1. Frédéric Henry-Couannier CPPM/RENOIR Marseille www.darksideofgravity.com The Dark Side of Gravity and our Universe

2. Motivations for alternative theories of gravity Anomalous gravity effects?: Pioneer effect Anisotropies in CMB quadrupôle Cosmology ?=? GR+ Dark matter + Inflation + Dark energy + … ?!?! Local PN gravity tests dont tell us that GR is right in the cosmological domain (strong gravity) !

3. From non gravitational theory to GR 1. Requirement: equations should be invariant under general coordinate transformations 2. Covariantisation program:  new field g  (and derivatives) 3. g  is not only a pseudoforce but describes a genuine interaction: gravity 1. & 2. &3. & simplicity  GR: satisfies by construction the equivalence principle.

4. GR: a geometric theory ? 1. GR equations: atoms&photons interact with g  field  gravity affects the measured space and time intervals. 2. g  has the properties of a metric The Geometrical viewpoint: 1.+2.  g  is the metric of space-time. The geometrical properties of g  tell us about the geometry of space-time (Deformations, Curvature)  Trajectories = geodesics

6. The non geometrical viewpoint g  is just a field, spacetime is a flat and static manifold with true metric  .  many possibilities: 1. Keep GR: the covariant theory of g ,    is not observable (not in the equations!) 2. Multimetric theories : 1. Introduce    in equations: (Rosen) 2. Introduce two or more independent g  type fields (Petit, Linde, Damour…) 3. Introduce non independent g  type fields: Dark Gravity

7. DG: Gravity with its Dark side  DG = bigravity theory: Our side Srandard Model lives in gravity Other side Standard Model lives in gravity  is dark from our side viewpoint But two gravities are not independent  gravity connection between the 2 worlds

8. DG rehabilitates global space-time symmetries Spacetime is flat as in QFT with metric  we recover Global Lorentz-Poincaré invariance  Noether currents Global space-time discrete symmetries DG cosmological solution satisfies  Two universes are conjugate under time reversal !

9. DG equations T New equations Extremum action & eliminate

11. Local gravity As in Petit theory: Objects living in the same gravity attract each other Objects living in different gravity reppel each other

12. DG: RG: Schwarschild Gravity

13. Cosmology in DG

14. Cosmology No source term (exact compensation)  symmetries completely determine the universes global gravity : Spatially flat universes No Big Bang singularity in conformal coo One universe is constantly accelerated in comoving coordinates  Negligible expansion rate in early universe Our universe is twice older than in SM

15. Universe A(t)(dt 2 -d  2 ) GR: Reversing time = Going backward in time Time reversal Dark gravity: Reversing time = Jumping into another universe 1 A(t)~ t -2 A -1 (t) t=0: Big Bang t → + ∞ - ∞ ← t A(t)~e -t Universe A(t)(dt 2 -d  2 )

16. Magnitude vs redshift SNA test (SCP 2003) Fit a(t) ∝ t     = 1.6±0.3(stat) OK with constant acceleration  =2

17. From the CMB to large scale structures Universe expansion rate negligible relative to fluctuations growing rate Baryonic matter only, same density as in SM  Exponentially growing fluctuations early reach the nonlinear regime

18. No need for Dark Matter ? Universe twice older: 26 billion years Oldest galaxies (z=5): 17 billion years Repelling gravity  each galaxy creates a void in conjugate universe equivalent to a Halo

19. Other predictions of DG Longitudinal spin0 gravitational waves Different Schwarzschild solution (different PPN parameters, no BH) Pioneer effect (postdiction) Possibly new frame-dragging effects Gravitational discontinuity effects

20. Discontinuities in gravity ? Discontinuity could have trapped 3.10 6 solar masses < 0 in twin universe:  mimics a central BH Conjugate universe void dominates: idem dark matter Halo Matter dominates r v ? A star

21. Conclusion DG essentials are now well understood DG has one free parameter, no coincidence problem, no epicycles DG has fascinating outlooks and provides an original and promissing framework to compete with the cosmological SM DG needs detailed simulations to see if it can actually compete with (do better than ?) the cosmological SM.

22. RG vs DG The metric is the object one must use to raise and lower indices on any tensor field RG: is the metric  RG is the theory of DG: is the metric  DG is the theory of non independent and

24. La symétrie x/t (II) Si A=i:  Symétrie x/t OK 