Integrated Sachs-Wolfe tomography with orthogonal polynomials

Abstract

Topic of this article are tomographic measurements of the integrated Sachs-Wolfe effect with specifically designed, orthogonal polynomials which project out statistically independent modes of the galaxy distribution. The polynomials are contructed using the Gram-Schmidt orthogonalisation method. To quantify the power of the iSW-effect in contraining 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 SDSS, NVSS and 2MASS. For the cross-spectra our tomographic method provides a 16% increase in the signal to noise ratio and an improvement of up to 30% in conditional errors on parameters. Including all spectra, the marginalised errors approach an inverse square-root dependence with increasing cumulative polynomial order which underlines the statistical independence of the weighted signal spectra.Comment: 9 pages, 12 figures, submitted to MNRA

The cross-correlation between 3D cosmic shear and the integrated Sachs–Wolfe effect

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Parameter constraints from weak-lensing tomography of galaxy shapes and cosmic microwave background fluctuations

“…Although one might naively think that statistically independent measurements should be best at constraining a model, it is rather the fact that the additional information in the crosscorrelation with its parameter constraining power is advantageous to exploit: Firstly, on large scales there is a non-vanishing correlation of observed galaxy shapes and the CMB temperature due to the integrated Sachs Wolfe (iSW) effect, which has been investigated in a three-dimensional analysis by Zieser & Merkel (2016), as a generalization of tomographic measurements (e.g. Ho et al 2008;Jürgens & Schäfer 2012). Secondly, both weak lensing of the CMB and of galaxies are caused by the very same large scale structure.…”