Inhomogeneous matter distribution and supernovae

Abstract

This work investigates a simple inhomogeneous cosmological model within the Lema[Formula: see text]tre–Tolman–Bondi (LTB) metric. The mass-scale function of the LTB model is taken to be [Formula: see text] and would correspond to a fractal distribution for [Formula: see text]. The luminosity distance for this model is computed and then compared to supernovae (SNe) data. Unlike LTB models which have, in the most general case, two free functions, our model has only two free parameters as the flat Standard Model of cosmology. The best-fit obtained is a matter distribution with an exponent of [Formula: see text] revealing that SNe data do not favor those fractal models.