Related papers: A note on the dynamical system formulations in $f(…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
We investigate the cosmological behavior of mimetic F(R) gravity. This scenario is the F(R) extension of usual mimetic gravity classes, which are based on re-parametrizations of the metric using new, but not propagating, degrees of freedom,…
Instead of assuming a form of gravity and demand cosmology fit with $\Lambda CDM$, a potentially `viable' $f(R)$ gravity model is derived assuming an alternative model of cosmology. Taking the `designer' approach to $f(R)$, a new class of…
In this paper, we have performed the dynamical system analysis of $f(T)$ gravity cosmological models at both background and perturbation levels. We have presented three models pertaining to three distinct functional forms of $f(T)$. The…
We consider a model for gravity that is invariant under global scale transformations. It includes one extra real scalar field coupled non-minimally to the gravity fields. In this model all the dimensionful parameters like the gravitational…
We perform a phase space analysis of a non-minimally coupled modified gravity theory with the Lagrangian density of the form $\frac{1}{2} f_{1}(R)+[1+\lambda f_{2}(R)]{{\cal{L}}_{m}}$, where $f_1(R)$ and $f_2(R)$ are arbitrary functions of…
One of the so-called viable modified gravities is analyzed. This kind of gravity theories are characterized by a well behavior at local scales, where General Relativity is recovered, while the modified terms become important at the…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
Anisotropic cosmological models are investigated in the frame work of $f(R)$ gravity in the metric formalism. Plane symmetric models are considered to incorporate anisotropy in the expansion rates along different spatial directions. The…
The $f(T)$ gravity is one of the extensions of teleparallel equivalent of general relativity, in which more general functions of the torsion scalar $T$ can be described. With the proposed functional form of $f(T) = \alpha T - \beta u^{-n} +…
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades…
Using an approach that treats the Ricci scalar itself as a degree of freedom, we analyze the cosmological evolution within an f(R) model that has been proposed recently (exponential gravity) and that can be viable for explaining the…
In this work we shall investigate the occurrence of future cosmological finite-time singularities in the dynamical system corresponding to two cosmological theories, namely that of vacuum $f(R)$ gravity and that of three fluids. The vacuum…
A brief introduction on the issue of stability in generalized modified gravity is presented and the dynamical system methods are used in the investigation of the stability of spatially flat homogeneous cosmologies within a large class of…
Discrepancies between observations at early and late cosmic epochs, and the vacuum energy problem associated with the interpretation of cosmological constant, are questioning the $\Lambda$CDM model. Motivated by these conceptual and…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
The exploration of teleparallel gravity has been done from a dynamical systems point of view in order to be tested against the cosmological evolution currently observed. So far, the proposed autonomous systems have been restrictive over a…
This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…