Studying light propagation in a locally homogeneous universe through an extended Dyer-Roeder approach

TL;DR

This paper extends the Dyer-Roeder approach to account for light traveling through denser regions than average, showing that allowing the smoothness parameter to exceed unity can reconcile supernova and CMB data in cosmology.

Contribution

It introduces an extended Dyer-Roeder model with a smoothness parameter greater than one, supported by statistical analysis of supernova data and a toy model involving cosmic voids.

Findings

Extended DR parameter $oldsymbol{ extalpha_E}$ can be greater than 1.

$oldsymbol{ extalpha_E=1.26^{+0.68}_{-0.54}}$ from supernova data.

Higher $oldsymbol{ extalpha_E}$ alleviates tension between low and high redshift observations.

Abstract

Light is affected by local inhomogeneities in its propagation, which may alter distances and so cosmological parameter estimation. In the era of precision cosmology, the presence of inhomogeneities may induce systematic errors if not properly accounted. In this vein, a new interpretation of the conventional Dyer-Roeder (DR) approach by allowing light received from distant sources to travel in regions denser than average is proposed. It is argued that the existence of a distribution of small and moderate cosmic voids (or "black regions") implies that its matter content was redistributed to the homogeneous and clustered matter components with the former becoming denser than the cosmic average in the absence of voids. Phenomenologically, this means that the DR smoothness parameter (denoted here by $\alpha_E$) can be greater than unity, and, therefore, all previous analyses constraining it should be rediscussed with a free upper limit. Accordingly, by performing a statistical analysis involving 557 type Ia supernovae (SNe Ia) from Union2 compilation data in a flat $\Lambda$CDM model we obtain for the extended parameter, $\alpha_E=1.26^{+0.68}_{-0.54}$ ($1\sigma$). The effects of $\alpha_E$ are also analyzed for generic $\Lambda$CDM models and flat XCDM cosmologies. For both models, we find that a value of $\alpha_E$ greater than unity is able to harmonize SNe Ia and cosmic microwave background observations thereby alleviating the well-known tension between low and high redshift data. Finally, a simple toy model based on the existence of cosmic voids is proposed in order to justify why $\alpha_E$ can be greater than unity as required by supernovae data.