Optimization of the CMB-galaxy cross-correlation signal for studying the Integrated Sachs-Wolfe effect - Meirelles, Arthur Diniz (2024)
In this work, we study the use of the Integrated Sachs-Wolfe (ISW) Effect as a tool for cosmological analysis. We do this with the use of the cross-correlation spectrum between Cosmic Microwave Background (CMB) temperature maps and galaxy contrast maps, which are used as gravitational potential tracers. We discuss how this spectrum is calculated, the influence of the galaxy redshift distribution on the correlation signal and propose a method capable of finding an optimized distribution that maximizes the cross-correlation signal, which is commonly dominated by cosmic variance, an irreducible source of fluctuation in the spectrum. With this method, we obtained a galaxy survey selection function capable of reducing in $3\\%$ the the probability of compatibility with the null hypothesis, that is, a null cross-correlation signal. Furthermore, we explore the methods used to extract cross-correlation data points from masked CMB temperature and galaxy contrast maps, and use these results to calculate the likelihood profiles for the $\\Lambda$CDM $\\Omega_m$ parameter using WMAP\'s CMB temperature maps and 2MASS galaxy contrast maps for the first time in the literature. The results obtained for the likelihoods using only cross-correlation data show low constraining power. Combining the cross-correlation data with galaxy contrast autocorrelation data strongly tightens the constraints on $\\Omega_m$, and all the results in this combination are compatible with Planck\'s best-fit parameters. We also show the likelihood profile for two synthetic cross-correlation spectra calculated, one using the $\\Lambda$CDM model and the other using the value of $\\Omega_m$ that maximizes the likelihood found for band 4, found for band 4 of 2MASS, both having error bars consistent with this band. The results still showed a low constraining power, but are considerably better relative to the previous ones, even when compared with the likelihood that combines all the bands.