Related papers: On dynamical systems approaches and methods in $f(…
We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear…
In this paper, we investigate and analyze the cosmological dynamics of the universe, with an effect of modified $f(R)$ gravity emerging at cosmological scale. We choose the Einstein frame as a physical frame. We consider phase portraits of…
We consider the field equations for a flat FRW cosmological model, in a generic $f(R)$ gravity model and cast them into a, completely normalized-dimensionless, system of O.D.Es for the scale factor and the function $f(R)$, with respect to…
In this work, we use the dynamical system approach to explore the cosmological background evolution of the scalar-tensor representation of $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the stress-energy tensor. The…
We investigate the impact of conformal transformations on the physical properties of solution trajectories in nonmetricity gravity. Specifically, we explore the phase-space and reconstruct the cosmological history of a spatially flat…
In this work we shall investigate the cosmological dynamical system of $f(R)$ gravity, by constructing it in such a way so that it is rendered autonomous. We shall study the vacuum $f(R)$ gravity case, but also the case that matter and…
We propose a new model of modified $F(R)$ gravity theory with the function $F(R) = (1/\beta) \arcsin(\beta R)$. Constant curvature solutions corresponding to the flat and de Sitter spacetime are obtained. The Jordan and Einstein frames are…
We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory, where a scalar field is coupled to gravity. Matter is modelled by a $\gamma$-law perfect fluid, including false-vacuum energy as a special case. Through a…
We show that f(R)-gravity can, in general, give rise to cosmological viable models compatible with a matter-dominated epoch evolving into a late accelerated phase. We discuss the various representations of f(R)-gravity as an ideal fluid or…
This thesis investigates a toy model for inflation in a class of modified theories of gravity in the metric formalism. Instead of the standard procedure -- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from a…
Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the $\Lambda$CDM model, based on General Relativity and standard…
In this paper we apply dimensional analysis (D.A.) to two cosmological models: Einstein-de Sitter and one Friedmann-Robertson-Walker (FRW) with radiation predominance. We believe that this method leads to the simplest form of solution the…
We present a unified dynamical systems framework for spatially flat FLRW cosmology in $f(Q)$ gravity, covering all three connection branches via a single set of Hubble-normalised variables without fixing $f(Q)$ \textit{a priori}. This…
We extend the idea of unimodular gravity to the modified $f(R,T)$ theories. A new class of cosmological solutions, that the unimodular constraint on the metric imposes on the $f(R,T)$ theories, are studied. This extension is done in both…
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…
To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on…
We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lema\^itre-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of…
A new method of solving the Einstein-Friedmann dynamical equations of a spatially homogeneous and isotropic universe is presented. The method is applicable when the equation of state of the material content assumes the form P=(g -1) rho, g…
$F(R)$ inflationary models are analyzed without the Weyl transformation to the Einstein frame. Sufficient conditions for existence of global inflationary attractors in $F(R)$ models are provided. Following that, the procedure for…
A nonlocal gravity model which does not assume the existence of a new dimensional parameter in the action and includes a function $f(\Box^{-1} R)$, with $\Box$ the d'Alembertian operator, is studied. By specifying an exponential form for…