Parameter estimation biases due to contributions from the Rees-Sciama effect to the integrated Sachs-Wolfe spectrum

TL;DR

This paper investigates nonlinear contributions to the integrated Sachs-Wolfe spectrum, quantifies their impact on parameter estimation, and assesses their detectability with current and future cosmological data sets.

Contribution

It derives third-order perturbation corrections to the iSW spectrum and analyzes their effects on cosmological parameter estimation and bias.

Findings

Nonlinear iSW spectrum detectable at 0.8σ significance

Nonlinear corrections dominate from multipole l=100

Parameter biases are less than 0.1σ and smaller than other systematics

Abstract

The subject of this paper is an investigation of the nonlinear contributions to the spectrum of the integrated Sachs-Wolfe (iSW) effect. We derive the corrections to the iSW-auto spectrum and the iSW-tracer cross-spectrum consistently to third order in perturbation theory and analyse the cumulative signal-to-noise ratio for a cross-correlation between the PLANCK and EUCLID data sets as a function of multipole order. We quantify the parameter sensitivity and the statistical error bounds on the cosmological parameters Omega_m, sigma_8, h, n_s and w from the linear iSW-effect and the systematical parameter estimation bias due to the nonlinear corrections in a Fisher-formalism, analysing the error budget in its dependence on multipole order. Our results include: (i) the spectrum of the nonlinear iSW-effect can be measured with 0.8\sigma statistical significance, (ii) nonlinear corrections dominate the spectrum starting from l=100, (iii) an anticorrelation of the CMB temperature with tracer density on high multipoles in the nonlinear regime, (iv) a much weaker dependence of the nonlinear effect on the dark energy model compared to the linear iSW-effect, (v) parameter estimation biases amount to less than 0.1 sigma and weaker than other systematics.