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Nuclear Limits on Non-Minimally Coupled Gravity

We explore alternate theories of gravity where the gravitational term in the Lagrangian $\frac{R}{8πG}$ 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 $^4$He nucleus, for $f_1(R)=\frac{R}{8πG}$ and $f_2(R)=1+λR$, we find a limit of $|λ| < 5\times 10^{-12}\, \hbox{m}^2$, more than thirty orders of magnitude stronger than the previous limit.