Probing the Largest Scale Structure in the Universe with Polarization Map of Galaxy Clusters

Abstract

We introduce a new formalism to describe the polarization signal of galaxy clusters on the whole sky. We show that a sparsely sampled, half-sky map of the cluster polarization at z 1 would allow us to better characterize the very large scale density fluctuations. While the horizon length is smaller in the past, two other competing effects significantly remove the contribution of the small scale fluctuations from the quadrupole polarization pattern at z 1. For the standard CDM universe with vanishing tensor mode, the quadrupole moment of the temperature anisotropy at z 0 is expected to have a 32% contribution from fluctuations on scales below 6:3 h ÿ1 Gpc. This percentage would be reduced to 2% level for the quadrupole moment of polarization pattern at z 1. A cluster polarization would shed light on the potentially anomalous features of the largest scale fluctuations. [4,5] or inflationary physics [see, e.g., [6] ], and at the same time, evidenced the importance of independent observational methods to probe the largest scale structure in the Universe.The low-l moments of the present temperature anisotropies are usually assumed to probe the largest scales, but in fact they carry information about perturbations on a fairly broad range of scales. In this Letter we point out that the polarization signal from high-redshift clusters could probe the largest scales with less contamination from intermediate ones.Light scattered off a free electron is polarized, if the electron sees a quadrupole anisotropy of its incident light. This effect, which causes, for example, the large-scale polarization signal in a reionized universe [7,8], is responsible for the major polarization signal in SunyaeveZeldovich (SZ) galaxy clusters. As first pointed out by [9], the polarization pattern of clusters at different redshifts may shed light on the quadrupole amplitude at earlier times and at different positions [see also [10] in relation to the low observed quadrupole moment]. The cluster polarization has also been investigated as a potential tool to determine the nature of dark energy that is sensitive to the integrated Sachs-Wolfe effect [10,11].In this Letter we develop a transparent formalism for the calculation of the relevant observable quantities of the cluster's polarization signal, and show that the polarization

Searching for integrated Sachs–Wolfe effect beyond temperature anisotropies: CMB E-mode polarization–galaxy cross-correlation

“…Such a decrease in power is expected to make slight modifications to the polarization signal and to result in a lower polarization signal at large angular scales than assumed with no modifications to the primordial spectrum (e.g., Cline et al 2003). In fact, CMB polarization towards galaxy clusters may provide a mechanism to look for the cut-off in primordial power spectrum (e.g., Seto & Pierpaoli 2005). If there is a cut-off in the spectrum at small scales, ISW signal remain unaffected and the ratio of ISW-to-SW contribution to polarization may be higher when compared to a model where large-scale power is not affected.…”

Measuring the tensor to scalar ratio from CMB B-modes in the presence of foregrounds

“…The polarised Sunyaev Zel'dovich effect (Sazonov & Sunyaev 1999;Audit & Simmons 1999;Seto & Pierpaoli 2005), is expected to be very subdominant and is neglected here.…”

Reconstructing the Thomson Optical Depth due to Patchy Reionization with 21 cm Fluctuation Maps

“…Thomson scattering of the primordial quadrupole at lower redshifts has been discussed in the context of using galaxy clusters as Thomson scatterers (Kamionkowski & Loeb 1997;Sazonov & Sunyaev 1999;Baumann & Cooray 2003;Portsmouth 2004;Seto & Pierpaoli 2005;Bunn 2006;Shimon et al 2006). High-redshift 21 cm emission has several important advantages: (1) the Thomson optical depth can be accurately reconstructed from the 21 cm map, while galaxy cluster optical depths derived from Sunyaev-Zel'dovich measurements are weighted by the Compton y-parameter and thus are not appropriate for this purpose (Knox et al 2004); (2) the overlap in information of the CMB quadrupole at and our measured z ∼ 10 CMB sky is much reduced when compared with clusters at (local clusters are better as probes of the integrated z ∼ 0.2-0.5 Sachs-Wolfe effect); and 3) the CMB polarization signal will not be correlated with a large Sunyaev-Zel'dovich effect, gravitational lensing of the CMB, radio halos, quasar and galaxy overdensities, or strongly lensed background objects.…”