Related papers: Revisiting Fractional Cosmology
The effective evolution of an inhomogeneous universe model in Einstein's theory of gravitation may be described in terms of spatially averaged scalar variables. This evolution can be modeled by solutions of a set of Friedmann equations for…
We present an alternative cosmology based on conformal gravity, as originally introduced by H. Weyl and recently revisited by P. Mannheim and D. Kazanas. Unlike past similar attempts our approach is a purely kinematical application of the…
We use higher derivative classical gravity to study the nonlinear coupling between the cosmological expansion of the universe and metric oscillations of Planck frequency and very small amplitude. We derive field equations at high orders in…
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…
We consider a class of metric f(R) modified gravity theories, analyze them in the context of a Friedmann-Robertson-Walker cosmology and confront the results with some of the known constraints imposed by observations. In particular, we focus…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
We investigate the cosmological applications of Myrzakulov $F(R,T)$ gravity. In this theory ones uses a specific but non-special connection, and thus both curvature and torsion are dynamical fields related to gravity. We introduce a…
We study a universe filled with cold dark matter in the form of discrete inhomogeneities (e.g., galaxies) and dark energy in the form of a continuous perfect fluid. We develop a first-order scalar perturbation theory in the weak gravity…
The paper deals with a dynamical system analysis related to phantom cosmological model . Here gravity is coupled to phantom scalar field having scalar coupling function and a potential. The field equations are reduced to an autonomous…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
In this paper, we derive the field equations of modified Gauss-Bonnet gravity termed as $f(R,G)$ gravity for the non-flat Friedmann-Robertson-Walker (FRW) spacetime. We utilize the dynamical system approach to study the cosmic dynamics of…
Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the…
A new formalism is presented for finding equilibrium distribution functions for axisymmetric systems. The formalism, obtainded by using the concept of fractional derivatives, generalizes the methods of Fricke (1952), Kalnajs (1972) and…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
Cosmological solutions of the equations with scalar interaction are being studied. It is shown, that the scalar field can effectively change the equation of state of statistical system, that leads to series of cosmological consequences.