The Dark Side of Gravity and our Universe

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

2. Motivations for alternativetheories 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 !

3. From non gravitational theory to GR • Requirement: equations should be invariant under general coordinate transformations • Covariantisation program:  new field gmn (and derivatives) • gmn 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 ? • GR equations: atoms&photons interact with gmn field  gravity affects the measured space and time intervals. • gmn has the properties of a metric The Geometrical viewpoint: 1.+2.  gmn is the metric of space-time. The geometrical properties of gmn tell us about the geometry of space-time (Deformations, Curvature)  Trajectories = geodesics

5. The non geometrical viewpoint gmn is just a field, spacetime is a flat and static manifold with true metric hmn.  many possibilities: • Keep GR: the covariant theory of gmn hmn is not observable (not in the equations!) • « Multimetric » theories : • Introduce two or more independent gmn type fields (Petit, Linde, Damour…) • Introduce hmn in equations: (Rosen) • Introducehmn through gmn  gmn is a Janus field: Respect the symetry between the two faces  Dark Gravity (mimics class 1.)

6. DG: Gravity with its Dark sideDG mimics bigravity theories: Our side Srandard Model lives in gravity Other side Standard Model lives in gravity is dark from our side viewpointTwo gravities are related  anti-gravitational connection between 2 worlds

7. 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 and Lorentz group « bad » representations (negative energies, tachyons…) • DG cosmological solution satisfies  Two faces of our universe are conjugate under time reversal !

8. DG equations T New equations Extremum action & eliminate

9. Global space-time symmetries  freeze degrees of freedom • ‘Isotropic form:’ • Symmetry between space and time (links tachyons to bradions)  2 theories: and Gravity Pioneer effect Cosmology GW

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

11. Schwarschild Gravity DG: RG:

12. Cosmology in DG

13. 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 now constantly accelerated in comoving coordinates  • Negligible expansion rate in early universe • Our universe is twice older than in SM

14. Universe A(t)(dt2-ds2) Time reversal GR: Reversing time = Going backward in time t → + ∞ Universe A(t)(dt2-ds2) Dark gravity: Reversing time = Jumping into hidden face of universe A-1(t) 1 A(t)~e-t A(t)~ t -2 -∞ ← t t → + ∞ t=0: Big Bang

15. Magnitude vs redshiftSNA test (SCP 2003) Fit a(t)∝ta  • = 1.6±0.3(stat) OK with constant acceleration • =2

16. 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

17. 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

18. 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

19. Conclusion • DG is essentially the other option of a binary choice at the level of the conceptual fondations of GR • DG has no coincidence problem, no epicycles • DG is a stable theory with repelling gravity • DG is OK with all local tests of gravity and explains the Pioneer anomaly • DG provides a promissing framework to compete with the cosmological SM but DG needs detailed simulations to see if it can actually compete with (do better than SM?).

20. 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

21. La symétrie x/t • Forme la plus générale de  If , C viole la symétrie x/t 

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

23. Discontinuities in gravity ? Discontinuity could have trapped 3.106 solar masses < 0 in twin universe:  mimics a central BH v Conjugate universe void dominates: idem dark matter Halo Matter dominates r ? A star