A Modified Gravitational Theory of the Matter Sector of the Type $\phi(R,T)\mathcal{L}_{m}$

Abstract

We investigate a modified gravity framework where the geometric Einstein--Hilbert sector remains untouched while the matter Lagrangian is weighted by a nontrivial function $\phi(T)$ of the energy--momentum trace. Unlike $f(R,T)$ or $f(R,\mathcal L_m)$ theories, this construction alters how matter curves spacetime without introducing extra geometric degrees of freedom, thereby remaining consistent with local tests of gravity. Physically, the factor $\phi(T)\mathcal L_m$ can be interpreted as an effective renormalization of the matter sector, relevant at high densities and smoothly reducing to GR at low densities. Within this setup we identify a robust window in parameter space leading to a smooth and nonsingular cosmological bounce, with bounded density, finite $\dot H>0$ at the bounce, and preservation of the infrared limit where $\Lambda$CDM is recovered. This mechanism provides a natural route to singularity resolution while retaining the empirical successes of standard cosmology.