1. ERE 2008September 15-19, 20081 Spanish Relativity Meeting 2008, Salamanca, September 15-19 (2008) Avoiding the DARK ENERGY coincidence problem with a COSMIC VECTOR Antonio L. MAROTO and Jose BELTRÁN JIMÉNEZ Universidad Complutense de Madrid Phys. Rev. D 78, 063005 (2008)

2. ERE 2008September 15-19, 20082 The accelerated expansion of the universe d L (z) relation from SN Ia data Supernova Cosmology Project : 42 SNe Ia, z<0.83 High-z Supernova Search Team : 14 SNe Ia, z < 0.62, Hubble Space Telescope (Gold Set): 157 SNe Ia, + 16 with z > 1.25. Deceleration - acceleration transition at z > 0.46  0.13 SNLS 71 SNe Ia z < 1 Reduced systematics (single instrument) 1998 2004 2005 Accelerated Decelerated-accelerated Decelerated

3. ERE 2008September 15-19, 20083 The need for dark energy Friedmann equation Einstein’s equations in flat FRW backgrounds Acceleration requires negative pressure: DARK ENERGY

4. ERE 2008September 15-19, 20084 Dark energy equation of state p DE = w DE  DE Gold Set Flat models (  M +  DE = 1 ) Favors w DE < -1 Gold set SNLS set w DE = const. The need for dark energy

5. ERE 2008September 15-19, 20085 Crossing the phantom divide w DE < -1? Gold Set ODEP: CMB, BAO, growth factor Nesseris, Perivolaropoulos, ‘07 w DE = w DE (z) The need for dark energy

6. ERE 2008September 15-19, 20086 Cosmological constant p   = -   G = (10 19 GeV) -2 G   8  G (T   g  )   ~ (10 - 3 eV) 4 Coincidence problem The dark energy coincidence problem

7. ERE 2008September 15-19, 20087 Quintessence: scaling regime Scaling M has to be fixed in order to get  DE The dark energy coincidence problem

8. ERE 2008September 15-19, 20088 The dark energy coincidence problem Dark Energy models  scalar, f(R),…  require unnatural dimensional parameters in their Lagrangians or initial conditions Our aim is to find a model: without dimensional scales (apart from G), with the same number of parameters as  CDM, with natural initial conditions, with good fits to SNIa data Vector models can do the job ! Why  DE ~  M  today ?

9. ERE 2008September 15-19, 20089 The model G only dimensional scale in the model No free parameters No potential terms (Kiselev, Armendariz, ’04, Boehmer, Harko ’07, Mota, Koivisto `07) Vector-tensor action

10. ERE 2008September 15-19, 200810 The model Equations of motion Flat Robertson-Walker metric

11. ERE 2008September 15-19, 200811 The model Explicit solutions: radiation and matter eras Matter Radiation Scaling during radiation era

12. ERE 2008September 15-19, 200812 Energy densities Matter Radiation Vector dark energy Cosmological constant Final singularity Scaling

13. ERE 2008September 15-19, 200813 Equation of state Radiation Vector field evolution (M P units) W=1/3 W= -0.457 phantom line

14. ERE 2008September 15-19, 200814 Fitting SNe type Ia data Distance modulus Luminosity distance Data sets SNLS (Astier et al. ’06) z<1Gold (Riess et al ’04) z<1.7 157 (previous)+ 16 (HST z>1) = 173 SNe44 (previous)+ 71 (new z<1) = 115 SNe

15. ERE 2008September 15-19, 200815 Fitting SNe type Ia data: VCDM vs.  CDM Gold set

16. ERE 2008September 15-19, 200816 Other parametrizations with the Gold set Lazkoz, Nesseris, Perivolaropoulos, ‘05 VCDM: Vector dark energy: best fit to Gold dataset to date

17. ERE 2008September 15-19, 200817 Initial conditions and the end of the universe Natural initial conditions: Nojiri, Odintsov, Tsujikawa, ‘05 Bouhmadi, González, Martin, ’07 Type III “Big-freeze” singularity “Imminent” final singularity: t end –t 0 = 690 million years (h=0.7) ~ earliest fossils

18. ERE 2008September 15-19, 200818 Stability and local gravity tests PPN parameters Static parameters agree with GR Preferred frame effects Present bounds Classical stability Will, ’81, Nordtvedt Real propagation speed for scalar, vector and tensor perturbations Quantum stability: ghosts?

19. ERE 2008September 15-19, 200819 Conclusions Vector model for dark energy with: No potential terms No dimensional scales (apart from G) No free parameters Standard kinetic terms Excellent fit to Gold dataset and compatible with SNLS: definite predictions for cosmological parameters Scaling behaviour during radiation and natural initial conditions (No coincidence problem) Phantom dark energy today: BAO, CMB?

20. ERE 2008September 15-19, 200820 Evolution of density perturbations Sub-Hubble modes Radiation era Matter era Matter or radiation eras Density contrast (matter and radiation) PRELIMINARY

21. ERE 2008September 15-19, 200821 Evolution of density perturbations Super-Hubble modes Matter and radiation eras Density contrast (matter and radiation) PRELIMINARY