The effect of inhomogeneities on dark energy constraints

Abstract

Constraints on models of the late time acceleration of the universe assume the cosmological principle of homogeneity and isotropy on large scales. However, small scale inhomogeneities can alter observational and dynamical relations, affecting the inferred cosmological parameters. For precision constraints on the properties of dark energy, it is important to assess the potential systematic effects arising from these inhomogeneities. In this study, we use the Type Ia supernova magnitude-redshift relation to constrain the inhomogeneities as described by the Dyer-Roeder distance relation and the effect they have on the dark energy equation of state (w), together with priors derived from the most recent results of the measurements of the power spectrum of the Cosmic Microwave Background and Baryon Acoustic Oscillations. We find that the parameter describing the inhomogeneities (η) is weakly correlated with w. The best fit values w = −0.933 ± 0.065 and η = 0.61 ± 0.37 are consistent with homogeneity at < 2 σ level. Assuming homogeneity (η =1), we find w = −0.961 ± 0.055, indicating only a small change in w. For a time-dependent dark energy equation of state, w0 = −0.951 ± 0.112 and wa = 0.059 ± 0.418, to be compared with w0 = −0.983 ± 0.127 and wa = 0.07 ± 0.432 in the homogeneous case, which is also a very small change. We do not obtain constraints on the fraction of dark matter in compact objects, fp, at the 95% C.L. with conservative corrections to the distance formalism. Future supernova surveys will improve the constraints on η, and hence, fp, by a factor of ∼10.