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Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to…
This thesis explores the cosmological implications of modified gravity, focusing on nonmetricity-based $f(Q)$ gravity as an alternative to the $\Lambda$CDM model in explaining cosmic acceleration. Chapter I lays the theoretical groundwork…
Motivated by the exciting features and a recent proposed general form of the function of non-metricity scalar Q, we investigate the cosmological implications in $f(Q)$ gravity, through the resulting effective dark energy sector, extracting…
We present a comprehensive phase-space analysis of a quadratic dark energy model where the pressure includes a nonlinear term proportional to the square of the energy density. This minimal extension beyond the $\Lambda$CDM framework…
In this paper, we have outlined the development of an autonomous dynamical system within a general scalar-tensor gravity framework. This framework encompasses the overall structure of the non-minimally coupled scalar field functions for…
The study addresses matter-coupled modified gravity, particularly $f (T, \mathcal{T})$ gravity, unveiling distinct formalism. The research further discusses stability analysis, and the dynamical system approach, exploring the dynamics of…
In this work, we perform a detailed dynamical analysis for the cosmological applications of a nonminimal torsion-matter coupled gravity. Two alternative formalisms are proposed, which enable one to choose between the easier approach for a…
We investigate the evolution of linear perturbations in the Symmetric Teleparallel Gravity, namely $f(Q)$ gravity, for which we design the $f(Q)$ function to match specific expansion histories. We consider different evolutions of the…
In this work we try to understand the late time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe…
In this article, we investigate the modified symmetric teleparallel gravity or $f(Q)$ gravity, where $Q$ is the non-metricity, to study the evolutionary history of the universe by considering the functional form of $f(Q)=\alpha Q^n$, where…
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 $B$…
In this work, we have carried on dynamical system analysis of hessence field coupling with dark matter in $f(T)$ gravity. We have analysed the critical points due to autonomous system. The resulting autonomous system is non-linear. So, we…
The $f(Q,T)$ cosmological model has emerged as a promising framework for understanding various aspects of cosmic evolution. In this study, we focused on obtaining the constraints of the free parameters in the non-linear form of…
The so called $f(X)$ hybrid metric-Palatini gravity presents a unique viable generalisation of the $f(R)$ theories within the metric-affine formalism. Here the cosmology of the $f(X)$ theories is studied using the dynamical system approach.…
We present a systematic analysis of the dynamics of flat Friedmann-Lema\^{i}tre-Robertson-Walker cosmological models with radiation and dust matter in generalized teleparallel $f(T)$ gravity. We show that the cosmological dynamics of this…
New high-precision observations are now possible to constrain different gravity theories. To examine the accelerated expansion of the Universe, we used the newly proposed $f(Q,T)$ gravity, where $Q$ is the non-metricity, and $T$ is the…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
In this paper, the cosmological model of the Universe has been presented in $f(Q)$ gravity and the parameters are constrained from the cosmological data sets. At the beginning, we have employed a well motivated form of $f(Q) = \alpha +…
This work investigates the dynamical evolution of the universe within the framework of symmetric teleparallel $f(Q,\mathcal{T})$ gravity, where $Q$ is the non-metricity scalar and $\mathcal{T}$ is the trace of the energy-momentum tensor. We…
Cosmological approaches of autonomous dynamical system in the framework of $f(T)$ gravity are investigated in this paper. Our methods applied to flat Friedmann-Robertson-Walker equations in $f(T)$ gravity, consist to extract dynamical…