Physical characteristics and causality of cosmological models in generalized matter-geometry coupling gravity theory with observational constraints

In the generalized matter-geometry coupling theory, we investigate the physical characteristics and causality of some new cosmological models for a flat, homogeneous, and isotropic spacetime filled with stiff, radiation, dust, and curvature fluid sources. We obtain a particular cosmological model corresponding to each source fluid, called Models I, II, III, and IV, respectively. We make observational constraints on each model using the joint analysis of $31$ Cosmic Chronometer (CC) Hubble dataset and $1048$ Pantheon datasets to estimate the current values of model parameters. Using these statistical results, we have analyzed the information criteria, effective EoS parameter, causality of the models, and viability of this generalized gravity theory. Subsequently, we investigate the effective equation of state and deceleration parameter for each model. We found that all models in the late-time universe exhibit transit-phase acceleration, and Models I and II show both the early as well as late-time accelerating phase of the expanding universe. We found the current values of the deceleration parameter in the range $-0.886\le q_{0}\le-0.54$ with transition redshift $0.5137\le z_{t}\le0.6466$ and the effective EoS parameter in the range $-0.924\le\omega_{eff}\le-0.6933$. We analyzed the square sound speed condition $c_{s}^{2}\le c^{2}$ for each model.