Dynamical study of NTADE and SMHDE models within Rastall gravity

This paper is mainly focused to investigate the cosmological implications of Rastall gravity with the help of two dark energy models, i.e., new Tsallis agegraphic dark energy (NTADE) and Sharma–Mittal holographic dark energy (SMHDE). The background of flat FLRW space–time is being considered to develop the dynamical system of equations. To check the viability of these models and to distinguish them, we develop some important cosmological parameters. By constraining the involved model parameters, it is observed that the equation of state (EoS) parameter for the NTADE model lies in the phantom region whereas, for SMHDE, it shows quintom as well as quintessence regions depending on the values of model parameter δ. The deceleration parameter shows the phase transition from decelerating to the accelerating phase for both models. The ωD−ωD′ pair shows freezing and thawing regions for NTADE, and the freezing region for SMHDE. The pair (j,s) for SMHDE indicates a rich behavior as it shows different DE eras, a phantom, the quintessence as well as Chaplygin gas but the NTADE model shows Chaplygin gas behavior only. We conclude that SMHDE is a more efficient model than the NTADE model because it approaches Λ CDM limit and the results for this model lie in a stable region as shown by graphical analysis of the square speed of sound.