Abstract

We discuss cosmology based on the cuscuton gravity theory to resolve the anomaly of the observational 4He abundance reported by the EMPRESS collaboration. We find that the gravitational constant Gcos in the Friedmann equation should be smaller than Newton’s constant GN such that ${\Delta G_{\rm N } }/{G_{\rm N } } \equiv (G_{\rm cos}-G_{\rm N})/{G_{\rm N } } = -0.085_{-0.028}^{+0.026} \ (68 \% \text{ C.L.})$ in terms of big-bang nucleosynthesis, which excludes ΔGN = 0 at more than 95% 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 μ. 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.