FRW universe with almost-pseudo-Ricci symmetry: Evolving equation of state

This paper explores an almost-pseudo-Ricci symmetric (APRS) Friedmann–Robertson–Walker (FRW) spacetime with a constant Ricci scalar, incorporating a dynamic cosmological term [Formula: see text] and a time-dependent equation of state (EoS) parameter [Formula: see text]. By employing the parametrization [Formula: see text], we construct cosmological models using the dynamical system approach. Two cases are considered: a linearly time-dependent EoS and a trigonometric EoS. In both models, the deceleration parameter transitions from a decelerating to an accelerating phase, and the Hubble parameter exhibits a gradual decline, reflecting a universe expanding at a nearly steady rate. These results align with observational evidence of late-time cosmic acceleration, reinforcing the viability of the chosen [Formula: see text] parametrization in describing dark energy’s role in cosmic evolution.