Dark energy. P. Binétruy AstroParticule et Cosmologie, Paris. Zakopane, 15 June 2007

Transcription

1 Dark energy P. Binétruy AstroParticule et Cosmologie, Paris Zakopane, 15 June 2007

2 Context : the twentieth century legacy

3 Two very successful theories : General relativity A single equation, Einstein s equation, successfully predicts tiny deviations from classical physics and describes the universe at large as well as its evolution. R µν - (R/2) g µν = 8πG N T µν geometry matter QuickTime et un décompresseur Cinepak sont requis pour visionner cette image.

4 Quantum theory Describes nature at the level of the molecule, the atom, the nucleus, the nucleons, the quarks and the electrons.

5 Difficult to reconcile general relativity with the quantum theory: best illustration is the vacuum problem ( cosmological constant pb) Classically, the energy of the fundamental state (vacuum) is not measurable. Only differences of energy are (e.g. Casimir effect). 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:

6 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

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10 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

11 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 Such a term tends to accelerate the expansion of the universe : H 2 = 8 πg (ρ + ρ Λ ) /3 - k/a 2 ρ Λ λ / (8 πg ) curvature term Present observations (k=0, ρ < ρ Λ ) yield ρ Λ ~ H 0 2 / 8 πg ~ (10-3 ev) 4

12 Note that ρ Λ ~ H 0 2 / 8 πg λ -1/2 ~ H 0-1 =10 26 m size of the presently visible universe A very natural value for an astrophysicist!

13 Note that ρ Λ ~ H 0 2 / 8 πg λ -1/2 ~ H 0-1 =10 26 m size of the presently visible universe A very natural value for an astrophysicist! A high energy theorist would compute the vacuum energy and find λ -1/2 ~ M W -1 ~ m electroweak scale or λ -1/2 ~ m P -1 ~ m Planck scale

14 Related questions : why now? why is our Universe so large, so old?

15 1. The observational facts

16 Supernovae of type Ia may be used as standard candles to test the geometry of spacetime

17 Distant supernovae appear less bright than in an expanding universe accelerated expansion

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19 m B = 5 log(h 0 d L ) + M - 5 log H q luminosity distance d L = l H0 z ( z + ) q 0 deceleration parameter q 0 = - a.. a / a. 2

20 QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image.

21 Could this be explained by a cosmological constant? Plot (Ω Λ, Ω M ) : Ω Λ =ρ Λ /ρ c, Ω M = ρ M /ρ c q 0 = Ω M /2 - Ω Λ Concordance model

22 A detailed knowledge of the acoustic peaks allows to have access to the cosmological parameters: Baryon density Ω b h 2 = 0.015,

23 Matter density Ω M h 2 = 0.16,...,0.33

24 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 form of energy Friedmann equation : H 2 = 8 πg ρ /3 - k/a 2

25 Dark energy Assume the existence of a new component assmilated to a perfect fluid with pressure p and energy density ρ : equation of state p = w ρ Acceleration of the expansion : - 4πG (ρ+3p) /3 Hence requires a component with negative pressure : p<0. Non-relativistic matter has w=1/3. Vacuum energy has w=-1. Quite generally, the eqn of state parameter may be varying with time i.e. redshift.

26 The energetic budget of the Universe

27 Angular diameter distance CMB w = -1.8,..,-0.2 When combined with measurement of matter density constrains data to a line in Ω M -w space

28 Large scale structure surveys : 2dF : completed ( galaxies) QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image. Sloan Digital Sky Survey (SDSS) : on-going (goal: galaxies) 2nd data release: 3324 sq. deg. imaging 2627 sq. deg. spectroscopy with galaxies quasars (z < 2.3) quasars (z > 2.3)

29 Testing dark energy : p dark energy = w ρ dark energy w equation of state parameter Ω Λ Ω M Ω M

30 Using distant Sn observed with the Hubble Space Telescope QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image. astro-ph/ Hubble plot : magnitude vs redshift

31 Starting to test candidates for dark energy (quintessence) : w(z) = w 0 + w 1 z + tests the dynamical nature of dark energy w w 0 Golden set of Sn1a : w/o HST discovered w/ HST discovered

32 Results from WMAP (3 years) w WMAP+SDSS WMAP+2dF Ω k WMAP+Sn WMAP+SNLS (in black: WMAP alone) Ω M WMAP+2dF+SDSS+Sn

33 Baryon oscillations are really discriminating for dark energy Acoustic oscillations are seen in the CMB. Look for the the same waves in the galaxy correlations. ΛCDM Ω M = 0.88, Ω v =0.12, H 0 = 46 SNe ignored. Blanchard et al 2003 cannot accommodate Λ=0 with baryon acoustic peak. Blanchard, Douspis, Rowan-Robinson, Sarkar 2005

34 w=-1 Confidence Contours Ω Tot =1 BAO: Baryon Acoustic Oscillations (Eisenstein et al 2005, SDSS) 68.3, 95 et 99.7% CL

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36 Ω DE (z)

37 2. Back to the cosmological constant

38 According to present observations, a cosmological constant is, to first order, a good modelization of dark energy. H 2 = ( 8 πg ρ + λ ) /3 - k/a 2 c = 1 λ l Λ -2 ρ c = 3 H 02 / 8 πg ρ Λ = λ / 8 πg Ω Λ ρ Λ / ρ c = (H 0-1 / l Λ ) 2 / 3 ~ 0.7 l Λ ~ H 0-1 ~ m

39 Introduce h More generally, Planck m P ~10 27 ev l P ~10-34 m e.g. λ m Λ ~10-33 ev l Λ ~10 26 m

40 UV cut-off IR cut-off

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42 Cosmic coincidence problem: Why does the vacuum energy starts to dominate at a time t Λ (z Λ ~ 1) which almost coincides with the epoch t G of galaxy formation (z G ~ 3)?

43 3. Models for the cosmological constant

44 Adjustment mechanisms A no-go theorem by S. Weinberg : not possible to have a vanishing λ As a consequence of the equation of motion of some fields.

45 Anthropic approach Vilenkin, Weinberg,Linde,string theorist Consider regions (universes) with different values of t G and t Λ : when ρ Λ starts to dominate (at t Λ ), the Universe enters A de Sitter phase of exponential expansion galaxy formation (at t G ) must precede this phase (otherwise no observer available) Hence t G t Λ Regions with t Λ» t G have not undergone yet any de Sitter phase of reacceleration and are thus phase space suppressed compared with regions with t Λ ~ t G : Hence t Λ ~ > t G ρ Λ ~ ρ M

46 4. More dynamics: why scalar fields?

47 Models for accelerating the expansion of the Universe Extended gravity Dark energy L = f (R) Brane models (DGP model) Quintessence PGB String inspired Brane models Ratra-Peebles Exp. K-essence Chaplygin gas Tachyon

48 To be compared with models for dark matter Dark matter Modification of gravity baryonic non-baryonic MOND TeVeS Clumped Hydrogen Primordial Black holes Exotic particles Extra dimensions dust MACHO thermal nonthermal Light ν WIMPS SuperWIMPS axion Wimpzillas

49 Why scalar fields to model dark energy? Scalar fields easily provide a diffuse background Speed of sound c s2 = (δp / δρ) adiabatic In most models, c s 2 ~ 1, i.e. the pressure of the scalar field resists gravitational clustering : scalar field dark energy does not cluster

50 First example (quintessence) V w = p ϕ /ρ ϕ =. ϕ 2 /2- V(ϕ). ϕ 2 /2+ V(ϕ) ϕ

51 The problems of scalar field models of dark energy Example of quintessence : V ϕ has to be very light : m ϕ ~ H 0 ~ ev ϕ exchange would provide a long range force : ϕ has to be extremely weakly coupled to matter HOPELESS FOR COLLIDERS ϕ

52 Second class Point particle :

53 Explicit realization: K-essence Armendariz-Picon, Mukhanov, Steinhardt Chiba, Okabe, Yamaguchi S= d 4 x -g [R/2 + K(φ) p(x)], X D µ φ D µ φ/2 Pressure p k = K(φ) p(x) Energy density ρ k = K(φ) ρ(x), ρ(x) 2X p (X) - p(x) Hence w k = p(x) / ρ(x) = p(x) / [2X p (X) - p(x) ] c s 2 = p (X) / ρ (X)... K (φ) ρ(x) Equation of motion : φ + 3Hc 2 s φ + = 0 K(φ) ρ (X)

54 Two classes of attractors : ρ φ / ρ B = cst and w φ = w B ρ φ / (ρ B + ρ φ ) 0 or 1 and w φ w B Some k-essence models may help to understand the coincidence pb radiation domination: ρ φ / ρ rad = cst matter domination: p φ < 0 ρ φ / ρ matter until ρ φ dominates

55 Tachyon Sen, Effective Lagrangian for the tachyon on a non-bps D-3 brane : S = - d 4 x V(φ ) -det ( g µν + µ φ ν φ). ρ t = V(φ) / 1 - φ 2. p t = - V(φ) 1 - φ 2 w = p t t / ρ. t = φ 2-1. Hence acceleration for φ 2 < 2/3 Note: power law expansion a ~ t p for the tachyon potential V(φ) = (2p/4πG) (1-2/3p) 1/2 φ -2 Tachyon potentials which are less steep lead to an acceleration.

56 5. The future observations Future programs both in space (SNAP/JDEM/DUNE) and on the ground (SDSS, LSST, SKA/FAST, ) QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image. QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image.

57 Expected Planck performance on dark energy equation of state w = w 0 + w 1 z Seo & Eisenstein 2003 Huterer & Turner 2001

58 Other standard candles Gamma ray bursts Determine the luminosity through a relation between the collimation corrected energy E γ and the peak energy coalescence of supermassive black holes

59 QuickTime et un décompresseur Codec YUV420 sont requis pour visionner cette image.

60 Inspiral phase Key parameter : chirp mass M (z) = (m 1 m 2 ) 3/5 (m 1 + m 2 ) 1/5 (1+z)

61 Inspiral phase Key parameter : chirp mass M (z) = (m 1 m 2 ) 3/5 (m 1 + m 2 ) 1/5 (1+z) Amplitude of the gravitational wave: frequency f(t) = dφ/2πdt h(t) = M(z) 5/3 f(t) 2/3 d L F (angles) cos Φ(t) Luminosity distance

62 Inspiral phase Key parameter : chirp mass M (z) = (m 1 m 2 ) 3/5 (m 1 + m 2 ) 1/5 (1+z) Amplitude of the gravitational wave: h(t) = M(z) 5/3 f(t) 2/3 d L F (angles) cos Φ(t) Luminosity distance poorly known in the case of LISA θ~ 10 arcmin 1 SNR Hz f GW

63 z = 1, m 1 = 10 5 M, m 2 = M 3 δθ (arcminutes) 5% δd L /d L Holz & Hughes

64 Using the electromagnetic counterpart Allows both a measure of the direction and of the redshift 0.5% δd L /d L Limited by weak gravitational lensing? Holz and Hughes