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 $2\ensuremath{\sigma}$ level of accuracy. Our novel tool provides that the parameter $\ensuremath{\beta}$ parametrizing the quadratic curvature term in the gravitational Lagrangian of Palatini $f(R)$ gravity is constrained to $\ensuremath{\beta}\ensuremath{\lesssim}{10}^{9}\text{ }\text{ }{\mathrm{m}}^{2}$, while the Eddington-inspired Born-Infeld gravity parameter $\ensuremath{\epsilon}$ is restricted to $\ensuremath{\epsilon}\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{9}\text{ }\text{ }{\mathrm{m}}^{2}$. We also discuss further enhancements to the proposed method, aimed at imposing even more stringent constraints on modified gravity proposals.