The effect of inhomogeneities on dark energy constraints

TL;DR

This paper investigates how small-scale inhomogeneities affect dark energy parameter constraints using supernova data, finding that current effects are small but future surveys could significantly improve understanding.

Contribution

It introduces a method to quantify the impact of inhomogeneities on dark energy constraints and assesses their influence using current and future supernova observations.

Findings

Inhomogeneity parameter $ta$ correlates with dark energy equation of state $w$.

Current data show inhomogeneities have a small effect on $w$ within 2 sigma.

Future supernova surveys could improve constraints on inhomogeneities and dark matter fraction by a factor of 10.

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 ($\eta$) is correlated with $w$. The best fit values $w = -0.933 \pm 0.065$ and $\eta = 0.61 \pm 0.37$ are consistent with homogeneity at $< 2 \sigma$ level. Assuming homogeneity ($\eta =1$), we find $w = -0.961 \pm 0.055$, indicating only a small change in $w$. For a time-dependent dark energy equation of state, $w_0 = -0.951 \pm 0.112$ and $w_a = 0.059 \pm 0.418$, to be compared with $w_0 = -0.983 \pm 0.127$ and $w_a = 0.07 \pm 0.432$ in the homogeneous case, which is also a very small change. Current data are not sufficient to constrain the fraction of dark matter (DM) in compact objects, $f_p$ at the 95$\%$ C.L., however at 68$\%$ C.L. $f_p < 0.73$. Future supernova surveys will improve the constraints on $\eta$, and $f_p$, by a factor of $\sim$ 10.