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

• Published in: Monthly notices of the Royal Astronomical Society Vol. 416; no. 2; pp. 1302 - 1310
• Main Authors: Schäfer, Björn Malte, Kalovidouris, Angelos Fotios, Heisenberg, Lavinia
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 11.09.2011; Wiley-Blackwell; Oxford University Press
• Subjects: Astronomy; cosmic background radiation; cosmological parameters; Cosmology; Density; Earth, ocean, space; Error analysis; Error detection; Exact sciences and technology; Formalism; large-scale structure of Universe; Mathematical models; Multipoles; Nonlinearity; Parameter estimation; Spectrum analysis; cosmic background radiation; cosmological parameters; large-scale structure of Universe; Perturbation theory; Parameter estimation; High density; Third order; Cosmic background radiation; Signal-to-noise ratio; Large-scale structure; Cross correlations; Anticorrelation; Cosmological parameter; Multipoles; Cosmology; Models; Sachs Wolfe effect; Dark energy; Corrections; Tracers
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2011.19125.x

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.