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

Schäfer, Björn Malte ; Kalovidouris, Angelos Fotios ; Heisenberg, Lavinia

In: Monthly Notices of the Royal Astronomical Society, 2011, vol. 416, no. 2, p. 1302-1310

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    Summary
    The subject of this paper is an investigation of the non-linear contributions to the spectrum of the integrated Sachs-Wolfe (iSW) effect. We derive the corrections to the iSW autospectrum 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 Ωm, σ8, h, ns and w from the linear iSW effect and the systematical parameter estimation bias due to the non-linear corrections in a Fisher formalism, analysing the error budget in its dependence on multipole order. Our results include the following: (i) the spectrum of the non-linear iSW effect can be measured with 0.8σ statistical significance, (ii) non-linear corrections dominate the spectrum starting from ℓ≃ 102, (iii) an anticorrelation of the CMB temperature with tracer density on high multipoles in the non-linear regime, (iv) a much weaker dependence of the non-linear effect on the dark energy model compared to the linear iSW effect and (v) parameter estimation biases amount to less than 0.1σ and weaker than other systematics