Integrated Sachs-Wolfe Effect & Dark Energy

1. Integrated Sachs-Wolfe Effect&Dark Energy In collaboration with Asantha Cooray, Pier-Stefano Corasaniti & Alessandro Melchiorri Tommaso Giannantonio ICG, University of Portsmouth Paris, 7 dec 2005

2. Introduction to Dark Energy • General Relatvity + • High-z supernovae + • Cosmic microwave background anisotropies (WMAP) All together they give [Perlmutter et al. ’99] [Spergel et al. ’03]

3. -1 -1/2 0 w Λ phantom excluded 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 Quintessence Chaplygin gas

4. Perturbations exists in a proportion of 10-5 Primary and secondary perturbations Perturbative metric & variables [WMAP data] 14 Gy 0 300 ky t z 1100 0 CMB perturbations e- neutral H Free propagation Compton scattering but gravitational interactions!

5. T Sachs-Wolfe effects r • Unintegrated SW: • Integrated SW • No effect in matter epoch ( ) • Early ISW in radiation epoch • Late ISW in DE epoch [Sachs & Wolfe, ’67]

6. Early & late ISW Total spectrum Early ISW Late ISW The peak position corresponds to the horizon’s size at the epoch of origin

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 LCDM LCDM, no ISW

8. [WMAP & SDSS] 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 , ,

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

10. Dependence on w (cs2=0) • As before if • Conversely, if the clustering effect causes ulterior growth [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 [Fosalba, Gaztañaga’04]

13. Theory and practice The five experimental correlations at peak in function of <z> [Fosalba, Gaztañaga ‘04] w=-0.8 w=-0.4 w=-4 The cross-correlation amplitude at the peak in function of <z>, w and cs2

14. Likelihood analysis [Corasaniti, TG, Melchiorri ‘04] • The likelihood function is defined and plotted

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 cs2

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 Tensor perturbed FRW metric Perfect fluid appr. Relativistic particle damping term

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).

19. [Seljak et al. ‘04] 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 [Cooray, Corasaniti, TG, Melchiorri ‘05]

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