Transcript Extended quintessence by cosmic shear

Extended quintessence by cosmic shear
Carlo Schimd
DAPNIA/SPP, CEA Saclay
 LAM Marseille
XXIII Colloquium IAP
July 2007
Beyond LCDM: do we need it?
 JP Uzan’s talk
Cosmological constant 
Copernican principle + GR/Friedmann eqs + {baryons, g, n} + DM
ok w.r.t. CMB + SnIa + LSS + gravitational clustering + Ly-alpha ...
...but dufficult to explain on these basis
1. naturalness pb: rL = WL rcr,0  10-47 GeV4
 rvac @ EW – QCD - Planck
2. coincidence pb: WL  Wm,0
 Alternative :
 Other (effective) “matter” fields violating SEC?
quintessence, K-essence, Chaplygin gas / Dirac-Born-Infeld action, ...

GR : not valid anymore?
f(R) /scalar-tensor theories, higher dimensions (DGP-like,...), TeVeS, ...
 8 GN T = G [ g n ]  G  g n  ?
backreaction of inhomogeneities, local Hubble bubble, LTB, ...

in any case: L has to be replaced by an additional degree of freedom
Beyond LCDM1
Scalar-tensor theories – Extended Quintessence
R
Standard Model
  DM
dynamically equivalent to f(R) theories, provided f’’()  0
e.g. Wands 1994
F() = const : GR
F()  const : scalar-tensor

~ quintessence

space-time variation of G and post-Newtonian parameters gPPN and PPN :
Gcav  const = G* A2 [* ] 1   2 [* ]

modified background evolution: F()  const
distances, linear growth factor:

anisotropy stress-energy tensor:
1 F
  =

F 
   
 ln F
= 2 


2
Aim
 Sanders’s & Jain’s talks
deviations from LCDM by
Local (= Solar-System + Galactic) – cosmic-shear joint analysis
Outline:
 Three runaway models: Gcav, g_PPN, cosmology
 Weak-lensing/cosmic-shear: geometric approach, non-linear regime
 2pt statistics: which survey ? very prelilminary results
 Concluding remarks
3
Three EQ benchmark models
idea: models assuring the attraction mechanism toward GR (Damour & Nordvedt 1993)
and stronger deviation from GR in the past
Non-minimal couplings:
1.
exp coupling in Jordan/string frame
:
2.
generalization of quadratic coupling in JF :
3.
exp coupling in Einstein frame:
F ( ) = exp(  )
(...dilaton)
2

1



F ( ) = exp(  2 ) 
 0
 (* )   ln A(* ) = B exp(  * )
*
4  
+ inverse power-law potential: V (* ) = M *
(runaway dilaton)
Gasperini, Piazza & Veneziano 2001
Bartolo & Pietroni 2001
WL + 2 parameters
F 1 ( ) = A2 (* )
well-defined theory
4
Local constraints: Gcav and gPPN
Cassini :
gPPN-1=(2.12.3)10-4
Gcav
gPPN
ok
 = 10-4,  = 0.1
 = 10-4,  = 0.1
= 10,  = 1
B=0.008
Range of structure formation
cosmic-shear
ok
Cosmology: DA & D+ deviation w.r.t. concordance LCDM
DDA/DA
DD+/D+
 = 10
 = 10-3 b = 510-4
 = 0.1 b = 510-4
 = 0.1 b = 10-3
 = 10-3 b = 0.1
 = 0.1 b = 0.1
 = 0.1 b = 0.2
 = 0.5 B = 510-3
 = 1.0 B = 510-3
 = 1.0 B = 10-2
Remarks:

The interesting redshift range is around 0.1-10, where structure
formation occurs and cosmic shear is mostly sensitive

For the linear growth factor, only the differential variation matters,
because of normalization

Pick
and
for tomography-like exploitation?
6
Weak lensing: geometrical approach
kl, g1l, g2l:
geodesic deviation equation
Sachs, 1962
Solution: gn= gn+ hn  order-by-order
ds 2 = a 2 ( )  (1  2 )d 2  Bi d dx i  ((1  2 )g ij  2 Eij ) dx i dx j 
0th
1st
C.S. & Tereno, 2006
Hyp: K = 0
     Bi k i  Eij k i k j
7
Non-linear regime
EQ  GR
no vector & tensor ptbs
 modified Poisson eq.
allowing for  fluctuations
extended Newtonian limit (N-body):
Perrotta, Matarrese, Pietroni, C.S. 2004

matter fluctuations grow non-linearly, while
EQ fluctuations grow linearly (Klein-Gordon equation)

C.S., Uzan & Riazuelo 2004
matter perturbations: ...
8
Onset of the non-linear regime
Let use a Linear-NonLinear mapping...
NLP (k,z)
m
= f[LPm(k,z)]
e.g. Peacock & Dodds 1996
Smith et al. 2003
 Ansatz: c, bias, c, etc. not so much dependent on cosmology
 at every z we can use it, but...
...normalized to high-z (CMB):
LIN
m
P
D2 ( z ) LIN
(k , z ) = 2
Pm (k , zlss )
D ( zlss )
...and using the correct linear growth factor :

the modes k enter in non-linear regime
( s(k)1 ) at different time

different effective spectral index
3 + n_eff = - d ln s2(R) / d ln R

different effective curvature
C_eff = - d2 ln s2(R) / d ln R2
9
Map2 : which survey? deviation from LCDM
work in progress
JF
EF
z_mean = 0.8, z_max = 0.6
z_mean = 1.0, z_max = 0.6
z_mean = 1.2, z_max = 1.1
 = 10-3  = 510-4
 = 0.1  = 510-4
 = 0.1  = 10-3


 = 0.5 B = 510-3
 = 1.0 B = 510-3
 = 1.0 B = 10-2
To exploit the differential deviation, a wide range of scales should be covered
For a given model, a deep survey globally enhances the relative deviation
Remark: exp 2  exp 
10
“Focused” tomography: deviation from LCDM
work in progress
R=
top-hat var. @ n>(z): z_mean = 1.2, z_max = 1.1
top-hat var. @ n<(z): z_mean = 0.8, z_max = 0.6
 = 10
DDA/DA
DD+/D+
R / R_LCDM
>20%
2%
Concluding remarks

geometric approach to weak-lensing / cosmic shear allows to deal with generic metric
theories of gravity (e.g. GR, scalar-tensor)

three classes of Extended Quintessence theories showing attraction toward GR
 no parameterization, but well-defined theories

including vector and tensor perturbations (GWs) in non-flat RW spacetime

consistent pipeline allowing for joint analysis of high-z (CMB) and low-z (cosmic shear,
Sne, PPN, ...) observables  no stress between datasets

NL regime: adapted L-NL mapping (caveat), but N-body / some perturbation theory /
analytic model (e.g. Halo model) are required

Measuring deviation from LCDM: it seems to be viable if looking over a wide range of
scales, from arcmin to > 2deg ( + mildly non-linear / linear regime)

“Focused” tomography: it seems (too?!) promising

To e done:
1.
Fisher matrix analysis (parameters)  Bayes factor analysis @ Heavens,
Kitching & Verde (2007) (models)
2.
“Focused” tomography: error estimation
3.
Look at CMB, ...
Thank you