In this paper, we have emphasized the stability analysis of the accelerating cosmological models obtained in f(T) gravity theory. The behaviour of the models based on the evolution of the equation of state parameter shows phantom-like behaviour at the present epoch. The scalar perturbation technique is used to create the perturbed evolution equations, and the stability of the models has been demonstrated. Also, we have performed the dynamical system analysis for both the models. In the two specific f(T) gravity models, three critical points are obtained in each model. In each model, at least one critical point has been observed to be stable.

Gravastars have been considered as a serious alternative to black holes in the past couple of decades. Stable models of gravastar have been constructed in many of the alternate gravity models besides standard general relativity (GR). The Randall-Sundrum (RS) braneworld model has been a popular alternative to GR, especially in the cosmological and astrophysical context. Here, we consider a gravastar model in RS brane gravity. The mathematical solutions in different regions have been obtained with calculation of matching conditions. Various important physical parameters for the shell have been calculated and plotted to note their variation with radial distance. We also calculate and plot the surface redshift to provide a very cursory check on the stability of the gravastar within the purview of RS brane gravity.