light bending as a probe for geometric dark energy
DESCRIPTION
EDEN in Paris: 7th-9th December 2005, LPNHE, Paris France. Light Bending as a probe for Geometric Dark Energy. Alessandro Gruppuso (INAF/IASF, Bologna) In collaboration with Fabio Finelli & Matteo Galaverni (INAF/IASF, Bologna). Introduction - PowerPoint PPT PresentationTRANSCRIPT
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Light Bending
as a probe for
Geometric Dark Energy
Alessandro Gruppuso (INAF/IASF, Bologna)
In collaboration with
Fabio Finelli & Matteo Galaverni (INAF/IASF, Bologna)
EDEN in Paris: 7th-9th December 2005, LPNHE, Paris France
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Plan of the Talk
• Introduction• Light Bending as a preferred general relativistic
test to distinguish between a Cosmological Constant and other Dark Energy models
• Focus on Geometric Dark Energy models• Analytic Results• Applications to Astrophysical sets-up• Conclusions
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Introduction
• Supernova and WMAP observations provide clear evidence that the CDM model is not suitable to describe our universe.
• A Cosmological Term Λ is the simplest explanation for the mismatch between theory and observation
• But its value is completely at odd with naive estimate of the vacuum energy of quantum fluctuations! (fine-tuning!)
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
• 2nd way: modify LHS i.e. changing the Einstein Tensor (DGP model, Weyl Gravity,…)
Introduction
• Are there alternatives to Λ? Or otherwise stated: How modify Einstein Equations in order to be compatible with observations?
• 1st way: modify RHS i.e. considering an additional field such that p/ρ < -1/3 (quintessence models,…)
Dynamical Dark Energy models
Geometric Dark Energy models
GTRgR 82
1
)(82
1 TTGRgR
GTgfRgR 8)(2
1
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Introduction
Up to now observational data have not been able to discriminate between ΛCDM model and other Dark Energy models (both geometric and dynamical)
The aim of this talk is to analyze DE effects at astrophysical level (for systems that are decoupled from the cosmological expansion)
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Introduction
Light Bending!
The importance of DE effects in Astrophysical tests is already known. In particular the perihelion precession of Mars in DGP model is found to be close to the sensitivity
of the next experiments.
Dvali, Gruzinov & Zaldarriaga PRD (2003)
Lue & Strakman PRD (2003)
Lue astro-ph/0510068 (2005)
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Light Bending
0r
)(r
observer sourcemass
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Light Bending
Why is it preferred among general relativistic tests? 22222 )()( drdrrAdtrBds
21
3
21)()( r
r
GMrArB
Schwarzschild solution
in presence of
S
r
r
rrrBrrrB
dr
r
rBrAS
01
21200
2sin2
)()(
)()(2
0
S
r
r
rrrBrrrB
dr
r
S
01
21200
2sin2
)()(
12
0
drops out!!!
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Light Bending
2
00, 2
8
1524
r
GM
r
GM
does not deflect light!!!
In agreement with Islam PLA (1983)
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Focus on Geometric DE models
Consider a metric of the following form
rr
GMrB 2
21)( r
r
GMrA 1
1 21)(
22222 )()( drdrrAdtrBds
A solution of this kind come from gDE
2/1 and2
21 /2/ crGM DGP model Dvali, Gabadadze & Porrati PLB (2000)
In DGP theory there is a maximum scale (Vainshtein scale)
1 andNr/121 Weyl gravity
Mannheim & Kazanas ApJ (1989)
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Focus on Geometric DE models
CSrr Therefore at scalesmuch smaller than cosmological ones,
there are some deviation from Schwarzschild results
(Cluster of Galaxies!)
2CSr Cosmological Scale
112/2 GMr Critical Scale
A parametrization of this kind introduces two scales
In DGP model this coincides with Vainshtein radius.
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
DESCHWII
SCHWI )()(
S
SCHWI
r
r
r
GM 0
0
)( 14
S
SCHWII
r
r
r
GM 0
2
0
)( 28
152
2/120
02210
1
1
rr
rrIr
S
SDE
2
012
1
0
,22
3,
22
1,
2
1
1
1
)2/1(
2/2/1
2 S
S
r
rF
r
rI
Analityc Results
F.Finelli, M.Galaverni & A.G. (2005)
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
DGP model
2/120
02210
1
1
rr
rrIr
S
SDE
2/120
2/10
22/1
0
1
10
rr
rrr
S
SDE
This is why the deflection of light in this model is not rigorously vanishing!
3/1
CCV r
GMrr
Cr is the crossover scale between 4D and 5D behaviour
In contrast with Lue & Starkman PRD (2003)
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
DGP model
• Since has to be positive in order to describe at cosmological level the recent acceleration of the universe, then the sign
of is positive.
gr
rr
rrr
S
SDE
2/1022/12
0
2/102/1
02
1
1
2
2
DE
g
0/ rrS
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
DGP model
• In which astrophysical system the contribution is the largest?
• Since (and is constrained by cosmology to be of the order of 5 Gpc) we found that it is the largest for Cluster of galaxies.
2/12
0
2/102/1
02
1
1
rr
rrr
S
SDE
2
22 2 CrGM
DE
Cr
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
DGP model
For a Cluster we find
with ( , , ) .
• analytic expression is checked to be good at 0.03%
•
•
2/12
0
2/102/1
02
1
1
rr
rrr
S
SDE
2
%4.0/ SCHWDE
GpcrC 5 Mpcr 10 MpcrS 10
)(210 IISCHWDE
SV rr
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
DGP model
Total = Schw1 + Schw2 + DE
1st order Schwarzschild
1st + 2nd order Schwarzschild
0/ rMG
0/ rMG
Total = Schw1 + Schw2 + DE
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Weyl gravity
2/120
02210
1
1
rr
rrIr
S
SDE
gr
rr
rrr
S
SDE 202/12
0
020
1
10
when is much larger than 1 0/ rrS 0rDE
0/ rrS
g
Edery and Paranjape PRD (1998)
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Weyl gravity
• can be positive or negative depending on the sign of .
• As in DGP case the contribution is the largest for the largest astrophysical system (i.e.: cluster of galaxies)
2/12
0
00
1
1
rr
rrr
S
SDE
DE
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Weyl gravity
For a cluster we find
With ( , )
2/12
0
00
1
1
rr
rrr
S
SDE
%74/ SCHWDE
Mpcr 10 GpcrN 101 )(410 II
SCHWDE •
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Weyl gravity
0/ rMG
0/ rMG
1st order Schwarzschild
1st + 2nd order Schwarzschild
GpcrN 1
GpcrN 5
Total = Schw1 + Schw2 + DE
Total = Schw1 + Schw2 + DE
Total = Schw1 + Schw2 + DE
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Conclusions
• Light Bending is studied in a static spherically symmetric space time non asymptotically flat ( ). These terms cannot be parametrized in the usual PPN approach!
• This kind of solution is justified in the context of gDE models but it might be that also dDE models are included in the parametrized metric
• Since Λ does not deflect light, it is a preferred test for the study of DE models in astrophysical context
r
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
ConclusionsConclusions
• In both cases the DE contribution to light deflection is much greater than Schw one at higher orders
• In both cases the main deviation from Λ is given by Cluster of Galaxies.
• In DGP model we have a small effect with respect to Weyl gravity for two reasons 1) The coefficient is smaller and 2) the geometric factor is smaller.
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
DGP model
Cr
sun
gal
g.gal
cluster
tot )( ISCHW DE)( II
SCHW
5109.5 5109.5 9107.1 0
6109.1 6109.1 12108.1 10100.4
5107.1 5107.1 10106.1 8103.2
5105.6 5105.6 9103.3 7106.8
Light Bending as a probe of Geometric Dark Energy models EDEN, Paris December 8,2005
Weyl gravity
Cr
sun
gal
g.gal
cluster
tot )( ISCHW DE)( II
SCHW
5109.5 5109.5 9107.1 19106.6
6109.3 6109.3 12108.1 6100.2
5109.3 5109.3 10108.1 5100.2
4109.4 5108.9 9107.4 4100.4