Angular distribution of cosmological parameters: measurement of inhomogeneities from type Ia supernovae

C. Sofia Carvalho, Katrine Marques

Published 2015-12-24Version 1

We measure the inhomogeneity of the large-scale structure and cosmic acceleration by measuring for the first time the angular distribution on the sky of the cosmological parameters that affect the luminosity distance, estimated from supernova data. We used the combination of SDSS-II and SNLS type Ia supernova samples. We divide the supernovae into equal-surface area pixels and estimate the cosmological parameters that minimize the chi-squared of the fit to the distance modulus in each pixel, hence producing maps of the cosmological parameters {Omega_{M}, Omega_{Lambda}, H_{0}}. We measure fluctuations about the average values of order 5-95% for the matter energy density Omega_{M}, of order 1-25% for the dark energy density Omega_{Lambda} and of order up to 5% for the Hubble parameter H_{0}. In poorly sampled pixels, these 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 parameters' maps up to ell=3. The power spectra of the energy densities have a local maximum at the quadrupole ell=2; in contrast, the power spectrum of H_{0} increases with the multipole, meaning that the maximum anisotropy can be at scales smaller than the minimum scale probed by the pixels. 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} the corresponding average over the pixels in the absence of backreaction. In this model, backreaction is not a viable dynamical mechanism to emulate cosmic acceleration.