ρ χ ~ M χ (ϕ) n χ ~ a -3(1+W) with W = - λ/(λ+β) ~ a -3

54 Chameleon dark energy Khoury, Weltmann; Brax, van de Bruck, Davis, Khoury, Weltman; V eff (φ) = V(φ) + A(φ) ρ m e.g. Then, possible to have a heavy enough scalar field (m φ > 10-3 ev) in matter where constraints on the fifth force or equivalence principle apply, whereas it can be ultralight outside matter. long range force matter short range force matter short range force

55 V V eff V V eff φ in φ φ out φ large ρ small ρ Thin shell effect : a tiny fraction of large objects (e.g. planets) is sensitive to the long range force. Not so for smaller objects: hence tests with satellites bring new constraints. φ out M φ in R r m 1 thin shell Φ N = GM/R A(φ) = exp(βφ)

56 More on vacuum energy

57 Indeed, if we compute the vacuum energy, we obtain typically ρ Λ ~ m P 4 ~ ρ observed ħ=c=1 There should be a cancellation mechanism of most of the vacuum energy, Or there is a selection principle for our Universe to have a much lower vacuum energy than expected. string vacuum inflation

58 Note that the rationale behind the naive computation is as follows: l P l P energy m P c 2 l P ρ = = m P 4 in units ħ = c = 1 m P c 2 l P 3

59 But consider a macroscopic region of size R R E = (4πR 3 /3) ρ = (4π/3) m P (Rm P ) 3 But this object will undergo gravitational collapse unless R > R schwarschild = 2 G N E = E/(4π m P2 ) = (Rm P ) 3 / 3m P i.e. R < 1/m P = l P

60 R < R schwarschild = 2 G N E In other words, gravitational collapse prevents us from storing in a region of macroscopic size R an energy larger than R/2G N, i.e. an energy density larger than ρ max = E/(4πR 3 /3) = 3 8πG N R 2 Apply this to the whole observable Universe (R = H 0-1 ) ρ < 3 H 0 2 8πG N = ρ c P.B. arxiv: [gr-qc]

61 Could our (causal) horizon have properties similar to the horizon of a black hole? concept of holography in cosmology t Hooft, Susskind, Bousso, Jacobson, Padmanabhan,

62 causal horizon us period close to the big bang

63 How does the Universe look like at times close to the big bang? Most probably, spacetime is a «long» distance notion, no longer valid at distances of order l P or times t P. Notion of emergent spacetime But if spacetime is emergent, its symmetries should also be emergent!

64 e.g. one expects non-commutativity of the coordinates [x µ,x ν ] = 1 Θ µν Λ 2 LV Θ µν is a constant tensor; hence Λ LV is the scale of Lorentz violations. But observational constraints on Lorentz invariance tend to give Λ LV m P

65 Einstein s equivalence principle: Weak Equivalence Principle: universality of free fall η Nordtvedt Local Lorentz Invariance : independence on the velocity of the freely falling reference frame for nongravitational experiments c 2 1 Local Position Invariance : independence on the location in time and space where the nongravitational experiment is performed nonconstancy of csts grav. redshift δ = c -2-1 ν/ν=(1+α) U

66 Conclusions The Universe is powered by gravity. It may very well be that significant information will be obtained on vacuum/dark energy by testing the laws of gravity. If no violation is found, this is a very precious and constraining information. In many instances, tests of the laws of gravity are the only way to go beyond the very efficient but very limited models that we have at hand (Standard Model of high energy physics or of cosmology). The XXI st century will be gravitational.

67 THE END