Angular distribution of cosmological parameters as a probe of space-time inhomogeneities

Understand

We develop a method based on the angular distribution on the sky of cosmological parameters to probe the inhomogeneity of large-scale structure and cosmic acceleration.

• We demonstrate this method on the largest type Ia supernova (SN) data set available to date, as compiled by the Joint Light-curve Analysis (JLA) collaboration and, hence, consider the cosmological parameters that affect the luminosity distance.
• We divide the supernova sample into equal surface area pixels and estimate the cosmological parameters that minimize the chi-square of the fit to the distance modulus in each pixel, hence producing maps of the cosmological parameters $\{\Omega_{M}, \Omega_{\Lambda}, H_{0}\}.$ In poorly sampled pixels, the measured fluctuations are mostly due to an inhomogeneous coverage of the sky by the SN surveys; in contrast, in well-sampled pixels, the measurements are robust enough to suggest a real fluctuation.
• We also measure the anisotropy of the parameters by computing the power spectrum of the corresponding maps of the parameters up to $\ell=3.$ For an analytical toy model of an inhomogeneous ensemble of homogeneous pixels, we derive the backreaction term in the deceleration parameter due to the fluctuations of $H_{0}$ across the sky and measure it to be of order $10^{-3}$ times the corresponding average over the pixels in the absence of backreaction.