Related papers: Fractional Action Cosmology with Power Law Weight …
We propose a new type of cosmological model derived from the fractional variational principle when it is applied to the gravitational sector of action functional. In contrast to the fractional cosmological model developed earlier by the…
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…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
The present work deals with a combined test of the so-called Fractional Action Cosmology (FAC) on the example of a specific model obtained by the author earlier. In this model, the effective cosmological term is proportional to the Hubble…
Fractional cosmology modifies the standard derivative to Caputo's fractional derivative of order $\mu$, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on $\mu$…
We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…
For the fractional action cosmological model, derived earlier by the author from the variational principle for a fractional action functional, the exact solutions are obtained. The case of a quasi - vacuum state of matter that fills the…
In modern cosmology, the curiosity of ultimately understanding the nature of the dark energy controlling the recent acceleration of the Universe motivates us to explore its properties by using some novel approaches. In this work, to explore…
I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the…
We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of fractality in the large scale structure of…
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…
We derive a model of dark energy which evolves with time via the scale factor. The equation of state $\omega=(1-2\alpha)/(1+2\alpha)$ is studied as a function of a parameter $\alpha$ introduced in this model. In addition to the recent…
In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 78, 024031 (2008)], a model of dark matter and dark energy based on the concept of gravitational polarization was investigated. This model was shown to recover the concordance…
The cosmological constant is the most economical candidate for dark energy. No other approach really alleviates the difficulties faced by the cosmological constant because, in all other attempts to model the dark energy, one still has to…
We consider that the cosmological constant is associated with the vacuum energy density of a particle physics model. In the path integral formalism of euclidean quantum gravity and in the background of the Robertson Walker metric we…
We investigate some basic applications of Fractional Calculus (FC) to Newtonian mechanics. After a brief review of FC, we consider a possible generalization of Newton's second law of motion and apply it to the case of a body subject to a…
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…
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…
Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in…