The Complementarity of Redshift-space Distortions and the Integrated Sachs-Wolfe Effect: A 3D Spherical Analysis

TL;DR

This paper explores how redshift-space distortions and the integrated Sachs-Wolfe effect, analyzed through a spherical 3D approach, can complement each other in constraining the evolution of the linear velocity power spectrum in cosmology.

Contribution

It introduces a spherical Fourier-Bessel analysis to accurately combine RSD and ISW signals, revealing their low correlation and potential for improved constraints on cosmological parameters.

Findings

ISW and RSD signals are weakly correlated.

ISW can enhance constraints on $f\sigma_8$ by over 10% on large scales.

Future precise RSD measurements will diminish ISW's constraining power but still serve as consistency checks.

Abstract

Assuming General Relativity is correct on large-scales, Redshift-Space Distortions (RSDs) and the Integrated Sachs-Wolfe effect (ISW) are both sensitive to the time derivative of the linear growth function. We investigate the extent to which these probes provide complementary or redundant information when they are combined to constrain the evolution of the linear velocity power spectrum, often quantified by the function $f(z)\sigma_8(z)$, where $f$ is the logarithmic derivative of $\sigma_8$ with respect to $(1+z)$. Using a spherical Fourier-Bessel (SFB) expansion for galaxy number counts and a spherical harmonic expansion for the CMB anisotropy, we compute the covariance matrices of the signals for a large galaxy redshift survey combined with a CMB survey like Planck. The SFB basis allows accurate ISW estimates by avoiding the plane-parallel approximation, and it retains RSD information that is otherwise lost when projecting angular clustering onto redshift shells. It also allows straightforward calculations of covariance with the CMB. We find that the correlation between the ISW and RSD signals are low since the probes are sensitive to different modes. For our default surveys, on large scales ($k<0.05 \Mpc/h$), the ISW can improve constraints on $f\sigma_8$ by more than 10% compared to using RSDs alone. In the future, when precision RSD measurements are available on smaller scales, the cosmological constraints from ISW measurements will not be competitive; however, they will remain a useful consistency test for possible systematic contamination and alternative models of gravity.