Distance-Redshift Relation in a Realistic Inhomogeneous Universe

TL;DR

This paper examines how inhomogeneities in the universe's mass distribution affect the distance-redshift relation, revealing deviations up to 10% and implications for dark energy measurements.

Contribution

It introduces a realistic inhomogeneous universe model based on the Sheth-Tormen mass function and connects it to the Dyer-Roeder distance, highlighting effects on cosmological parameter estimation.

Findings

Distance deviations up to 10% depending on halo mass cutoff.

The derived distance aligns with the Dyer-Roeder approximation using a calculated clumpiness parameter.

Inhomogeneities significantly impact dark energy parameter estimates from supernova data.

Abstract

We investigate the distance-redshift relation in a realistic inhomogeneous universe where the mass distribution is described by the mass function of Sheth and Tormen. It is found that the derived distance deviates systematically from the standard distance up to 10% depending on the choice of the lowest halo mass in which baryonic matter condensed to form luminous object such as galaxies. Remarkably the derived distance is well approximated by the Dyer-Roeder distance if we choose the clumpiness parameter \alpha calculated by our model.We also discuss the effect of inhomogeneities in the determination of dark energy parameter in the supernovae observation, and find that this effect must be taken into account for the future high redshift supernovae observation.