Planetary seismology as a test of modified gravity proposals

We demonstrate that it is possible to test models of gravity, such as Palatini $f(R)$ and Eddington-inspired Born-Infeld models, using seismic data from Earth. By incorporating additional limitations on Earth's moment of inertia and mass given from observational data, the models' parameters can be restricted to a $2\sigma$ level of accuracy. Our novel tool provides that the parameter $\beta$ parametrizing the quadratic curvature term in the gravitational Lagrangian of Palatini $f(R)$ gravity is constrained to $\beta\lesssim 10^9 \text{m}^2$ while the Eddington-inspired Born-Infeld gravity parameter $\epsilon$ is restricted to $\epsilon\lesssim 4\cdot 10^9 \text{m}^2$. We also discuss further enhancements to the proposed method, aimed at imposing even more stringent constraints on modified gravity proposals.