Integrated Sachs-Wolfe Effect

&Dark Energy

Tommaso Giannantonio

ICG, University of Portsmouth

Paris, 7 dec 2005

In collaboration with

Asantha Cooray,Pier-Stefano Corasaniti &

Alessandro Melchiorri

2

Introduction to Dark Energy

General Relatvity + High-z supernovae + Cosmic microwave background anisotropies (WMAP)

All together they give

[Spergel et al. ’03]

1/ 2;q 2 / 3 0;K

[Perlmutter et al. ’99]

3

The Dark Energy

Strongly supported (even by universe's age) Difficult to understand with standard physics Different models, different equation of state:

Different sound speed:

This is related with clustering via Jeans length

/w p -1/2-1 0

excludedΛphantom

w

2 if adiabatics

p pc

QuintessenceChaplygin gas

2 1sc 2sc w

J sc G

4

CMB perturbations

Perturbations exists in a proportion of 10-5

Primary and secondary perturbations Perturbative metric & variables

/ /T T

t0 300 ky 14 Gy

z 1100 0Compton scattering

Free propagation

neutral He-

but gravitational interactions!

[WMAP data]

2 2(1 2 ) 2 ( ) [(1 2 ) ]i i ji ij ijds dt w a t dtdx h dx dx

5

Sachs-Wolfe effects

Unintegrated SW: Integrated SW

1. No effect in matter epoch ( )2. Early ISW in radiation epoch3. Late ISW in DE epoch

USW

2 [ ( ), ]ISW r t t dt

0m a

2 24 Gaa

0 if

r

T

[Sachs & Wolfe, ’67]

6

Early & late ISW

The peak position corresponds to the horizon’s size at the epoch of origin

Early ISWTotal spectrum

Late ISW

7

What we can measure

The multipole momenta

They are strongly dependent on DE features

But the ISW is only 10% of the total!

Cosmic variance problem

*ISW ISW ISWl lm lmC

22 1

l

l

CC l

LCDM

LCDM, no ISW

8

The cross-correlation

Late ISW is coupled with matter distribution Primary anisotropies are not

Cross-correlation CMB-matter can extract the late ISW [Crittenden, Turok ‘95]

The bias must be estimated depends mostly on the survey on , ,

*gal ISW gal ISWl lm lmC

galISW w 2

sc m

[WMAP & SDSS]

z

9

Dependence on w (cs2=1)

If the effect decreases due to loss of DE

As well if the dark energy becomes important in more recent times, giving a smaller effect

0w

1w

[Matter visibility function gaussian, <z> = 0.5]

10

Dependence on w (cs2=0)

As before if Conversely, if

the clustering effect causes ulterior growth

0w

1w

[Matter visibility function gaussian, <z> = 0.5]

11

Dependence on <z>

A higher z means older times, and so less DE and smaller horizon (bigger l)

A lower z means more DE, but a bigger horizon (smaller l)

The correlation is best observed at intermediate z

[Matter visibility function gaussian]

12

Experimental correlations

Survey band <z>Correlation

authors

2MASS IR 0.1 Afshordi et al. ‘04

APM vis 0.15Fosalba,

Gaztañaga ‘04

SDSS vis0.3; 0.5

Fosalba, Gaztañaga ‘03

Scranton et al. ‘03

NVSS radio 0.9 Boughn, Crittenden ‘04HEAO X 0.9

[Fosalba, Gaztañaga ’04]

13

Theory and practice

The cross-correlation amplitude at the peak in function of <z>, w and cs

2

The five experimental correlations at peak in function of <z>[Fosalba, Gaztañaga ‘04]

w=-0.8w=-0.4w=-4

14

Likelihood analysis

The likelihood function is defined and plotted

[Corasaniti, TG, Melchiorri ‘04]

12 sc

02 sc

15

Results [Corasaniti, TG, Melchiorri ‘04]

For cs2 = 1 we have a degeneracy that is

orthogonal to the Snae Ia one. Constraints on w

-1.51 < w < -0.72, if cs2 = 0

-1.81 < w < -0.53, if cs2 = 1

@ 95% c. l. No valid constraints on cs

2

16

Discussion

Results are similar to previous, but obtained in an independent way [Bean & Doré ‘04; Weller & Lewis ‘03]

Not dependent on many parameters Only 5 points: possible improvements in future

(LSST, KAOS, ALPACA & PLANCK)

17

Tensor modes of perturbations

Can be originated by inflation We can study their evolution separately in linear regime:

The Einstein equation is

Freely propagating until horizon entering , after damped At recombination ( ), only large scale modes survive G waves: they can’t produce structures

2 2 2 ( )( ) i jij ijds dt a t h dx dx 0

0

0 0 0ij

h h

h h h

2, , , 2

02

16 ( ) ( )

ah h k h

aa

Tensor perturbed FRW metric

Perfect fluid appr.

Relativistic particle damping term

0 100k 00.02 1k

18

Limit on tensor amplitude

Commonly measured with: CMB TT, matter or polarization (search for B modes)

New method: CMB anisotropies amplitude is

ISW-gal cross-correlation amplitude is

(because clustered structures arise from scalar fuctuations) We can constrain r assuming a model (flat ΛCDM).

(1 )S T SA A A A r

SA

/T Sr A A

19

Results

Bias estimation introduce an extra 20% error (only linear dependence)

DE dependent Small ΩΛ gives small ISW, so

less r allowed(in fact to increase r one must

increase ΩΛ)

r < 0.5 @ 95% c. l.

From WMAP alone: r < 0.9

0.1lgT

l lgg TT

C

C C

[Cooray, Corasaniti, TG, Melchiorri ‘05]

[Seljak et al. ‘04]

20

How can it be improved?

At large scale: If we know all parameters with only cosmic

variance error, we have

This can be slightly improved considering cross-correlation to extract ISW to

SW ISW GWT T T T

2

2 2 min 0.06T l T

GWl

A C Al T

C

A

'min 0.056TA

2

2 1l

XC l

X

Cl