Related papers: On observational signatures of multi-fractional th…
We investigate the evolution of matter density perturbations within a fractional cosmological framework inspired by fractal space-time constructions in field theory, where a deformation of the integration measure induces non-locality and…
We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with $q$-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints…
In this paper, we explore a fractal model of the universe proposed by Calcagni [JHEP{\bf03}(2010)120] for a power-counting renormalizable field theory living in a fractal spacetime. Considering a timelike fractal profile, we derived field…
We compare a large suite of theoretical cosmological models to observational data from the cosmic microwave background, baryon acoustic oscillation measurements of expansion, Type Ia SNe measurements of expansion, redshift space distortion…
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…
A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The…
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters $H_0$ (Hubble constant) and $q$ (deceleration parameter). We investigate the constraints on these parameters using the…
We study the accelerated expansion phase of the universe by using the {\textit{kinematic approach}}. In particular, the deceleration parameter $q$ is parametrized in a model-independent way. Considering a generalized parametrization for…
The cosmic deceleration parameter $q$ has been reconstructed in a non-parametric way using various combinations of recent observational datasets. The Pantheon compilation of the Supernova (SN) distance modulus data, the Cosmic Chronometer…
In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale $q-$derivative in the non-extensive statistical mechanics and the axiomatic metric…
We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) $q$-derivatives. Both theories can be formulated in two different frames, called fractional…
The dynamics of expansion of the Universe and evolution of scalar perturbations are studied for the quintessential scalar fields $Q$ with the classical Lagrangian satisfying the additional condition $w=const$ or $c^2_a=0$. Both…
The recent extension of the Hubble diagram of Supernovae and quasars to redshifts much higher than 1 prompted a revived interest in non-parametric approaches to test cosmological models and to measure the expansion rate of the Universe. In…
Recently, we have demonstrated that there exists a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis' scenario, with a local form of…
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…
The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally…
Considering a well-motivated $f(R)$ modified-gravity model, in which an exponential function of the curvature is included, in this paper we implement a statistical data analysis to set constraints on the parameters of the model, taking into…
By means of the present geometrical and dynamical observational data, it is very hard to establish, from a statistical perspective, a clear preference among the vast majority of the proposed models for the dynamical dark energy and/or…
Current measurements of the Hubble constant $H_0$ on scale less than $\sim100$ Mpc appear to be controversial, while the observations made at high redshift seem to provide a relatively low value. On the other hand, the Hubble expansion is…
This paper is a review on the observational Hubble parameter data that have gained increasing attention in recent years for their illuminating power on the dark side of the universe --- the dark matter, dark energy, and the dark age.…