Integrated Sachs–Wolfe tomography with orthogonal polynomials




The topic of this article is tomographic measurements of the integrated Sachs–Wolfe effect (iSW) with specifically designed, orthogonal polynomials that project out statistically independent modes of the galaxy distribution. The polynomials are constructed using the Gram–Schmidt orthogonalization method. To quantify the power of the iSW effect in constraining cosmological parameters, we perfom a combined Fisher-matrix analysis for the iSW, galaxy and cross-spectra for wCDM cosmologies using the survey characteristics of Planck and EUCLID. The signal-to-noise ratio has also been studied for other contemporary galaxy surveys, such as the Sloan Digital Sky Survey (SDSS), NRAO VLA Sky Survey (NVSS) and Two Micron All-Sky Survey (2MASS). For w = −0.9 our tomographic method provides a 15 per cent (10 per cent for w = −1.0) increase for the cross-spectra in the signal-to-noise ratio and an improvement of up to 30 per cent in conditional errors in the parameters for EUCLID. Including all spectra, the marginalized errors approach an inverse square-root dependence with increasing cumulative polynomial order, which underlines the statistical independence of the weighted signal spectra.