Constraints on the parameters of modified Chaplygin–Jacobi and modified Chaplygin–Abel gases in f(T) gravity

In this work, we explore the parameter constraints of two dark energy models, namely the Modified Chaplygin–Jacobi gas (MCJG) and Modified Chaplygin–Abel gas (MCAG), within the context of [Formula: see text] gravity model in a non-flat Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Our investigation involves comparing the equation of state for the MCJG and MCAG dark energy models with the equation of state derived from the [Formula: see text] gravity model. To derive constraints for the dark energy and [Formula: see text] gravity models, we use recent astronomical datasets, including [Formula: see text] data, type Ia supernovae observations, Gamma Ray Bursts data, quasar data, and Baryon Acoustic Oscillation (BAO) measurements. We present the reduced Hubble parameter in terms of observable parameters such as [Formula: see text] (density parameter of radiation), [Formula: see text] (density parameter of dark matter), [Formula: see text] (density parameter associated with spatial curvature), [Formula: see text] (density parameter of Modified Chaplygin–Jacobi gas), [Formula: see text] (density parameter of Modified Chaplygin–Abel gas), and [Formula: see text] (present value of the Hubble parameter). We explore the cosmological evolution through various cosmic diagnostic parameters, including the deceleration parameter, [Formula: see text] diagnostic, and statefinder diagnostic pair [Formula: see text]. These diagnostic parameters offer valuable insights into the expansion dynamics and the nature of dark energy in the universe. We have also assessed the viability of the models using the information criteria. Our aim is to shed light on the nature of dark energy and its connection to the [Formula: see text] gravity model, and ultimately gain a deeper understanding of the underlying mechanisms driving the accelerated expansion of our universe.

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