Equality scale-based and sound horizon-based analysis of the Hubble tension

TL;DR

This paper compares early dark energy and dark radiation models using equality scale and sound horizon data to address the Hubble tension, finding dark radiation more consistent with standard rulers.

Contribution

It introduces a comparative analysis of EDE and dark radiation models using $k_{eq}$ and $r_s$ data, highlighting the better consistency of dark radiation in fitting standard rulers.

Findings

Dark radiation model shows smaller $ riangle H_0$ between datasets.

EDE model increases $ riangle H_0$, indicating less consistency.

Forecasts suggest dark radiation aligns better with Planck $ m{ extbf{H}_0}$ estimates.

Abstract

The Hubble horizon at matter-radiation equality ($k^{-1}_{\rm{eq}}$) and the sound horizon at the last scattering surface ($r_s(z_*)$) provides interesting consistency check for the $\Lambda$CDM model and its extensions. It is well known that the reduction of $r_s$ can be compensated by the increase of $H_0$, while the same is true for the standard rulers $k_{\rm{eq}}$. Adding extra radiational component to the early universe can reduce $k_{\rm{eq}}$. The addition of early dark energy (EDE), however, tends to increase $k_{\rm{eq}}$. We perform $k_{\rm{eq}}$- and $r_s$-based analyses in both the EDE model and the Wess-Zumino Dark Radiation (WZDR) model. In the latter case we find $\Delta H_0 = 0.4$ between the $r_s$- and $k_{\rm{eq}}$-based datasets, while in the former case we find $\Delta H_0 = 1.2$. This result suggests that the dark radiation scenario is more consistent in the fit of the two standard rulers ($k_{\rm{eq}}$ and $r_s$). As a forecast analyses, we fit the two models with a mock $k_{\rm{eq}}$ prior derived from \emph{Planck} best-fit $\Lambda$CDM model. Compared with the best-fit $H_0$ in baseline $\Lambda$CDM model, we find $\Delta H_0 = 1.1$ for WZDR model and $\Delta H_0 = - 2.4$ for EDE model.