Quintom-like transit universe models in Metric-affine Myrzakulov $f(R,T,Q,T_m)$ gravity

Abstract: The current transit universe model is a precise solution to the equations of a new type of gravity theory called metric-affine Myrzakulov $f(R,T,Q,T_m)$ [Herko et al. Phys. Dark Univ. 34 (2021) 100886]. We find a hyperbolic solution and determine the limits on the model's parameters using the latest observational data. We examine how certain cosmological factors, like the deceleration parameter $q(z)$, effective equation of state parameter $\omega_{eff}$, dark energy equation of state parameter $\omega_{de}$, and matter energy density parameter $\Omega$, change over time to help explain the properties of the observable universe. We establish a hyperbolic solution and obtain the observational constraints on the model parameters using the latest observational datasets. We study the evolution of several cosmological parameters, including the deceleration parameter $q(z)$, effective equation of state (EoS) parameter $\omega_{eff}$, dark energy EoS parameter $\omega_{de}$, to explain the properties of the observable universe. We perform the Om diagnostic test for the model, and it represents the phantom scenarios of the model. The behavior of the dark energy EoS parameter $\omega_{de}$ reveals the quintom-A-type universe characteristics.