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 !

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 two or more independent gtype fields (Petit, Linde,

Damour…)

2. Introduce in equations: (Rosen)

3. Introducethrough g gis a Janus field: Respect the symetry between the two faces Dark Gravity (mimics

class 1.)

DG: Gravity with its Dark side

DG mimics bigravity theories: Our side Srandard Model lives in

gravity Other side Standard Model lives in

gravity is dark from our side viewpoint

Two gravities are related

anti-gravitational connection between 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 and Lorentz group

« bad » representations (negative energies, tachyons…)

DG cosmological solution satisfies

Two faces of our universe are conjugate under time reversal !

( ) ( ) ( )T

g t g t g t

DG equations

T

New equations

RG RGS S Extremum action

& eliminate

g

Global space-time symmetries freeze degrees of freedom

‘Isotropic form:’

Symmetry between space and time (links tachyons to bradions) 2 theories:

and

B A1/B A

1

1

1

1

1

1, ,

1

1

B B

A Ag g

A A

A A

Cosmology

GW

Gravity

Pioneer effect

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 now 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 hidden face of 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

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 epicyclesDG is a stable theory with repelling gravity DG is OK with all local tests of gravity and explains the Pioneer anomalyDG 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?).

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

Forme la plus générale de

If , C viole la symétrie x/t

2 2 21d C Adx dt

A

2 2 21 1d dx Adt

C A

2 2 21 d Adx dt

A

A i

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

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