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Extended quintessence by cosmic shear

Carlo Schimd

DAPNIA/SPP, CEA Saclay

LAM Marseille

XXIII Colloquium IAP July 2007

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

Beyond LCDM: do we need it?

JP Uzan’s talk

Dark energy H(z) - Hr+m+GR(z)

Cosmological constant

Copernican principle + GR/Friedmann eqs + {baryons, g, n} + DM

ok w.r.t. CMB + SnIa + LSS + gravitational clustering + Ly-alpha ...

( 106 GeV4 )EWor ( 10-3 GeV4 )QCDor ( 1076 GeV4 )Planck

...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, ...

?

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

Beyond LCDM

1

Scalar-tensor theories – Extended Quintessence

~ quintessence

Standard Model

F(j) = const: GR

F(j) const: scalar-tensor

hyp:

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

e.g. Wands 1994

space-time variation of G and post-Newtonian parameters gPPN and bPPN :

Gcav const

modified background evolution:F(j) const

distances, linear growth factor:

anisotropy stress-energy tensor:

2

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

idea: models assuring the attraction mechanism toward GR (Damour & Nordvedt 1993)

and stronger deviation from GR in the past

Non-minimal couplings:

- exp coupling in Jordan/string frame :
- generalization of quadratic coupling in JF :
- exp coupling in Einstein frame:

(...dilaton)

(runaway dilaton)

Gasperini, Piazza & Veneziano 2001

Bartolo & Pietroni 2001

+ inverse power-law potential:

WL + 2 parameters

well-defined theory

4

Local constraints: Gcav and gPPN

Cassini :

gPPN-1=(2.12.3)10-4

Gcav

gPPN

ok

- = 10, a = 1

B=0.008

ok

x = 10-4,a = 0.1

Range of structure formation

cosmic-shear

x = 10-4,a = 0.1

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

DDA/DA

DD+/D+

b = 10

- = 10-3 b = 510-4
- = 0.1 b = 510-4
- = 0.1 b = 10-3

- = 0.5 B = 510-3
- = 1.0 B = 510-3
- = 1.0 B = 10-2

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

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

1st

C.S. & Tereno, 2006

Weak lensing: geometrical approach

k(l), g1(l), g2(l):

geodesic deviation equation

Sachs, 1962

Solution: gmn= gmn+ hmn order-by-order

Hyp: K = 0

7

hor

...gauge pb

Non-linear regime

no vector & tensor ptbs

- modified Poisson eq.

allowing for j fluctuations

EQ GR

extended Newtonian limit (N-body):

x: F x

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

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

late growth

a

LCDM

...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

WQ = Wm -1

different effective curvature

C_eff = - d2 ln s2(R) / d ln R2

Onset of the non-linear regime

Let use a Linear-NonLinear mapping...

e.g. Peacock & Dodds 1996

Smith et al. 2003

NLPm(k,z) = f[LPm(k,z)]

- Ansatz:dc, bias, c, etc. not so much dependent on cosmology

at every z we can use it, but...

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

- = 10-3x = 510-4
- = 0.1 x = 510-4
- = 0.1 x = 10-3

- = 0.5 B = 510-3
- = 1.0 B = 510-3
- = 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(x j2) exp(x j)

10

DDA/DA

DD+/D+

“Focused” tomography: deviation from LCDM

work in progress

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

R =

R / R_LCDM

>20%

2%

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

astro-ph/0611xxx

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:

Fisher matrix analysis (parameters) Bayes factor analysis @ Heavens,

Kitching & Verde (2007) (models)

“Focused” tomography: error estimation

Look at CMB, ...

Thank you

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