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

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 $Λ$CDM model are also provided.

Figures (3)

• Figure 1: The Hubble function (left) and deceleration parameter (right) for initial conditions $\varphi_0 = 1.7$, $\varphi_0 = 1.8$ and $\varphi_0=1.9$ with scalar potential $U(\varphi,\psi) = \alpha\varphi +\beta\varphi^2 -(1/2\gamma)\psi^2$. Each case is compared with the $\Lambda$CDM model and model I in Bouali_2023. Additionally, the Hubble function is compared with cosmic chronometer data.
• Figure 2: The $Om(z)$ diagnostic (left) and jerk parameter (right) for initial conditions $\varphi_0 = 1.7$, $\varphi_0 = 1.8$ and $\varphi_0=1.9$ with scalar potential $U(\varphi,\psi) = \alpha\varphi +\beta\varphi^2 -(1/2\gamma)\psi^2$.
• Figure 3: The Herglotz field (left) and scalar field $\varphi$ (right) for initial conditions $\varphi_0 = 1.7$, $\varphi_0 = 1.8$ and $\varphi_0=1.9$ with scalar potential $U(\varphi,\psi) = \alpha\varphi +\beta\varphi^2 -(1/2\gamma)\psi^2$.