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D ark energy

D ark energy. P. Binétruy AstroParticule et Cosmologie, Paris. UniverseNet, Barcelona, 28-29 September 2009. Context : th e twentieth century legacy. The observational case. Some conventional explanations. More dynamics: why scalar fi elds ?. Modification of gravity.

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D ark energy

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  1. Dark energy P. Binétruy AstroParticule et Cosmologie, Paris UniverseNet, Barcelona, 28-29 September 2009

  2. Context : th e twentieth century legacy The observational case Some conventional explanations More dynamics: why scalar fi elds ? Modification of gravity More about the couplings of dark energy Future observations Back to the cosmological constant

  3. Context : th e twentieth century legacy

  4. 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 - (R/2) g = 8GN T geometry matter

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

  6. Difficult to reconcile general relativity with the quantum theory • Three possible manifestations: • vacuum energy • equivalence principle : mi = mg • extra spatial dimensions (Kaluza-Klein, string theory)

  7. Vacuum energy: Classically, the energy of the fundamental state (vacuum) is not measurable. Only differences of energy are (e.g. Casimir effect). Einstein equations: R - R g/2 = 8G T geometry energy Hence geometry may provide a way to measure absolute energies i.e. vacuum energy: R - R g/2 = 8G T + 8G < T > vacuum energy similar to the cosmological term introduced by Einstein : R - R g/2 = 8G T +  g

  8. . H = a/a Einstein equations  Friedmann equation c = 1 H2 = ( 8 G  + ) /3 - k/a2 c = 3 H02 / 8 G   l-2  =  / 8 G    / c = (H0-1 / l)2 / 3 ~ 0.7  l ~ H0-1 ~ 1026 m A very natural value for an astrophysicist !

  9. Introduce h Planck length lP = 8GNh/c3 = 8.1x10-35m

  10. . H = a/a Einstein equations  Friedmann equation c = 1 H2 = ( 8 G  + ) /3 - k/a2 c = 3 H02 / 8 G   l-2  =  / 8 G    / c = (H0-1 / l)2 / 3 ~ 0.7  l ~ H0-1 ~ 1026 m A very natural value for an astrophysicist ! A very unnatural value for a Universe which presumably started in a quantum state!

  11. UV cut-off IR cut-off Cosmological constant problem : where the two ends meet

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

  13. Cosmic coincidence problem: Why does the vacuum energy starts to dominate at a time t (z ~ 1) which almost coincides with the epoch tG of galaxy formation (zG ~ 3)?

  14. Vacuum energy and global supersymmetry 1 H = ___  Qr2 r 4 < 0 | H | 0 > = 0  Qr | 0 > = 0 for all r Hence supersymmetry is the space time symmetry connected with the vacuum energy. But supersymmetry breaking scale is in the TeV range, not in the 10-3 eVrange!

  15. Are there more general ways than a cosmological constant to account for the acceleration of the expansion? Dark energy Einstein equations: R - R g/2 = 8G T geometry matter-energy modify gravity add new effects or a new form of energy Friedmann equation : H2 = 8 G  /3 - k/a2 new contributions to the Friedmann equation modified Friedmann equation

  16. The observational case

  17. Les pantoufles Samuel Van Hoogstraten 1654-1662 Musée du Louvre

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

  19. Distant supernovae appear less bright than in an expanding universe  accelerated expansion

  20. mB = 5 log(H0dL) + M - 5 log H0 + 25 1-q0 luminosity distance dL = lH0 z ( 1 + ------- z + …) 2 q0 deceleration parameter .. . q0 = - a a / a2

  21. Could this be explained by a cosmological constant ? Plot ( , M) :  =/c , M=M/c Concordance model Note: if this is so, the vacuum energy takes the value expected in the context of gravity. Associated energy scale : ~10-3 eV

  22. The energetic budget of the Universe

  23. Dark energy Assume the existence of a new component assmilated to a perfect fluid with pressure p and energy density  : equation of state p = w  Note: vacuum energy has w=-1 Friedmann equation at late epochs : H2 = H02 [  m (1+z)3 + DE(1+z)3(1+w) DE ~ 1- m In the case of z dependent w, w in previous formula is some averaged value

  24. .. Acceleration of the expansion : 3 a / a = - 4G (+3p) /3 Then redshift at beginning of acceleration : 1 + zacc = [(3 w(zacc) + 1)(m -1)/ m]-1/3w astro-ph/0610574

  25. WDE(z)

  26. WMAP

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

  28. WMAP Large scale structure surveys : • 2dF : completed • (250 000 galaxies) • Sloan Digital Sky Survey (SDSS) : on-going • (goal: 1 000 000 galaxies) • 2nd data release: 3324 sq. deg. imaging • 2627 sq. deg. spectroscopy with 260 490 galaxies • 32 241 quasars (z < 2.3) • 3 791 quasars (z > 2.3)

  29. 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. CDM Blanchard, Douspis, Rowan-Robinson, Sarkar 2005

  30. 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. CDM M = 0.88, v=0.12, H0 = 46 SNe ignored. cannot accommodate =0 with baryon acoustic peak. Blanchard et al 2003 Blanchard, Douspis, Rowan-Robinson, Sarkar 2005

  31. Confidence Contours Tot=1 w=-1 BAO: Baryon Acoustic Oscillations (Eisenstein et al 2005, SDSS) 68.3, 95.5 et 99.7% CL

  32. Some conventional explanations to the acceleration observed : our inhomogeneous universe

  33. Our Universe is only homogeneous in its largest scales Proof: success of the standard model which assumes a Robertson- Walker metric (homogeneity and isotropy built in) But otherwise the Universe is claearly inhomogeneous. What is the effect of inhomogeneities?

  34. Quantities averaged over a domain D obey a modified Friedmann equation (aD volume scale factor) T. Buchert, 1999 . aD2 3 ___ = 8GN  - <(3)R> /2 - Q /2 2 aD2 Q  __ (<2>-< >2)- <> .. 3 aD 3 ___ = - 4GN  + Q aD expansion rate back reaction shear large enough back reaction Q can lead to acceleration of the expansion But how can this effect become leading?

  35. Other possibility: our observations are prejudiced because we leave in a local inhomogenity We may live in a « void » of size of a few Gpc Geometry described locally by a Lemaître-Tolman-Bondi Universe which is isotropic but non-homogeneous Leads to a dimming of the distant supernovae Constraint from CMB dipole: we must be close to the centre of the void.

  36. J. Garcia-Bellido and T. Haugboelle, 0810.4939 [astro-ph] SnIa BAO CMB 1, 2 and 3  contours in (out = 1) H0 in km.s-1.Mpc-1 See also K. Enqvist, M. Mattsson and G. Rigopoulos, 0907.4003 [astro-ph.CO]

  37. More dynamics: why scalar fi elds ?

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

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

  40. Why scalar fields to model dark energy? Scalar fields easily provide a diffuse background Speed of sound cs2 = (p / )adiabatic In most models, cs2 ~ 1, i.e. the pressure of the scalar field resists gravitational clustering : scalar field dark energy does not cluster

  41. First example (quintessence) =(mPV’/V)2 /2«1 V  mP . 2/2- V() > -1 w = p/ = . 2/2+ V()

  42. Exponential potential e.g. gaugino condensation <> ~ MS3 exp(-3/2bg02) ~ exp(-3S/2b) V ~ |< >|2 ~ exp(-3S/b) V S

  43. Ratra-Peebles potential: V() = M4+/ May be obtained in the context of SUSY QCD PB,… SU(Nc) with Nf<Nc flavours (quarks Qi and antiquarks Qi) At scale , formation of condensates ij = Qi Qj Effective theory: W = (Nc - Nf) 3(Nc-Nf)/(Nc-Nf) (Det )1/(Nc-Nf) w = -1 + (1+wB)(Nc+Nf)/2Nc

  44. Since the region of interest is at  > MP, supergravity corrections must be taken into account . Brax, Martin The simplest model yields a potential: V = M4+  - exp(2/MP2) This potential has a minimum and thus gives an equation of state parameter w closer to -1.

  45. The problems of scalar field models of dark energy Example of quintessence :  has to be very light : m ~ H0~ 10-33 eV V =(mPV’/V)2 /2«1  mP  pseudo-Golstone boson?

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