Study of a novel equation of state with statefinder hierarchy and growth rate of structure

In this paper, we examine a cosmological model with a new parametrization of the dark energy equation of state using a single parameter, [Formula: see text], to measure departures from the typical [Formula: see text]CDM case. The growth rate of cosmic structure and the statefinder hierarchy is used as diagnostics to analyze the model. A [Formula: see text] analysis is also performed, in which [Formula: see text] represents the dark energy equation of state parameter and the prime signifies differentiation with regard to [Formula: see text], where [Formula: see text] is the scale factor. We also investigate the evolution of the apparent magnitude and the Hubble parameter, contrasting the model’s predictions with those of [Formula: see text]CDM and with observable data from Type Ia Supernovae and Hubble parameter observations. We find that the cosmos accelerates after decelerating in the recent cosmic past, but does not asymptotically approach a de Sitter phase in the far future as does the classic [Formula: see text]CDM model. Rather, a second transition — from acceleration to deceleration — is what the model anticipates. Last, as a diagnostic of the model’s behavior under minor perturbations, we evaluate the squared sound speed to determine the dynamical stability of the model.