Narrow Results

In this paper, we examine the stability condition of $f(T)$ gravity theory where T is the Torsion scalar using interacting and non-interacting models with the help of dynamical system. We let the $f(T)$ function be $f(T)=\alpha T+\beta$, where T is Torsion scalar and $\alpha$ and $\beta$ are the arbitrary constants. We calculated the critical points and study the stability behavior for this model. We analyze the system’s phase graphs and examined the physical interpretation. We demonstrate all of the cosmological parameters including ${\mathrm{\Omega }}_m$, ${\mathrm{\Omega }}_{\varphi }$, q, and ${\omega }_{\mathrm{\text{Tot}}}$ at each critical point and contrast them with values from observations. Then, we assume hybrid scale factor and transform it into the equation of redshift and time. Using this equation, we convert all the parameters into terms of redshift and analyze their behavior. Our model illustrates the Universe’s accelerating expansion. The energy conditions are examined in terms of redshift for the model. As a result, we conclude that our $f(T)$ model is stable and all the observed values are in agreement with observations.

In this work, the cosmological inflationary parameters in the correspondence of teleparallel gravity for the scalar–tensor theory are investigated. After the review of $f(T)$ and $f(T,B)$ gravity cosmology, we use the slow-roll approximations to study the behavior of the inflationary parameters namely the spectral index $n_s$ and tensor-to-scalar ratio $r$, and a comparison with observational data for different paradigmatic $f(T)$ gravity models such as exponential, Linder and power-law models is considered. We also consider the boundary term $B$ associated with these three models. The obtained behavior of the parameters under consideration shows that it is possible to constrain $f(T)$ and $f(T,B)$ models based on observational data.