Qualitative Stability Analysis of Cosmological Parameters in $f(T,B)$ Gravity

Abstract

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 two specific cosmological models. For first model, we consider $f(T,B)=f_0(B^k+T^m)$, where $k$ and $m$ are constants. For second model, we consider $f(T,B)=f_{0}TB$. 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 both models, we get four critical points. The phase plots of this system are analyzed in detail and study their geometrical interpretations also. In both model, we evaluated density parameters such as ${\Omega }_r$, ${\Omega }_m$, ${\Omega }_{\Lambda }$ and ${\omega }_{eff}$ and deceleration parameter $(q)$ and find their suitable range of the parameter $\lambda$ for stability. For first model, we get ${\omega }_{eff}=-0.833,-0.166$ and for second model, we get ${\omega }_{eff}=-\frac{1}{3}$. This shows that both the models are in quintessence phase. Further, we compare the values of EoS parameter and deceleration parameter with the observational values.

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References in corpus (15)

• f(R,T) gravity
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• On Born-Infeld Gravity in Weitzenbock spacetime
• Cosmological perturbations in f(T) gravity
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Solar system constraints on f(T) gravity
• Cosmology in cubic and $f(P)$ gravity
• Gravitoelectromagnetism, Solar System Test and Weak-Field Solutions in $f(T,B)$ Gravity with Observational Constraints
• de Sitter and Scaling solutions in a higher-order modified teleparallel theory
• Nonlocal Teleparallel Cosmology
• Thermodynamics of the viscous $f(T,B)$ gravity in the new agegraphic dark energy model
• Dynamical systems of cosmological models for different possibilities of $G$ and ${\rho }_{\Lambda }$
• Dynamical features of $f(T,B)$ cosmology

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• Accelerating cosmological models in $f(Q)$ gravity and the phase space analysis
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