Nuclear limits on nonminimally coupled gravity

We explore alternate theories of gravity where the gravitational term in the Lagrangian $\frac{R}{8\pi G}$ is replaced by a function $f_1(R)$ and the matter Lagrangian is multiplied by a function $f_2(R)$. We argue that nuclear physics can provide strong experimental constraints on such theories. In particular using energy conditions on the pressure in the ${}^4\mathrm{He}$ nucleus, for $f_1(R)=\frac{R}{8\pi G}$ and $f_2(R)=1+\lambda R$, we find a limit of $|\lambda |<5\times {10}^{-12}{\mathrm{m}}^2$, more than thirty orders of magnitude stronger than the previous limit.

Figure 1

The pressure to density ratio for the Gaussian density profile as a function of radius corresponding to the cutoff values of $\lambda$ as given in Table 1.

Figure 2

The pressure to density ratio for the experimental density profile as a function of radius corresponding to the cutoff values of $\lambda$ as given in Table 1.