Cosmological and Dynamical Aspects of Teleparallel Gravity and its Extension

TL;DR

The thesis analyzes late-time cosmic acceleration within teleparallel gravity and its extensions by employing dynamical-systems methods and confronting models with diverse cosmological data. It develops and studies $f(T)$, $f(T,\mathcal{T})$, and scalar–torsion theories (including Horndeski teleparallel and Galileon variants), extracting fixed points and assessing their background and perturbation stability. Across three $f(T)$ forms and multiple scalar-field models (quintessence, quintessence-like potentials, and axion- or hyperbolic-type DE), the work finds robust DE-dominated attractors yielding acceleration, with matter- and radiation-dominated epochs generally unstable at late times. Incorporating CC, SNIa, BAO data and $H_0$ priors (R21, TRGB) shows that some teleparallel models can accommodate observed expansion histories and can alleviate tensions in $H_0$ and growth observables like $f\sigma_8$, while ΛCDM remains a competitive baseline. Overall, modified teleparallel theories offer viable pathways to describe late-time acceleration and its interplay with cosmic structure formation, providing a framework for testing gravity beyond General Relativity with current and forthcoming data.

Abstract

This thesis investigates the characteristics of modified teleparallel gravity models that incorporate a scalar field and a trace of the energy-momentum tensor, with particular attention to their cosmological effects, especially regarding late-time cosmic acceleration. Teleparallel gravity, as an alternative framework to General Relativity, defines gravity through torsion rather than curvature, and when combined with a scalar field, it allows exploration of a wider variety of cosmological scenarios. This thesis examines the late-time acceleration of the Universe and its various phases through dynamical system analysis within the framework of modified teleparallel gravity theories. It presents the mathematical formulations of $f(T)$, $f(T, \mathcal{T})$, $f(T, φ)$, Horndeski teleparallel gravity, and the quintessence dark energy model, along with the application of dynamical systems and relevant cosmological datasets. Overall, the results demonstrate that these modified teleparallel gravity models provide viable descriptions of the late-time cosmic acceleration and offer insights into the dynamics of the Universe beyond standard cosmology.

Figures (47)

• Figure 1: 3D phase portrait for Model-I.
• Figure 2: Evolution of density parameters (Left panel) and the deceleration parameter (Right panel) for Model-I. The initial conditions $x = 10^{-2}$, $y =10^{-6}$ and $\beta = 0.0001$. The vertical dashed red line denotes the present time.
• Figure 3: 3D phase portrait for Model-II.
• Figure 4: Evolution of density parameters (Left panel) and the deceleration parameter (Right panel) for Model-II. The initial conditions $x = 10^{-3}$, $y =10^{-6}$ and $m = 0.5$. The vertical dashed red line denotes the present time.
• Figure 5: 3D phase portrait for Model-III.