Angular distribution of cosmological parameters as a probe of space-time
  inhomogeneities
  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.
We conclude that, for the toy model considered, backreaction is not a viable
dynamical mechanism to emulate cosmic acceleration.
