A Possible Solution to the Helium Anomaly of EMPRESS VIII by Cuscuton Gravity Theory

TL;DR

This paper explores how cuscuton gravity theory can resolve the helium abundance anomaly observed by EMPRESS VIII, suggesting a smaller gravitational constant during big-bang nucleosynthesis and indicating potential links to quantum gravity.

Contribution

It demonstrates that cuscuton gravity can account for the helium anomaly by modifying the effective gravitational constant during early universe nucleosynthesis.

Findings

Gravitational constant during nucleosynthesis is smaller than Newton's constant.

A negative mass squared scalar field is required, hinting at modified gravity theories.

Cuscuton gravity may connect to low-energy Hořava-Lifshitz gravity and quantum gravity.

Abstract

We discuss cosmology based on the cuscuton gravity theory to resolve the anomaly of the observational $^4$He abundance reported by the EMPRESS collaboration. We find that the gravitational constant $G_{\rm cos}$ in Friedmann equation should be smaller than the Newton's constant ${G_{\rm N}}$ such that ${\Delta G_{\rm N}}/{G_{\rm N}} \equiv (G_{\rm cos}-G_{\rm N})/{G_{\rm N}} = -0.085_{-0.028}^{+0.026} \quad(68 \% \text { C.L. })$ in terms of big-bang nucleosynthesis, which excludes ${\Delta G_{\rm N}}=0$ at more than 95~$\% \text { C.L. }$ To fit the data, we obtain a negative mass squared of a non-dynamical scalar field with the Planck-mass scale as $\sim - {\mathcal{O}}(1) {M_{\rm PL}^2} ({\mu}/{0.5 M_{\rm PL}})^{4}$ with the cuscuton mass parameter $\mu$. This fact could suggest the need for modified gravity theories such as the cuscuton gravity theory with a quadratic potential, which can be regarded as the low-energy Ho\v{r}ava-Lifshitz gravity and might give a hint of quantum gravity.