Dark Energy as a Violation of the Equivalence Principle

1. Dark Energy as a Violation of the Equivalence Principle How much dark energy weights? A. Füzfa and J.-M. Alimi LUTh – Observatoire de Paris A. Füzfa, J.-M. Alimi, Phys. Rev. D 73, 023520 (2006) A. Füzfa, J.-M. Alimi, under preparation

2. Evidences in favour of dark energy • Angular size of CMB anisotropies (WMAP): • Large-scale structures properties (baryon acoustic oscillation, galaxy counts, peculiar velocities, …) : Wm~0.3 What is the missing Dark Energy (DE)? (WX~0.7) • Effect on cosmic expansion : Hubble diagram of type Ia supernovae Wmh² Wbh² Fluctuations (C2l) WTOT~1.01 Wm~0.3 WTOTh² Angular size (°)

3. What is the effect of dark energy? • Hubble diagram of type Ia supernovae • Type Ia Supernovae appear fainter than expected: • Cosmic expansion has recently accelerated or (and?) • Supernovae are not standard candles at that time SNLS First year data set (2006) Old «  standard » cosmology WTOT=Wm=1 Distance moduli Baryons~5% Cold Dark Matter~25% Dark Energy~70% Radiations~0.01% Redshift The « concordance » model : Dark energy is a positive cosmological constant L

4. The cosmological constant problems • Cosmic acceleration : vacuum has non-vanishing energy • L=0 : space expands  less gravitational energy  less expansion • L>0 : space expands  more vacuum energy  more expansion • Quantum Theory : vacuum has a huge energy (uncertainty on ground state) • Observations: • Why is the cosmological constant that small? • Why is vacuum energy of the order of the critical energy today? (is it really constant?) Violation of the strong energy condition Total vacuum energy density: Fine-tuning problem! Coincidence problem!

5. Is dark energy (DE) a gravitational rebel? • The equivalence principle: • What if dark energy ALONE violates the equivalence principle? • Cosmic expansion is no more ruled by Friedmann laws in recent times • Fundamental constants vary (GN, gauge coupling constants, …) • Impacts on cosmology: All energies (including gravitational ones) are equivalent for producing gravitation Why should gravitation couple universally to any kind of matter? • OK if DE is a late process • Modification of luminous distance and GN • This DE should be TRANSIENT • Too few DE on small scales • Early universe (CMB, BBN) • Luminosity curves of SNe Ia • Precision tests of General Relativity • Observed Universality of free fall

6. Cosmology without equivalence principle • Tensor-scalar theories of gravitation (Dicke, Brans, Fierz, Jordan) (universal coupling => Weak equivalence principle) Cosmological dynamics Post-Newtonian Constraints General Relativity (GR)

7. Cosmology with non-equivalent dark energy • Cosmic soup : ordinary matter (baryons, photons, ...) ruled by the weak equivalence principle + dark energy sector violating the equivalence • The universal coupling to matter Amatter(j) defines the observable metric • Violation of the weak equivalence principle: • Competitive cosmological dynamics Attraction toward general relativity Repulsion term

8. Which candidate for non-equivalent DE? • DE is a late process: pDE<pmatter~0 • Transient mechanism : phase transition to positive pressures • no need anymore to violate the strong energy condition p<-r/3 • Ideal candidate : newgauge interaction of Born-Infeld type (renormalisation of point-like singularities, string theory, …) Low-energy limit: Yang-Mills dynamics (radiation) High-energy limit: Vacuum polarization (Nambu-Goto string gas) Phase transition

9. Illustration of the mechanism • Matter-dominated era : attraction toward GR • Born-Infeld gauge field domination: repulsion from GR • Phase transition of the BI gauge interaction into radiation and attraction toward GR Variation of G 2) Energy Density 1) 3) 2) 1) 3) 2) 3) Acceleration factor

10. The proof of the pudding :adequation to SNLS 1st year data LCDM : c2 /dof=1.03 NEBI: c2 /dof=1.09 Data from P. Astier et al., A & A. 447 (2006) Combined effect of varying GN and cosmic acceleration!

11. The proof of the pudding :adequation to SNLS 1st year data Dark Energy dominated Universe (as suggested by CMB, LSS) Constraints on General Relativity OK! The repulsing action of non-equivalent dark energy is not active today because of its radiative nature! (BI feature)

12. Conclusion : Is the violation of the equivalence principle a solution to the cosmological constant problems? L • A completely new picture of dark energy : • Dark Energy does not « fall » in the same way as ordinary matter • Deviation from GR during dark energy domination followed by a return to GR provided by ordinary matter • Good adequacy with Hubble diagrams (cosmic acceleration and variation of GN), constraints on GR and physics in the radiative era • Born-Infeld gauge interaction is an ideal candidate for non-equivalent dark energy (late domination, quicker decoupling, no violation of the energy condition) • Perspectives: • Post-recombination effect on CMB, effects on structure formation (GN(z)) • Search for similar mechanisms for inflation and lightness of vacuum energy