Early recombination as a solution to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> tension
Toyokazu Sekiguchi, Tomo Takahashi
Abstract
We show that the ${H}_{0}$ tension can be resolved by making recombination occur earlier, keeping the fit to cosmic microwave background (CMB) data almost intact. We provide a suite of general necessary conditions to give a good fit to CMB data while realizing a high value of ${H}_{0}$ suggested by local measurements. As a concrete example for a successful scenario with early recombination, we demonstrate that a model with a time-varying ${m}_{e}$ can indeed satisfy all of the conditions. We further show that such a model can also be well fitted to low-$z$ distance measurements of baryon acoustic oscillations (BAO) and type Ia supernovae (SNeIa) with a simple extension of the model. A time-varying ${m}_{e}$ in the framework of ${\mathrm{\ensuremath{\Omega}}}_{k}\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ is found to be a sufficient and excellent example of a solution to the ${H}_{0}$ tension, yielding ${H}_{0}={72.3}_{\ensuremath{-}2.8}^{+2.7}\text{ }\mathrm{km}/\mathrm{sec}/\mathrm{Mpc}$ from the combination of CMB, BAO, and SNeIa data even without incorporating any direct local ${H}_{0}$ measurements. Employing the Bayesian posterior predictive distribution, we find that this model can reduce the ${H}_{0}$ tension in the reference $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model from $4.8\ensuremath{\sigma}$ down to $2.2\ensuremath{\sigma}$. Apart from the ${H}_{0}$ tension, this model is also favored from the viewpoint of the CMB lensing anomaly.