Related papers: Fractional Derivative Cosmology
Whereas the nature of dark components in the Universe remains unknown, alternative models of gravity have been developed to offer a geometric explanation to the origin of such components. In this work we use the Minimal Geometric…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the…
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…
This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so called gravitational optics. Besides Schr\"odinger Newton…
Recently, a new field of study called fractional cosmology has emerged. It uses fractional calculus to modify the standard derivative equations and change the Friedmann equations. The evolution of cosmic species densities is also affected…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…
If torsion exists, it generates gravitational four-fermion interaction (GFFI). This interaction gets dominating on the Planck scale. If one confines to the regular, axial-axial part of this interaction, the results do not comply with the…
We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework…
We present a toy model for extending the Friedmann equations of relativistic cosmology using fractional derivatives. We do this by replacing the integer derivatives, in a few well-known cosmological results with fractional derivatives…
The cosmological scale factor $a(t)$ of the flat-space Robertson-Walker geometry is examined from a Hamiltonian perspective wherein $a(t)$ is interpreted as an independent dynamical coordinate and the curvature density $\sqrt {- g(a)}…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background…
We consider a nonlinear parabolic equation of fractional order in space and propose its numerical discretization. The fractional derivative is defined through a functional analytic setting, rather than the traditional definition of…
We consider the evolution of a flat Friedmann-Roberstson-Walker Universe in a higher derivative theories, including $\alpha R^{2}$ terms to the Einstein-Hilbert action in the presence of a variable gravitational and cosmological constants.…
In a universe where, according to the standard cosmological models, some 97% of the total mass-energy is still "missing in action" it behooves us to spend at least a little effort critically assessing and exploring radical alternatives.…
We study the possibility to obtain cosmological late-time acceleration from a geometry changing with the scale, in particular, in the so-called multifractional theories with $q$-derivatives and with weighted derivatives. In the theory with…
It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to…
We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…