Ricci-Determinant gravity: Dynamical aspects and astrophysical implications

The Palatini gravitational action is enlarged by an arbitrary function $f(X)$ of the determinants Ricci tensor and metric, $X=|\textbf{det}.R|/|\textbf{det}.g|$. resulting Ricci-determinant theory exhibits novel deviations from general relativity. We study a particular realization where extension characterized square-root Ricci-determinant, $f(X)=\lambda_\text{Edd}\sqrt{X}$, which corresponds to famous Eddington action. analyze obtained equations for perfect fluid source show that affine connection can be solved in terms energy density pressure through disformal metric. As application, we derive hydrostatic equilibrium relativistic stars inspect significant effects induced tensor. find upper bound on $\lambda_{\rm Edd}$, at predictions relativity neutron become prominent, hierarchy between Planck vacuum mass scales. gravity propose here expected have interesting implications other cosmological domains.