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S. M. M. Rasouli

Publications and source records attributed to S. M. M. Rasouli.

At least 19 recordsLinked to original sources
arXiv2026

Evolution of density perturbations in fractional cosmology

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 memory effects in the dynamics. Working in the matter-dominated era and adopting a covariant fluid-flow approach, we derive the modified growth equation for the density contrast and obtain exact analytical solutions. The resulting dynamics depends explicitly on the fractional parameter $α$ and smoothly reduces to the corresponding standard case in the limit $α=1$. We show that the model admits both growing and decaying modes, and we identify the parameter range in which structure formation is physically viable. Focusing on the growing mode, we compute the evolution of density fluctuations from recombination to the present epoch. By confronting theoretical predictions with observational constraints from large-scale structure, in particular the $σ_8$ normalization and the Sachs-Wolfe effect, we derive a stringent upper bound on the fractional parameter, $α\lesssim1.07$, which significantly improves upon previous constraints obtained at the background level. Our results show that the growth of density perturbations exhibits distinct fractional signatures, providing a sensitive observational probe of the underlying framework.

gr-qc↗
arXiv2026

Emergent inflation in fractional cosmology

We investigate the evolution of the early universe within the proposed fractional cosmological framework. The underlying formulation is conceptually rooted in generalized measure constructions, closely related to fractal geometries and scale-dependent effective dimensions. Within this framework, the cosmological dynamics are governed by a single fractional deformation parameter $α$, without introducing additional propagating dynamical degrees of freedom. Guided by the physical requirements, we identify a minimal fractional potential that, together with the fractional time-dependent kernel, leads to a non-singular pre-inflationary phase, a stable quasi-de Sitter inflationary attractor, followed by a graceful exit and a smooth transition to the standard radiation-dominated era. We further establish an explicit relation between the number of e-folds and the fractional parameter, demonstrating that observationally viable inflationary solutions arise for a well-defined range of $α$, thereby providing a direct connection between fractional cosmological dynamics and early universe phenomenology while resolving the horizon problem. Unlike conventional inflationary scenarios requiring an external inflaton field, the inflationary phase emerges entirely from the fractional modification of the Newtonian framework. Together with the previously established fractional cosmological framework describing the subsequent matter-dominated and late-time accelerated epochs, the present work completes the background cosmological evolution within a unified framework extending from the pre-inflationary universe to the present cosmic acceleration.

gr-qc↗
arXiv2026

Emergent $Λ$CDM cosmology from a measure-induced deformation of the Newtonian action

We propose a minimal extension of the Newtonian action by introducing a time-dependent fractional kernel characterized by a single deformation parameter $α$. This kernel admits a natural interpretation as a nontrivial integration measure defined by a time-dependent kernel, placing the formulation within measure-based approaches to anomalous or fractal dynamics. Despite the appearance of a friction-like term in the equations of motion, a conserved quantity is still obtained, containing a memory-like fractional kinetic energy contribution. Moreover, by generalizing the standard Newtonian potential to an effective $α$-dependent potential induced by the underlying measure, the resulting cosmological equations exhibit an effective correspondence with relativistic FLRW cosmology at the level of background dynamics. In the limit $α=1$, the framework reduces to standard Newtonian cosmology. We show that, with a single unified potential, the matter-dominated, radiation-dominated, and present accelerated phases are obtained self-consistently, while the latter two epochs cannot be described within standard Newtonian cosmology. The structural presence of $α$ in all physical observables allows theoretical and observational constraints to be imposed, indicating compatibility with observational data in the regime where $α$ is close to unity. Within this framework, an effective cosmological constant naturally arises, controlled by the small deviation of $α$ from the Newtonian limit. These results show that the proposed fractional framework can effectively reproduce the main background dynamical features of $Λ$CDM cosmology through a simple measure-induced deformation of the Newtonian action.

gr-qc↗
arXiv2026

Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology

Three theoretically plausible techniques to developing a fractional scalar field cosmological model are pointed in this paper; the time-dependent kernel weighted action being then selected. Upon this choice, we proceed to establish (i) a time weighted action associated with the generalized scalar field cosmology; and (ii) a fractional cosmological model in $n$ dimensions considering the FLRW metric and a generalized version of the Sáez-Ballester (SB) theory. Our study focuses on the following purposes. Firstly, to investigate the fundamental gravitational structural features of the model, we analyze the dynamical behavior of the field equations, the fulfillment of the Bianchi identities, the associated conservation laws, and the application of the second Noether theorem at the background and first-order perturbation levels. Moreover, the model's distinguishing characteristics and theoretical differences from the corresponding standard scenarios are also investigated. Secondly, we aim to obtain exact analytical solutions and analyze the time evolution of key cosmological quantities, considering the fractional parameter effects. Furthermore, the model's predictions are compared with those of the corresponding standard models. Lastly, we propose new ideas to further generalize our model, with a focus on constructing an effective potential and investigating the conditions under which bounce solutions may emerge.

gr-qc↗
arXiv2026

A minimal fractional deformation of Newtonian gravity

We consider a minimal fractional deformation of Newtonian gravity characterized by a single parameter $α$. In the limit $α\to 1$, the theory reduces to standard Newtonian gravity. Previous works showed that the $Λ$CDM cosmology consistently emerges from this framework. Using a single potential, the model reproduces the full sequence of cosmic evolution (from a nonsingular pre--inflationary phase and a stable inflationary attractor to the radiation- and matter-dominated eras and the present accelerated expansion) and accounts for the growth of large-scale structure for $|α-1|\ll1$, in agreement with current observations. Here we show that the same fractional Newtonian model also describes key weak--field tests, including the perihelion precession of Mercury and the gravitational deflection of light, using a unified potential with the same constraint on $α$. These results suggest that the minimal fractional Newtonian framework may provide a unified phenomenological description of gravitational dynamics from Solar-System scales to cosmology. Finally, this fractional cosmological framework may offer new perspectives on problems such as the cosmological constant, the hierarchy of cosmological scales, and the Hubble tension.

gr-qc↗
arXiv2025

White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era

The unification of quantum mechanics and general relativity has long been elusive. Only recently have empirical predictions of various possible theories of quantum gravity been put to test, where a clear signal of quantum properties of gravity is still missing. The dawn of multi-messenger high-energy astrophysics has been tremendously beneficial, as it allows us to study particles with much higher energies and travelling much longer distances than possible in terrestrial experiments, but more progress is needed on several fronts. A thorough appraisal of current strategies and experimental frameworks, regarding quantum gravity phenomenology, is provided here. Our aim is twofold: a description of tentative multimessenger explorations, plus a focus on future detection experiments. As the outlook of the network of researchers that formed through the COST Action CA18108 ``Quantum gravity phenomenology in the multi-messenger approach (QG-MM)'', in this work we give an overview of the desiderata that future theoretical frameworks, observational facilities, and data-sharing policies should satisfy in order to advance the cause of quantum gravity phenomenology.

gr-qc↗
arXiv2024

Phase space noncommutativity, power-law inflation and quantum cosmology

Considering an arbitrary dimensional FLRW universe in the framework of a generalized Sáez--Ballester (SB) theory, we establish a noncommutative (NC) cosmological model. We concentrate on the predictions of NC model and compare them with their commutative counterparts in both the classical and quantum regimes. For the classic case, taking a very small NC parameter, we apply two different methods to analyze the model features. First, we show through numerical analysis that our NC model is a successful inflationary model capable of overcoming the graceful exit and horizon problems. Furthermore, the NC traces are visible the late time, which supports the UV/IR mixing characteristic of the NC models. In the second method, we show that our NC model can correspond to the previously developed NC inflationary models. In the commutative quantum case, we obtain an exact wave function and then use the WKB approximation to show that the solutions of the corresponding classical regime are recovered. Finally, with regard to the NC quantum level, we focus on the special case for which we show that a constant of motion exists. The latter helps us to conveniently transform the corresponding complicated NC-WDW equation into an ordinary differential equation, which can be easily solved numerically for the general case or analytically for some special cases. The resultant solutions show a damping behavior in the wave function associated with the proposed NC model, which may be important in determining the viable initial states for the very early universe.

gr-qc↗
arXiv2024

Fractional Scalar Field Cosmology

Considering the Friedmann--Lemaître--Robertson--Walker (FLRW) metric and the Einstein scalar field system as an underlying gravitational model to construct fractional cosmological models has interesting implications in both classical and quantum regimes. Regarding the former, we just review the most fundamental approach to establishing an extended cosmological model. We demonstrate that employing new methodologies allows us to obtain exact solutions. Despite the corresponding standard models, we cannot use any arbitrary scalar potentials; instead, it is determined from solving three independent fractional field equations. This article concludes with an overview of a fractional quantum/semi-classical model that provides an inflationary scenario.

gr-qc↗
arXiv2023

Inflation and fractional quantum cosmology

The Wheeler--DeWitt equation for a flat and compact Friedmann--Lemaître--Robertson--Walker cosmology at the pre-inflation epoch is studied in the contexts of the standard and fractional quantum cosmology. Working within the semiclassical regime and applying the WKB approximation, we show that some fascinating consequences are obtained for our simple fractional scenario that are completely different from their corresponding standard counterparts: (i) The conventional de Sitter behavior of the inflationary universe for constant potential is replaced by a power-law inflation. (ii) The non-locality of the Riesz's fractional derivative produces a power-law inflation that depends on the fractal dimension of the compact spatial section of space-time, independent of the energy scale of the inflaton.

gr-qc↗
arXiv2022

Geodesic deviation in Saez--Ballester theory

We study the geodesic deviation (GD) equation in a generalized version of the Sáez--Ballester (SB) theory in arbitrary dimensions. We first establish a general formalism and then restrict to particular cases, where (i) the matter-energy distribution is that of a perfect fluid, and (ii) the spacetime geometry is described by a vanishing Weyl tensor. Furthermore, we consider the spatially flat FLRW universe as the background geometry. Based on this setup, we compute the GD equation as well as the convergence condition associated with fundamental observers and past directed null vector fields. Moreover, we extend that framework and extract the corresponding geodesic deviation in the \emph{modified} Sáez--Ballester theory (MSBT), where the energy-momentum tensor and potential emerge strictly from the geometry of the extra dimensions. In order to examine our herein GD equations, we consider two novel cosmological models within the SB framework. Moreover, we discuss a few quintessential models and a suitable phantom dark energy scenario within the mentioned SB and MSBT frameworks. Noticing that our herein cosmological models can suitably include the present time of our Universe, we solve the GD equations analytically and/or numerically. By employing the correct energy conditions plus recent observational data, we consistently depict the behavior of the deviation vector $η(z)$ and the observer area distance $r_0(z)$ for our models. Concerning the Hubble constant problem, we specifically focus on the observational data reported by the Planck collaboration and the SH0ES collaboration to depict $η(z)$ and $r_0(z)$ for our herein phantom model. Subsequently, we contrast our results with those associated with the $Λ$CDM model.

gr-qc↗
arXiv2022

Noncompactified Kaluza--Klein Gravity

We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space-Time-Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans-Dicke theory and the modified Sáez-Ballester theory are briefly explained. Finally, we apply the latter to the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological models in arbitrary dimensions and analyze the corresponding solutions.

gr-qc↗
arXiv2022

Generating CP violation from a modified Fridberg-Lee model

The overall characteristics of the solar and atmospheric neutrino oscillations are approximately consistent with a tribimaximal form of the mixing matrix $U$ of the lepton sector. Exact tribimaximal mixing leads to $θ_{13}=0$. However, the results from the Daya Bay and RENO experiments have established, such that in comparison to the other neutrino mixing angles, $θ_{13}$ is small. Moreover, the atmospheric and solar mass splitting differ by two orders of magnitude. These significant differences constitutes the great enthusiasm and main motivation for our research herein reported. Keeping the leading behavior of U as tribimaximal. We would make a response to the following questions: at some level, whether or not the small parameters such as the solar neutrino mass splitting and $U_{e3}$, which vanish in a new framework, can be interpreted as a modified FL neutrino mass model? Subsequently, a minimal single perturbation leads to nonzero values for both of them? Our minimal perturbation matrix is constructed solely from computing the third mass eigenstate, using the rules of perturbation theory. Let us point out that in contrast with~\cite{my}, this matrix is not ad hoc assumed, but is instead built following a series of steps we will outline. Also in compared to the original FL neutrino mass model which generalize it by inserting phase factors, our work is more accurate. Subsequently, we produce the following results that add new contributions to the literature: a) we obtain a realistic neutrino mixing matrix with $δ\neq0$ and $θ_{23}=45^\circ$; b) the solar mass splitting term is dominated by an imaginary term, which could induce the existence of Majorana neutrinos, along with explaining a large CP violation in nature.

hep-ph↗
arXiv2022

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate the value of this promising tool. Concretely, we take a spatially flat FRW model in the presence of a single scalar field, minimally coupled to gravity. Then, we extract the associated Schrödinger-Wheeler-DeWitt equation, allowing for a particular scope of factor ordering. Subsequently, we compute the corresponding supersymmetric partner Hamiltonians, $H_1$ and $H_2$. Moreover, we point out how the shape invariance property can be employed to bring a relation among several factor orderings choices for our Schrödinger-Wheeler-DeWitt equation. The ground state is retrieved, and the excited states easily written. Finally, the Hamiltonians, $H_1$ and $H_2$ are explicitly presented within a $N=2$ supersymmetric quantum mechanics framework.

gr-qc↗
arXiv2022

Two-zero textures based on $A_4$ symmetry and unimodular mixing matrix

Applying the $A_4$ symmetry in the scenario of unimodular second scheme of trimaximal $TM_2$ mixing matrix, where the charged lepton mass matrix is diagonal and the nature of neutrinos are Majorana, we investigate and analyze feasible two zeros neutrino mass matrices. Among the seven possible two-zero textures with $A_4$ symmetry, we have found that only two textures, namely the texture with $(e, e)$ and $(e,μ)$ vanishing element of mass matrix and its permutation, are consistent with the experimental data in the non-perturbation method. We also obtain new significant relations between phases of our model, namely $ρ+σ=ϕ\pmπ$ and $\sin^2{θ_{13}}=\frac{2}{3}R_ν$ where $R_ν=\frac{δm^2}{Δm^2}$. Subsequently, by admitting the experimental ranges of $R_ν$, we retrieve the allowed range of the unknown phase $ϕ$. Such a procedure assist us to determine the ranges of all the neutrino observable parameters, the masses of neutrinos, the CP-violating phases and $J$ parameter as well as to predict the normal hierarchy for the neutrino mass. Finally, we show that our predictions with respect to our herewith reported specific textures are consistent with the corresponding data reported from neutrino oscillation, cosmic microwave background and neutrinoless double beta decay experiments.

hep-ph↗
arXiv2022

Noncommutativity, Saez-Ballester theory and kinetic inflation

This paper presents a noncommutative (NC) version of an extended Sáez-Ballester (SB) theory. Concretely, considering the spatially flat Friedmann-Lema\^ıtre-Robertson-Walker~(FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and applying the Hamiltonian formalism, obtain deformed equations of motion. In our model, the NC parameter appears linearly in the deformed Poisson bracket and the equations of the NC SB cosmology. When it goes to zero, we get the corresponding commutative counterparts. Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; (ii) for the late times, there is a zero acceleration epoch. By establishing an appropriate dynamical framework, we show that the results (i) and (ii) can be obtained for many sets of the initial conditions and the parameters of the model. Finally, we indicate that, at the level of the field equations, one may find a close resemblance between our NC model and the Starobinsky inflationary model.

gr-qc↗
arXiv2021

Geodesic deviation equation in Brans-Dicke theory in arbitrary dimensions

In this paper, we study the geodesic deviation equation (GDE) within the context of the Brans-Dicke (BD) theory in $D$ dimensions. Then, we restrict our attention to the GDE for the fundamental observers and null vector field past directed. Concerning the latter, in order to apply the retrieved GDE for the cosmological models as well as examining exact solutions, we study some cosmological models in general relativity (GR) and in the context of the BD theory. For the BD framework, we provide two appropriate settings for dynamical system, which can be considered as the most extended case scenarios with respect to those studied previously. Then, we investigate a few well-known BD cosmological models, for which we present the modified and corrected exact solutions. Moreover, we show that the retrieved formalism of the GDE can also be properly applicable for the modified BD theory (MBDT), whose matter and potential emerge from the geometry. For all of our herein cosmological models, we investigate the energy conditions and depict the behavior of the deviation vector and observer area distance. We demonstrate that why the MBDT can be considered as a more appropriate candidate to describe the universe in accordance with the observational data as well as from theoretical viewpoint.

gr-qc↗
arXiv2021

Broadening quantum cosmology with a fractional whirl

We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically, we investigate and then discuss a model of stiff matter in a spatially flat homogeneous and isotropic universe. A new quantum cosmological solution, where fractional calculus implications are explicit, is presented and then contrasted with the corresponding standard quantum cosmology setting.

gr-qc↗