The impact of the cosmic variance on $H_0$ on cosmological analyses

TL;DR

This paper investigates how cosmic variance influences local measurements of the Hubble constant, showing it adds systematic errors but does not resolve the existing tension, and emphasizes including this variance in cosmological model constraints.

Contribution

It quantifies the impact of cosmic variance on local $H_0$ measurements and demonstrates its effect on model selection and tension alleviation in cosmology.

Findings

Cosmic variance introduces about 0.88 km s$^{-1}$ Mpc$^{-1}$ systematic error in $H_0$

Including cosmic variance does not significantly reduce the $3\sigma$ tension

Model selection results are sensitive to cosmic variance considerations

Abstract

The current $3.8 \sigma$ tension between local (arXiv:1804.10655) and global (arXiv:1605.02985) measurements of $H_0$ cannot be fully explained by the concordance $\Lambda$CDM model. It could be produced by unknown systematics or by physics beyond the standard model. On the other hand, it is well known that linear perturbation theory predicts a cosmic variance on the Hubble parameter $H_0$, which leads to systematic errors on its local determination. Here, we study how including in the likelihood the cosmic variance on $H_0$ affects statistical inference. In particular we consider the $\gamma$CDM, $w$CDM and $\gamma w$CDM parametric extensions of the standard model, which we constrain with the latest CMB, BAO, SNe Ia, RSD and $H_0$ data. We learn two important lessons. First, the systematic error from cosmic variance is - independently of the model - approximately $\sigma_{\text{cv}}\approx 0.88$ km s$^{-1}$ Mpc$^{-1}$ (1.2\% $H_0^{\text{loc}}$) when considering the redshift range $0.0233 \le z \le 0.15$, which is relative to the main analysis of (arXiv:1804.10655), and $\sigma_{\text{cv}}\approx 1.5$ km s$^{-1}$ Mpc$^{-1}$ (2.1\% $H_0^{\text{loc}}$) when considering the wider redshift range $0.01 \le z \le 0.15$. Although $\sigma_{\text{cv}}$ affects the total error budget on local $H_0$, it does not significantly alleviate the tension which remains at $\approx 3 \sigma$. Second, cosmic variance, besides shifting the constraints, can change the results of model selection: much of the statistical advantage of non-standard models is to alleviate the now-reduced tension. We conclude that, when constraining non-standard models it is important to include the cosmic variance on $H_0$ if one wants to use the local determination of the Hubble constant by Riess et al. (arXiv:1804.10655). Doing the contrary could potentially bias the conclusions.