Transcript Document 7618554

The Dark Side of
Gravity and our
Universe
Frédéric Henry-Couannier
CPPM/RENOIR Marseille
www.darksideofgravity.com
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 !
From non gravitational
theory to GR
1.
Requirement: equations should be invariant
under general coordinate transformations
2.
Covariantisation program:  new field gmn (and
derivatives)
3.
gmn is 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.
2.
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
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!)
1.
2.
« Multimetric » theories :
1.
2.
3.
Introduce two or more independent gmn type fields (Petit, Linde,
Damour…)
Introduce hmn in equations: (Rosen)
Introduce hmn through gmn  gmn is 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 g mn
Other side Standard Model lives in
gravity g mn
is dark from our side viewpoint
Two gravities are related
 anti-gravitational connection
between 2 worlds
DG rehabilitates global
space-time symmetries
Spacetime is flat as in QFT with metric


h
 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
T
g mn (t )g mn (t )  g mn (t )
 Two faces of our universe are conjugate under time
reversal !
DG equations
T
SRG  SRG
Extremum action
& eliminate
g mn
New equations
Global space-time
symmetries  freeze
degrees of freedom
‘Isotropic form:’
g mn
B





 B 1



A
, g  
mn


A


A

A1
A1

 1





1
 ,h  

mn



1



1
A1 

Symmetry between space and time (links tachyons to
bradions)
 2 theories:
B  1/ A
and
B  A
Gravity
Cosmology
Pioneer effect
GW
Local gravity
As in Petit theory:


Objects living in the same gravity attract each other
Objects living in different gravity reppel each other
Schwarschild Gravity
DG:
RG:
4
MG 3 M 2G 2
 MG 
gii (r )  1 

  1 2
2r 
r
2 r2

MG
M 2G 2
gii (r )  A  e
 1 2
2 2
2
MG


r
r
1 

2 2
3 3
MG
M 2G 2 3 M 3G 3
2r 
1 2 MG / r
MG
M G 4 M G g (r )  
 1 2
2 2 
00
2
 g00 (r )   e
 1 2
2 2 
3
r
r
2 r3
 MG 
A
r
r
3 r
1 

2r 

2 MG / r
Cosmology in DG
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

Universe
A(t)(dt2-ds2)
GR:
Time reversal
Reversing time
=
Going backward in time
t+
Universe
A(t)(dt2-ds2) A-1(t)
Dark gravity:
Reversing time
=
1 A(t)~e-t
-
t
A(t)~ t -2
t=0: Big Bang
Jumping into hidden
face of universe
t+
Magnitude vs redshift
SNA test (SCP 2003)
Fit a(t)∝ta

a= 1.6±0.3(stat)
OK with constant
acceleration
a=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 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?).
RG vs DG
The metric is the object one must use to raise and
lower indices on any tensor field
1
mn
m ns


g

g

g
g g s
g
RG: mn is the metric   mn 
RG is the theory of
g mn
DG: h mn is the metric 
 g mn 
1
 g mn  h mhns g s  g mn  h mhns g s
DG is the theory of non independent
g mn and g mn
La symétrie x/t
Forme la plus générale de
g mn
1


d 2  C  Adx 2  dt 2 
A 

d 2 
1 1 2
2
dx

Adt

C  A
 If A  i , C viole la symétrie x/t

1 2
d  Adx  dt
A
2
2
La symétrie x/t (II)
Si A=i:
d 2  C  dx 2  dt 2 
dˆ 2  C  dt 2  dx 2 
1
d   dx 2  dt 2 
C
1
dˆ 2  dt 2  dx 2 
C
2
 Symétrie x/t OK

2
2

d  C  dx  dt  , gˆ mn   g mn
2
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
r
matter Halo
dominates
?
A star