Impact of the cosmic variance on H0 on cosmological analyses

The current 3.8 sigma tension between local [A. G. Riess et al., arXiv:1804.10655.] and global [N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 596, A107 (2016).] measurements of Ho cannot be fully explained by the concordance ACDM model. It could be produced by unknown systematics or by physics beyond the standard model. In particular, nonstandard dark energy models were shown to be able to alleviate this tension. 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, wCDM and gamma wCDM 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(cv) approximate to 0.88 km s(-1) Mpc(-1) (1.2% H-0(loc)) when considering the redshift range 0.0233 <= z <= 0.15, which is relative to the main analysis of [A. G. Riess et al., arXiv:1804.10655.], and sigma(cv) approximate to 1.5 km s(-1) Mpc(-1) (2.1% H-0(loc)) when considering the wider redshift range 0.01 <= z <= 0.15. Although sigma(cv) affects the total error budget on local H-0, it does not significantly alleviate the tension which remains at approximate to 3 sigma. Second, cosmic variance, besides shifting the constraints, can change the results of model selection: much of the statistical advantage of nonstandard models is to alleviate the now-reduced tension. We conclude that, when constraining nonstandard 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.