Cosmological implications of LRS Bianchi type-I cosmological model in $f(T)$ gravity
Shivangi Rathore, S. Surendra Singh
TL;DR
This work analyzes the late-time cosmology of an anisotropic LRS Bianchi type-I universe within $f(T)$ gravity, choosing the viable form $f(T)=T+zeta T^{2}$ and including an energy transfer term $Q=\alpha\rho H$. By transforming the modified field equations into an autonomous dynamical system with dimensionless variables, the authors identify four equilibrium points and study their stability, finding a stable quintessence point $T_{2}$ and phantom-type fixed points $T_{1}$, $T_{3}$, and $T_{4}$. They compute cosmographic quantities $q$, $j$ and the state-finder pair $(r,s)$ to characterize expansion history and dark-energy behavior at these points, and provide phase-space analyses to illustrate the dynamics. The results indicate that the quadratic $T^{2}$ correction in $f(T)$ can yield viable accelerated expansion in an anisotropic setting, offering a framework for future observational comparisons with BAO, Pantheon, and Hubble data.
Abstract
We perform the dynamical system analysis of the Locally Rotationally Symmetric (LRS) Bianchi type-I cosmological model in f(T) gravity in the presence of energy interaction . A cosmologically viable form of $f(T)$ is chosen (where $T$ is the torsion scalar in teleparallelism) in the background of homogenous and anisotropic. For our model, we take $f(T) = T+ζT^{2}$ where $ζ$ is a constant. The evolution equations are reduced to the autonomous system of differential equations by suitable transformation of variables. The behaviour of the equilibrium points is examined by calculating the eigenvalues corresponding to these equilibrium points. We get four equilibrium points for our cosmological model out of which one equilibrium point is stable, two are saddle points and one is an unstable equilibrium point. Corresponding to equilibrium point $T_{2}$, our model is consistent with the quintessence dark energy cosmological model. Along the equilibrium points $T_{1},T_{3}$ and $T_{4}$, our model is consistent to phantom dark energy model. After that, we utilize the autonomous equations to analyse the cosmographic parameters along with the state-finder parameter. We demonstrate the phase plot analysis for our model.