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

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 $\varphi (T)$ 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 $\varphi (T){\mathcal{L}}_m$ 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.

Matches published version in European Physical Journal Plus

References in corpus (13)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Extra force in $f(R)$ modified theories of gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Quantum Nature of the Big Bang
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• f(R,L_m) gravity
• Towards a Nonsingular Bouncing Cosmology
• A Critical Review of Classical Bouncing Cosmologies
• Exploring Bouncing Cosmologies with Cosmological Surveys
• On the non-minimal gravitational coupling to matter
• Hubble tension in a nonminimally coupled curvature-matter gravity model
• Is cosmological data suggesting a nonminimal coupling between matter and gravity?