Qualitative stability analysis of cosmological parameters in f(T, B) gravity

Abstract

AbstractWe analyze the cosmological solutions of f(T, B) gravity using dynamical system analysis where T is the torsion scalar and B be the boundary term scalar. In our work, we assume three specific cosmological models. For first model, we consider $$ f(T,B)=f_{0}(B^{k}+T^{m})$$ f ( T , B ) = f 0 ( B k + T m ) , where k and m are constants. For second model, we consider $$f(T,B)=f_{0}T B$$ f ( T , B ) = f 0 T B , for third model, we consider $$f(T,B)=\alpha T^{2}$$ f ( T , B ) = α T 2 . We generate an autonomous system of differential equations for each models by introducing new dimensionless variables. To solve this system of equations, we use dynamical system analysis. We also investigate the critical points and their natures, stability conditions and their behaviors of Universe expansion. For first and second models, we get two stable critical points, while for third model we get one stable critical point. The phase plots of this system are analyzed in detail and study their geometrical interpretations also. For these three models, we evaluated density parameters such as $$\Omega _{r}$$ Ω r , $$\Omega _{m}$$ Ω m , $$\Omega _{\Lambda }$$ Ω Λ and $$\omega _{eff}$$ ω eff and deceleration parameter (q) and find their suitable range of the parameter $$\lambda $$ λ for stability. For first model, we get $$\omega _{eff}=-0.833,-0.166$$ ω eff = - 0.833 , - 0.166 and for second model, we get $$\omega _{eff}=-\frac{1}{3}$$ ω eff = - 1 3 . This shows that both the models are in quintessence phase. For third model we get accelerated expansion of the Universe. Further, we compare the values of EoS parameter and deceleration parameter with the observational values.