The Price of Shifting the Hubble Constant

TL;DR

This paper investigates how modifications to early time cosmology are necessary to reconcile higher local measurements of the Hubble constant with BAO data, finding that the inferred sound horizon scale is robust against different dark energy models.

Contribution

It demonstrates that the sound horizon scale $r_d$ remains nearly unchanged across various dark energy models and data combinations, highlighting the robustness of early universe constraints.

Findings

Best fit $r_d$ is insensitive to dark energy model variations.

Inclusion of local $H_0$ measurements does not significantly alter $r_d$.

Early time modifications are required to reconcile higher $H_0$ values.

Abstract

An anisotropic measurement of the baryon acoustic oscillation (BAO) feature fixes the product of the Hubble constant and the acoustic scale $H_0 r_d$. Therefore, regardless of the dark energy dynamics, to accommodate a higher value of $H_0$ one needs a lower $r_d$ and so necessarily a modification of early time cosmology. One must either reduce the age of the Universe at the drag epoch or else the speed of sound in the primordial plasma. The first can be achieved, for example, with dark radiation or very early dark energy, automatically preserving the angular size of the acoustic scale in the Cosmic Microwave Background (CMB) with no modifications to post-recombination dark energy. However it is known that the simplest such modifications fall afoul of CMB constraints at higher multipoles. As an example, we combine anisotropic BAO with geometric measurements from strong lensing time delays from H0LiCOW and megamasers from the Megamaser Cosmology Project to measure $r_d$, with and without the local distance ladder measurement of $H_0$. We find that the best fit value of $r_d$ is indeed quite insensitive to the dark energy model, and is also hardly affected by the inclusion of the local distance ladder data.