Frédéric Henry-Couannier

CPPM/RENOIR Marseille

www.darksideofgravity.com

The Dark Side of Gravity and our Universe

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 (strong gravity) !

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. gis not only a pseudoforce but describes a genuine interaction: gravity

1. & 2. &3. & simplicity GR: satisfies by construction the equivalence principle.

GR: a geometric theory ?1. GR equations: atoms&photons interact with g

field gravity affects the measured space and time intervals.

2. ghas the properties of a metric

The Geometrical viewpoint:

1.+2. gis the metric of space-time. The geometrical properties of gtell us about the geometry of space-time (Deformations, Curvature)

Trajectories = geodesics

The non geometrical viewpoint

gis 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 gtype fields (Petit, Linde, Damour…)

3. Introduce non independent gtype fields: Dark Gravity

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

g

g

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 !

( ) ( ) ( )T

g t g t g t

DG equations

T

New equations

RG RGS S Extremum action & eliminate

g

Local gravity

As in Petit theory:

Objects living in the same gravity attract each other Objects living in different gravity reppel each other

2 22 /

2

2 2 3 32 /

00 2 3

( ) 1 2 2

1 4( ) 1 2 2

3

MG rii

MG r

MG M Gg r A e

r r

MG M G M Gg r e

A r r r

DG: RG:

Schwarschild Gravity

4 2 2

2

2

2 2 3 3

00 2 2 3

3( ) 1 1 2

2 2

132( ) 1 2 22

12

ii

MG MG M Gg r

r r r

MGMG M G M Grg rr r rMG

r

Cosmology in DG

CosmologyNo source term (exact compensation) symmetries completely determine the universes global gravity : Spatially flat universesNo Big Bang singularity in conformal cooOne universe is constantly accelerated in

comoving coordinates Negligible expansion rate in early universeOur universe is twice older than in SM

Universe A(t)(dt2-d2)

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 → + ∞- ∞←t

A(t)~e-t

Universe A(t)(dt2-d2)

Magnitude vs redshiftSNA test (SCP 2003)

Fit a(t) t∝

= 1.6±0.3(stat)

OK with constant acceleration

=2

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

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

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

Discontinuities in gravity ?

Discontinuity could have trapped 3.106 solar masses < 0

in twin universe:

mimics a central BH

Conjugate universe void dominates: idem dark

matter HaloMatter dominates r

v

?A star

Conclusion

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

RG vs DGThe metric is the object one must use to raise andlower 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

g

1g g g g g

1g g g g g

g

g g

La symétrie x/t (II)

Si A=i:

Symétrie x/t OK

2 2 2d C dx dt

2 2 21d dx dt

C

2 2 2ˆd C dt dx

2 2 21ˆd dt dx

C

2 2 2 ˆ,d C dx dt g g