Dark Energy as a Violation of the Equivalence Principle
How much dark energy weights?
A. Füzfa and J.-M. Alimi
LUTh – Observatoire de Paris
A. Füzfa, J.-M. Alimi, Phys. Rev. D 73, 023520 (2006)
A. Füzfa, J.-M. Alimi, under preparation
Angular size of CMB anisotropies (WMAP):
Large-scale structures properties (baryon acoustic oscillation, galaxy counts, peculiar velocities, …) : m~0.3
What is the missing Dark Energy (DE)?
(X~0.7)
Effect on cosmic expansion : Hubble diagram of type Ia supernovae
Evidences in favour of dark energy
TOTh²
Flu
ctua
tions
(C
2l)
Angular size (°)
mh²
bh²
TOT~1.01m~0.3
Hubble diagram of type Ia supernovae
Type Ia Supernovae appear fainter than expected: Cosmic expansion has recently accelerated
or (and?) Supernovae are not standard candles at that time
What is the effect of dark energy?D
ista
nce
mod
uli
Old « standard » cosmology TOT=m=1
Redshift
SNLS First year data set (2006)
Baryons~5%
Cold Dark Matter~25%
Radiations~0.01%
Dark Energy~70%
The « concordance » model :Dark energy is a positive cosmological constant
The cosmological constant problems
Cosmic acceleration : vacuum has non-vanishing energy =0 : space expands less gravitational energy less expansion >0 : space expands more vacuum energy more expansion
Quantum Theory : vacuum has a huge energy (uncertainty on ground state)
Observations:
Why is the cosmological constant that small?
Why is vacuum energy of the order of the critical energy today?
(is it really constant?)
pa
a3
2
p4764 10 GeVmPlth Total vacuum energy density:
Fine-tuning problem!
4470, 10 GeVc
obs
Coincidence problem!
3 if 0
pa Violation of the
strong energy condition
Is dark energy (DE) a gravitational rebel?
The equivalence principle:
What if dark energy ALONE violates the equivalence principle? Cosmic expansion is no more ruled by Friedmann laws in recent times Fundamental constants vary (GN, gauge coupling constants, …)
Impacts on cosmology:
All energies (including gravitational ones)
are equivalent for producing gravitation
Early universe (CMB, BBN) Luminosity curves of SNe Ia
Precision tests of General Relativity Observed Universality of free fall
OK if DE is a late process Modification of luminous
distance and GN
This DE should be TRANSIENT Too few DE on small scales
Why should gravitation couple universally to any kind of matter?
Cosmology without equivalence principle Tensor-scalar theories of gravitation (Dicke, Brans, Fierz, Jordan)
(universal coupling => Weak equivalence principle)
gASRgxdS mattermmatter24 , 2
2
1
031'1'''²3
2
m
pp
d
Ad
ap
mm
log and
)log(with
Cosmological
dynamics
Post-NewtonianConstraints
V
112
520
10
10
yrG
G
General Relativity(GR)
Cosmology with non-equivalent dark energy
Cosmic soup : ordinary matter (baryons, photons, ...) ruled by the weak equivalence principle + dark energy sector violating the equivalence
The universal coupling to matter Amatter() defines the observable metric
Violation of the weak equivalence principle:
Competitive cosmological dynamics
gAS
gASRgxdS
DEDEDE
mattermmatter
2
24
,
, 22
1
gAg m2~ taAta m ~~
DEmatter AA
tda
adtH ~~
~~~ 2~
~~~~a
aatq
02
32
3 mmDEDEDE pH
Repulsion term Attraction toward general relativity
Which candidate for non-equivalent DE? DE is a late process: pDE<pmatter~0
Transient mechanism : phase transition to positive pressures no need anymore to violate the strong energy condition p<-/3 Ideal candidate : new gauge interaction of Born-Infeld type
(renormalisation of point-like singularities, string theory, …)
1
~
16
1
2
11
2
84
4
FFFF
cc
cBIL
Low-energy limit:Yang-Mills dynamics
(radiation)High-energy limit:Vacuum polarization
(Nambu-Goto string gas)
4cBI
4cBI
4cBI
Phase transition2 aBI
3 aBI
4 aBI
Illustration of the mechanism1) Matter-dominated era : attraction toward GR
2) Born-Infeld gauge field domination: repulsion from GR3) Phase transition of the BI gauge interaction into radiation and attraction toward GR
1)
2)
3)
2)
3)
1)
2) 3)
Energy Density
Variation of G
Acceleration factor
The proof of the pudding :adequation to SNLS 1st year data
CDM : /dof=NEBI: dof
Combined effect of varying GN and cosmic
acceleration!
Data from P. Astier et al., A & A. 447 (2006)
The proof of the pudding :adequation to SNLS 1st year data
Dark Energy dominated Universe(as suggested by CMB, LSS)
Constraints on General Relativity OK!
The repulsing action of non-equivalent dark energy is not active today because of its radiative nature! (BI feature)
Conclusion : Is the violation of the equivalence principle a solution to
the cosmological constant problems? A completely new picture of dark energy :
Dark Energy does not « fall » in the same way as ordinary matter Deviation from GR during dark energy domination followed by a return to GR
provided by ordinary matter Good adequacy with Hubble diagrams (cosmic acceleration and variation of GN),
constraints on GR and physics in the radiative era Born-Infeld gauge interaction is an ideal candidate for non-equivalent dark
energy (late domination, quicker decoupling, no violation of the energy condition)
Perspectives: Post-recombination effect on CMB, effects on structure formation (GN(z)) Search for similar mechanisms for inflation and lightness of vacuum energy
4Pl
th m
447
0, 10 GeVc