Conservative cosmology in scalar-tensor Herglotz $f(R,T)$ gravity

TL;DR

This paper extends scalar-tensor $f(R,T)$ gravity using the Herglotz variational principle, deriving new field equations and demonstrating a conservative cosmological model compatible with observations.

Contribution

It introduces a novel scalar-tensor Herglotz $f(R,T)$ gravity framework that ensures energy-momentum conservation and aligns with late-time cosmological data.

Findings

Derived generalized Friedmann equations in the new framework

Constructed a conservative cosmological model consistent with observations

Compared the model with $ abla T eq 0$ theories and $ abla T=0$ standard models

Abstract

The scalar-tensor representation of $f(R,T)$ gravity is extended to incorporate the Herglotz variational principle. The field equations are derived in both the geometric and scalar-tensor frameworks. Although the divergence of the energy-momentum tensor in matter-geometry coupling theories is generally nonvanishing, conservation can be achieved through the introduction of the Herglotz vector. The generalized Friedmann equations in scalar-tensor Herglotz $f(R,T)$ theory are obtained, and a conservative cosmological model is shown to be consistent with late-time observational data. Comparisons with analogous nonconservative models and with the standard $\Lambda$CDM model are also provided.