Cosmology in generalized hybrid metric-Palatini with matter-geometry coupling

TL;DR

The paper addresses the late-time acceleration problem by studying a generalized hybrid metric–Palatini gravity with a non-minimal matter–geometry coupling, recast as a bi-scalar–tensor theory with a dynamical $\phi$ coupled to geometry and a non-dynamical $\psi$ coupling to matter. It analyzes cosmological dynamics in a flat FRW background, solving two illustrative potentials: a linear case that fails to drive acceleration and a multiplicative case that yields a realistic expansion close to $\Lambda$CDM while allowing a quintessence-to-phantom transition near $z \approx 0.86$. The model is constrained by Cosmic Chronometers, Pantheon$^+$, and DESI DR2 BAO data, showing good agreement with observations and, for the full data combination, strong Bayesian evidence in favor of the NMHMP model over $\Lambda$CDM, with Planck $H_0$ compatibility and no significant $H_0$ tension. The results motivate NMHMP as a viable alternative to $\Lambda$CDM for background cosmology, while highlighting the need for perturbation-level tests and further observational probes. Overall, the work provides a concrete, data-driven framework where non-minimal matter–geometry coupling can account for late-time acceleration without invoking a strict cosmological constant.

Abstract

Cosmological implications of a class of hybrid metric-Palatini gravity with a non-minimal matter-geometry coupling is considered. The theory contains a metric curvature tensor, together with a curvature tensor constructed from an independent affine connection. We will show that the model could be written as a bi-scalar-tensor gravity with a non-minimal coupling between matter sector and a scalar field. The theory will then be confronted with observational data from Cosmic Chronometers, BAO dataset from DESI and the Pantheon$^+$ dataset. We will show that the theory could be a good alternative to the $Λ$CDM model with the difference that the conservation of the baryonic matter sector holds only at the background level. The statefinder analysis will also be applied to the theory and it is observed that the DE behavior of the theory exhibits a quintessence to phantom transition occurs at redshifts around $z\approx0.86$.

Figures (11)

• Figure 1: The corner plot of the values of parameters with their $1\sigma$ and $2\sigma$ confidence levels for the NMHMP model (left) and together with $\Lambda$CDM model (right).
• Figure 2: The Pearson correlation matrix of between the parameters of the NMHMP model. Moderate correlation of the model parameter $n$ with $\beta$ and $\Omega_{m0}$ can be seen from the figure.
• Figure 3: The behavior of the rescaled Hubble parameter $H/(1+z)$ (top panel) and the difference between the two models (bottom panel) as a function of the redshift for the best fit values of the parameters as given by table \ref{['bestfit']}. The shaded area denotes the $1\sigma$ error. Dashed lines represent $\Lambda$CDM model. The error bars correspond to the observational data of the Cosmic Chronometers dataset.
• Figure 4: The behavior of scalar fields $\bar{\psi}$ (dashed line) and $\phi$ (solid line) as functions of the redshift for NMHMP model for the best fit values of the parameters as given by table \ref{['bestfit']}. The vertical dashed line represent acceleration to deceleration transition redshift.
• Figure 5: The behavior of the deceleration parameter $q$as a function of the redshift $z$ for NMHMP model for the best fit values of the parameters as given by table \ref{['bestfit']}. The shaded area denotes the $1\sigma$ error. Dashed lines represent $\Lambda$CDM model. The vertical dashed line denotes the deceleration to acceleration phase transition redshift.