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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