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

Abstract 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 $f(T)$ gravity model in a non-flat Friedmann-Lema\^itre-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 $f(T)$ gravity model. To derive constraints for the dark energy and $f(T)$ gravity models, we use recent astronomical datasets, including $H(z)$ 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 $\Omega_{r0}$ (density parameter of radiation), $\Omega_{m0}$ (density parameter of dark matter), $\Omega_{k0}$ (density parameter associated with spatial curvature), $\Omega_{CJ0}$ (density parameter of Modified Chaplygin-Jacobi gas), $\Omega_{CA0}$ (density parameter of Modified Chaplygin-Abel gas), and $H_0$ (present value of the Hubble parameter). We explore the cosmological evolution through various cosmic diagnostic parameters, including the deceleration parameter, $Om(z)$ diagnostic, and statefinder diagnostic pair $\{r,s\}$. 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 $f(T)$ gravity model, and ultimately gain a deeper understanding of the underlying mechanisms driving the accelerated expansion of our Universe.