We 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.
We investigated the stability condition of [Formula: see text] gravity theory with interacting and noninteracting models by using dynamical system. We assume the [Formula: see text] function as [Formula: see text], where [Formula: see text] is the free parameter. We evaluated the critical points for this model and examined the stability behavior. We found two stable critical points for interacting model. The phase plots for this system are examined and the physical interpretation is discussed. We illustrate all the cosmological parameters such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] at each fixed point and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is [Formula: see text]. We transform all the parameters in terms of redshift by using this equation and examine the behavior of these parameters. Our model represents the accelerated expansion of the universe. The energy conditions are examined in terms of redshift and strong energy conditions are not satisfied for the model. We also find the statefinder parameters [Formula: see text] in terms of z and discuss the nature of r–s and r–q plane. For both pairs [Formula: see text] and [Formula: see text] our model represents the [Formula: see text]CDM model. Hence, we determine that our [Formula: see text] model is stable and it satisfies all the observational values.
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