Related papers: Revisiting Fractional Cosmology
As the universe expands astronomical observables such as brightness and angular size on the sky change in ways that differ from our simple Cartesian expectation. We show how observed quantities depend on the expansion of space and…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
This thesis investigates the characteristics of modified teleparallel gravity models that incorporate a scalar field and a trace of the energy-momentum tensor, with particular attention to their cosmological effects, especially regarding…
Assuming a fractal distribution of matter in the universe, consequences that follow from the General Theory of Relativity and the Copernican Principle for fractal cosmology are examined. The change in perspective necessary to deal with a…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
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)}…
The investigation of quantum gravity effects in order to avoid the big bang singularity is a requisite, so that the idea of oscillating universes is introduced as an alternative for standard cosmological model. Therefore, the Friedmann…
A spacetime interval connecting two neighbouring points can be measured in different unit systems. For instance, it can be measured in atomic unit defined in terms of fundamental constants existing in quantum theories. It is also possible…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
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…
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part…
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…
In this work, we investigate the dynamics of the interacting dark energy and dark matter in viable models of $f(R)$ gravity by using a standard framework of dynamical system analysis. A simple form of the interacting dark energy $Q=3\alpha…
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…
We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann…
We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical…
The transformation of the partial fractional derivatives under spatial rotation in $R^2$ are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed…
The manner in which one approaches the interface between gravitation and quantum theory is influenced by one's posture regarding quantum mechanics and the issues that revolve about its interpretational problems. We discuss here the way in…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
We consider different deductions of the mysterious Weinberg formula and show that this leads us back to the model of fluctuational cosmology which correctly predicted in advance, dark energy driven, accelerating universe with a small…