Dynamical system and statefinder analysis of cosmological models in f(T, B) gravity

TL;DR

This paper analyzes the cosmological dynamics of specific $f(T,B)$ gravity models using dynamical systems and statefinder diagnostics, revealing stable late-time acceleration solutions and distinguishing features from $\\Lambda$CDM.

Contribution

It introduces and analyzes two new $f(T,B)$ gravity models with power-law forms, deriving stability conditions and applying statefinder diagnostics to differentiate from standard cosmology.

Findings

Identification of de Sitter attractors explaining late-time acceleration

Analytical stability conditions for fixed points in the models

Numerical simulations showing spiral trajectories and oscillations

Abstract

This study systematically investigates the cosmological dynamics of two well-motivated functional forms in $f(T,B)$ gravity within a flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe. Here $T$ denotes the torsion scalar and $B$ the boundary term, with the special choice $f(T,B) = - T + B$ recovering General Relativity. We focus on a multiplicative power-law model $f(T,B) = c_1 T^\alpha B^\beta$ and an additive mixed power-law model $f(T,B) = c_2 T^\alpha + c_3 B^\beta$. Using dynamical system techniques, we construct autonomous systems and identify de Sitter attractors that naturally explain late-time cosmic acceleration. Analytical stability conditions for these fixed points are derived, and numerical simulations reveal characteristic evolutionary patterns, such as spiral trajectories and damped oscillations in the additive mixed power-law model. Furthermore, statefinder diagnostics are applied to quantitatively distinguish these models from the standard $\Lambda$CDM paradigm and other dark energy scenarios. The results indicate that $f(T,B)$ gravity offers a theoretically consistent and observationally distinguishable geometric framework for explaining cosmic acceleration, presenting a compelling alternative to conventional dark energy models.