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

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 $G_{\cos }$ in Friedmann equation should be smaller than the Newton's constant $G_{\mathrm{N}}$ such that $\Delta G_{\mathrm{N}}/G_{\mathrm{N}}\equiv (G_{\cos }-G_{\mathrm{N}})/G_{\mathrm{N}}=-0.085_{-0.028}^{+0.026}(68\%\text{ C.L. })$ in terms of big-bang nucleosynthesis, which excludes $\Delta G_{\mathrm{N}}=0$ 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 $\sim -\mathcal{O}(1)M_{\mathrm{PL}}^2(\mu /0.5M_{\mathrm{PL}}{)}^4$ 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 Hořava-Lifshitz gravity and might give a hint of quantum gravity.

Comments: 7 pages, 1 figure, to appear in PTEP