Related papers: Some remarks on the dynamical systems approach to …
We study higher-order theories of gravitation; in particular, we will focus our attention on the second-order theory, in which conformal symmetry can be implemented.
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and…
In this paper we show how the covariant gauge invariant equations for the evolution of scalar, vector and tensor perturbations for a generic $f(R)$-gravity theory can be recast in order to exploit the power of dynamical system methodology.…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
In this paper we study cosmological solutions of the $f(T,B)$ gravity using dynamical system analyses. For this purpose we consider cosmological viable functions of $f(T,B)$ that are capable of reproducing the dynamics of the Universe. We…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
We present a general procedure to solve the equations of motion for cosmological models driven by real scalar fields with first-order differential equations. The method seems to have great power, since it works for closed, flat or open…
Dynamical systems techniques are a powerful tool to analyse systems of ordinary differential equations, written in an appropriate form. For a given theory of gravity, the cosmological field equations typically lead to a system of ordinary…
Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's…
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…
Our first goal in this work is to study general and model-independent properties of cyclic cosmologies. The large number of studies of bouncing cosmologies and different cyclic scenarios published recently calls for a proper understanding…
We present two methods for describing, from a pedagogical point of view, the solutions of Einstein's equations applied to a homogeneous and isotropic universe. In the first method, we define an effective gravitational potential of the…
We describe what cosmology looks like in the context of the geometric theory of gravity (GSG) based on a single scalar field. There are two distinct classes of cosmological solutions. An interesting feature is the possibility of having a…
In the framework of the recently proposed models of massive gravity, defined with respect to a de Sitter reference metric, we obtain new homogeneous and isotropic solutions for arbitrary cosmological matter and arbitrary spatial curvature.…
We investigate the cosmological solutions of the $f(T)$ gravity theory using the method of dynamical systems. For this purpose a general form of the $f(T)$ function is considered and four conditions are defined that they have to satisfy in…
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 work investigates alternative theories of gravity, the solutions to their field equations and the constraints that can be imposed upon them from observation and experiment. Specifically, we consider the cosmologies and spherically…
We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in…
The Big Bang initial singularity problem can be solved by means of bouncing solutions. In the context of extended theories of gravity, we will look for covariant effective actions whose field equations contain up to fourth-order derivatives…
We argue that more cosmological solutions in massive gravity can be obtained if the metric tensor and the tensor $\Sigma_{\mu\nu}$ defined by St\"{u}ckelberg fields take the homogeneous and isotropic form. The standard cosmology with matter…