Revisiting the cosmological bias due to local gravitational redshifts

TL;DR

This paper revisits the impact of local gravitational redshift on cosmological parameter estimation, showing that degeneracies can cause biases, but these are negligible when combined with CMB data.

Contribution

It demonstrates that degeneracies amplify biases from local gravitational redshift, but these biases are insignificant with combined CMB data, refining previous assessments.

Findings

Degeneracy causes ~1% bias in cosmological parameters.

Adding CMB data reduces bias to below 0.1 sigma.

Biases are negligible when multiple data sets are combined.

Abstract

A recent article by Wojtak {\it et al} (arXiv:1504.00718) pointed out that the local gravitational redshift, despite its smallness ($\sim 10^{-5}$), can have a noticeable ($\sim 1\%$) systematic effect on our cosmological parameter measurements. The authors studied a few extended cosmological models (nonflat $\Lambda$CDM, $w$CDM, and $w_0$-$w_a$CDM) with a mock supernova data set. We repeat this calculation and find that the $\sim 1\%$ biases are due to strong degeneracy between cosmological parameters. When cosmic microwave background (CMB) data are added to break the degeneracy, the biases due to local gravitational redshift are negligible ($\lesssim 0.1 \sigma$).