Dynamical Complexity in Teleparallel Gauss-Bonnet Gravity

TL;DR

This paper investigates the dynamical behavior of the universe in teleparallel gravity extended with a Gauss-Bonnet term, identifying stable critical points and viable cosmological models consistent with current observations.

Contribution

It introduces and analyzes two cosmologically viable models within teleparallel Gauss-Bonnet gravity, exploring their stability and ability to describe different universe evolution phases.

Findings

Identification of stable critical points in the model

Models can describe accelerated and decelerated universe phases

Compatibility with current cosmological observations

Abstract

The stable critical points and their corresponding cosmology are derived in the teleparallel gravity with an added Gauss-Bonnet topological invariant term. We have analyzed the dynamics of the Universe by presenting two cosmological viable models, showing the potential to describe different phases of the evolution of the Universe. The value of the deceleration parameter ($q$), total equation of state parameter ($\omega_{tot}$) and dark energy equation of state parameter ($\omega_{DE}$) have been presented against each critical point. The existence and stability conditions are also presented. We study the behavior of the phase space trajectories at each critical point. Finally, the evolutionary behavior of the deceleration parameter and the equation of state parameters have been assessed with the initial condition of the dynamical variables, and compatibility has been observed in connection with the present cosmological scenario.