XXIII Colloquium IAP July 2007

Extended quintessence by cosmic shearExtended quintessence by cosmic shear

Carlo Schimd

DAPNIA/SPP, CEA Saclay LAM Marseille

Beyond CDM

Beyond CDM: do we need it?

Copernican principle + GR/Friedmann eqs + {baryons, , } + DM ok w.r.t. CMB + SnIa + LSS + gravitational clustering + Ly-alpha ...

GR : not valid anymore? f(R) /scalar-tensor theories, higher dimensions (DGP-like,...), TeVeS, ...

?

backreaction of inhomogeneities, local Hubble bubble, LTB, ...

Other (effective) “matter” fields violating SEC? quintessence, K-essence, Chaplygin gas / Dirac-Born-Infeld action, ...

1. naturalness pb: cr,0 10-47 GeV4 vac @ EW – QCD - Planck

2. coincidence pb: m,0

8 [ ]NG T G g G g

Alternative :

Cosmological constant

...but dufficult to explain on these basis

in any case: has to be replaced by an additional degree of freedom 1

JP Uzan’s talk JP Uzan’s talk

Scalar-tensor theories – Extended Quintessence

2

DM Standard Model~ quintessenceR

dynamically equivalent to f(R) theories, provided f’’() 0

F(F() = const) = const : GRF(F() ) const const : scalar-tensor

anisotropy stress-energy tensor:

1 F

F

ln2

F

* **2 2[ ] [ ]1AG

modified background evolution: F() const distances, linear growth factor:

e.g. Wands 1994

Gcav const space-time variation of G and post-Newtonian parameters PPN and PPN :

Aim

3

Three runaway models: Gcav, _PPN, cosmology

Weak-lensing/cosmic-shear: geometric approach, non-linear regime

2pt statistics: which survey ? very prelilminary results

Concluding remarks

Local (= Solar-System + Galactic) – cosmic-shear joint analysis

deviations from LCDM by

Outline:

Sanders’s & Jain’s talks Sanders’s & Jain’s talks

Three EQ benchmark models

1. exp coupling in Jordan/string frame :

2. generalization of quadratic coupling in JF :

3. exp coupling in Einstein frame:

Non-minimal couplings:

( ) exp( )F

4* *( )V M + inverse power-law

potential:

Gasperini, Piazza & Veneziano 2001Bartolo & Pietroni 2001

(runaway dilaton)

1 2*( ) ( )F A

idea: models assuring the attraction mechanism toward GR (Damour & Nordvedt 1993) and stronger deviation from GR in the past

(...dilaton)

2( ) exp( )F 20

1

** * *( ) ln ( ) exp( )A B

+ 2 parameters

well-defined theory4

Local constraints: Gcav and PPN

ok ok

Range of structure formationcosmic-shear

Cassini :PPN-1=(2.12.3)10-4

Gcav

PPN

= 10-4, = 0.1

= 10-4, = 0.1

= 10, = 1B=0.008

Cosmology: DA & D+ deviation w.r.t. concordance LCDM

= 10-3 b = 510-4

= 0.1 b = 510-4

= 0.1 b = 10-3

= 10-3 b = 0.1 = 0.1 b = 0.1 = 0.1 b = 0.2

= 0.5 = 510-3

= 1.0 = 510-3

= 1.0 = 10-2

DA/DA

D+/D+

= 10

The interesting redshift range is around 0.1-10, where structure formation occurs and cosmic shear is mostly sensitive

Remarks:

For the linear growth factor, only the differential variation matters, because of normalization

Pick and for tomography-like exploitation? 6

Weak lensing: geometrical approach

geodesic deviation equation

Solution: g= g+ h order-by-order2 2 2( ) (1 2 ) ((1 2 ) 2 )i i

i i jij jds a d d dx x dxB dE

C.S. & Tereno, 2006

0th

1st

Sachs, 1962

Hyp: K = 0 i i ji ijB k E k k

7

8

EQ GR modified Poisson eq. allowing for fluctuations

extended Newtonian limit (N-body):

Perrotta, Matarrese, Pietroni, C.S. 2004

matter perturbations: ...

matter fluctuations grow non-linearly, whileEQ fluctuations grow linearly (Klein-Gordon equation)

C.S., Uzan & Riazuelo 2004

Non-linear regimeno vector & tensor ptbs

Onset of the non-linear regime

Let use a Linear-NonLinear mapping...

NLPm(k,z) = f[LPm(k,z)]e.g. Peacock & Dodds 1996

Smith et al. 2003

Ansatz:Ansatz: c, bias, c, etc. not so much dependent on cosmology at every z we can use it, but...

2

2

( )( , ) ( , )

( )

LIN LINm m lss

lss

D zP k z P k z

D z

...normalized to high-z (CMB):...normalized to high-z (CMB):

...and using the correct linear growth factor :...and using the correct linear growth factor :

the modes k enter in non-linear regime ( (k)1 ) at different time

different effective spectral index3 + n_eff = - d ln (R) / d ln R

different effective curvatureC_eff = - d2 ln (R) / d ln R2

9

Map2 : which survey? deviation from LCDM

Remark: exp2exp

JF EF

= 0.5 = 510-3

= 1.0 = 510-3

= 1.0 = 10-2

z_mean = 0.8, z_max = 0.6z_mean = 1.0, z_max = 0.6z_mean = 1.2, z_max = 1.1

= 10-3 = 510-4

= 0.1 = 510-4

= 0.1 = 10-3

To exploit the differential deviation, a wide range of scales should be coveredFor a given model, a deep survey globally enhances the relative deviation

10

work in progress

= 10

“Focused” tomography: deviation from LCDM

work in progress

2%

DA/DA

D+/D+

>20%

top-hat var. @ n>(z): z_mean = 1.2, z_max = 1.1

top-hat var. @ n<(z): z_mean = 0.8, z_max = 0.6R =

R / R_LCDM

NL regime: adapted L-NL mapping (caveat), but N-body / some perturbation theory / analytic model (e.g. Halo model) are required

consistent pipeline allowing for joint analysis of high-z (CMB) and low-z (cosmic shear, Sne, PPN, ...) observables no stress between datasets

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

Concluding remarks

To e done:1. Fisher matrix analysis (parameters) Bayes factor analysis @ Heavens, Kitching & Verde (2007) (models)2. “Focused” tomography: error estimation3. Look at CMB, ...

Thank you

including vector and tensor perturbations (GWs) in non-flat RW spacetime

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