arXiv subjects

K. Nozari

Publications and source records attributed to K. Nozari.

At least 19 recordsLinked to original sources

arXiv2024

Linear-Quadratic GUP and Thermodynamic Dimensional Reduction

In this paper we investigate the statistical mechanics within the Linear-Quadratic GUP (LQGUP, i.e, GUP with linear and quadratic terms in momentum) models in the semiclassical regime. Then, some thermodynamic properties of a system of 3-dimensional harmonic oscillators are investigated by calculating the deformed partition functions. According to the equipartition theorem, we show that the number of accessible microstates decreases sharply in the very high temperatures regime. When the thermal de Broglie wavelength is of the order of the Planck length, three degrees of freedom are frozen in this setup. In other words, it is observed that there is an effective reduction of the degrees of freedom from 6 to 3 for a system of 3D harmonic oscillators in this framework. The calculations are carried out using both approximate analytical and exact numerical methods. The results of the analytical method are also presented in the form of thermal wavelengths for better understanding. Finally, the case of a 2-dimensional harmonic is treated as another example to comprehend the results, leading to a reduction of the degrees of freedom from 4 to 2.

gr-qc↗

arXiv2024

Quantum Gravity Effects on the Tachyon Inflation from Thermodynamic Perspective

By considering the Friedmann equations emerging from the entropy-area law of black hole thermodynamics in the context of the generalized uncertainty principle, we study tachyon inflation in the early universe. The presence of a minimal length modifies the Friedmann equations and hence the slow-roll and perturbation parameters in the tachyon model. These modifications, though small, affect the viability of the tachyon inflation in confrontation with observational data. We compare the numerical results of the model with Planck2018 TT, TE, EE +lowE+lensing+BAO+BK14(18) data and Planck2018 TT, TE,EE +lowE+lensing+BK14(18) +BAO+LIGO $\&$ Virgo2016 data at $68\%$ and $95\%$ CL. We show that while the tachyon inflation with power-law, inverse power-law and inverse exponential potentials is not observationally viable in comparison with the $1σ$ and $2σ$ confidence levels of the new joint data, in the presence of the minimal length the model becomes observationally viable.

astro-ph.CO↗

arXiv2020

Thermostatistics with an Invariant Infrared Cutoff

Quantum gravitational effects may affect the large scale dynamics of the universe. Phenomenologically, quantum gravitational effect at large distances can be encoded in an extended uncertainty principle that admits a minimal measurable momentum/energy or a maximal length. This maximal length can be considered as the size of the cosmological horizon today. In this paper we study thermostatistics of an expanding universe as a gaseous system and in the presence of an invariant infrared cutoff. We also compare the thermostatistics of different eras of the evolution of the universe in two classes, Fermions and Bosons.

gr-qc↗

arXiv2019

Probing Planck Scale Spacetime By Cavity Opto-Atomic $^{87}$Rb Interferometry

The project of \emph{"quantum spacetime phenomenology"} focuses on searching pragmatically for the Planck scale quantum features of spacetime. Among these features is the existence of a characteristic length scale addressed commonly by effective approaches to quantum gravity (QG). This characteristic length scale could be realized, for instance and simply, by generalizing the standard Heisenberg uncertainty principle (HUP) to a \emph{"generalized uncertainty principle"} (GUP). While usually it is expected that phenomena belonging to the realm of QG are essentially probable solely at the so-called Planck energy, here we show how a GUP proposal containing the most general modification of coordinate representation of the momentum operator could be probed by a \emph{"cold atomic ensemble recoil experiment"} (CARE) as a low energy quantum system. This proposed atomic interferometer setup has advantages over the conventional architectures owing to the enclosure in a high finesse optical cavity which is supported by a new class of low power consumption integrated devices known as \emph{"micro-electro-opto-mechanical systems"} (MEOMS). The proposed system comprises of a micro mechanical oscillator instead of spherical confocal mirrors as one of the components of high finesse optical cavity. In the framework of a bottom-up QG phenomenological viewpoint and by taking into account the measurement accuracy realized for the fine structure constant (FSC) from the Rubidium ($^{87}$Rb) CARE, we set some constraints as upper bounds on the characteristic parameters of the underlying GUP. In the case of superposition of the possible GUP modification terms, we managed to set a tight constraint as $0.999978<λ_0<1.00002$ for the dimensionless characteristic parameter.

hep-ph↗

arXiv2018

Realization of blue spectrum in generalized Galileon super-inflation models

In the spirit of Galileon inflation and by considering some sorts of non-canonical kinetic terms in the action, we realize a stage of super-inflation leading to a blue-tilted tensor perturbation. We show also that addition of Galileon-like term to the action leads to avoidance of ghost instabilities in this setup.

gr-qc↗

arXiv2017

A new bound on polymer quantization via an opto-mechanical setup

The existence of a minimal measurable length as a characteristic length in the Planck scale is one of the main features of quantum gravity and has been widely explored in the context. Various different deformations of spacetime have been employed successfully for the purpose. However, polymer quantization approach is a relatively new and dynamic field towards the quantum gravity phenomenology, which emerges from the symmetric sector of the loop quantum gravity. In this article, we extend the standard ideas of polymer quantization to find a new and tighter bound on the polymer deformation parameter. Our protocol relies on an opto-mechanical experimental setup that was originally proposed in Ref.\cite{ref:Igor} to explore some interesting phenomena by embedding the minimal length into the standard canonical commutation relation. We extend this scheme to probe the \emph{polymer length} deformed canonical commutation relation of the center of mass mode of a mechanical oscillator with a mass around the Planck scale. The method utilizes the novelty of exchanging the relevant mechanical information with a high intensity optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of the current technologies and, thus, it could uncover a decent realization of quantum gravitational phenomena thorough a simple table-top experiment.

gr-qc↗

arXiv2017

Cosmological Inflation in a Generalized Unimodular Gravity

We study some aspects of cosmological inflation in the framework of unimodular $f(R)$ gravity. To be more clarified, we consider a generic $f(R)$ of the type $f(R)=R+αR^{n}$. By considering Einstein frame counterpart of the unimodular $f(R)$ gravity, we set the scalaron to be responsible for cosmological inflation in this setup. We confront our model parameters space with observational data and impose some constraints on the value of $n$ in this manner. We show that for the number of e-folds $N=60$, the model is consistent with observation if $1.89<n<1.918$.

gr-qc↗

arXiv2017

Unimodular $f(R,T)$ Gravity

We extend the idea of unimodular gravity to the modified $f(R,T)$ theories. A new class of cosmological solutions, that the unimodular constraint on the metric imposes on the $f(R,T)$ theories, are studied. This extension is done in both Jordan and Einstein frames. We show that while the Lagrange multiplier (that imposes the unimodular constraint on the action) depends on the cosmic time in Jordan frame and therefore, can act as an evolving scalar field in the universe history, in the Einstein frame it acts as a cosmological constant. Then a general reconstruction method is used to realize an explicit form of the unimodular $f(R,T)$ corresponding to a given cosmological solution. By adopting a specific form of $f(R,T)$, the issue of cosmological inflation is studied in this setup. To see the observational viability of this model, a numerical analysis on the model parameter space is done in the background of Planck2015 observational data.

gr-qc↗

arXiv2016

Gravity's rainbow: a bridge between LQC and DSR

The doubly special relativity (DSR) theories are investigated in order to take into account an observer-independent length scale in special relativity framework. It is widely believed that any quantum theory of gravity would reduce to a DSR model at the flat limit when purely gravitational and quantum mechanical effects are negligible. Gravity's rainbow is a simple generalization of DSR theories to incorporate gravity. In this paper, we show that the effective Friedmann equations that are suggested by loop quantum cosmology (LQC) can be exactly reobtained in rainbow cosmology setup. The deformed geometry of LQC then completely fixes the modified dispersion relation and results in unique DSR model. In comparison with standard LQC scenario where only the geometry is modified, both of the geometry and matter parts get modifications in our setup. In this respect, we find that the total number of microstates for the universe is finite which suggests the statistical origin for the energy and entropy density bounds. These results explicitly show that the DSR theories are appropriate candidates for the flat limit of loop quantum gravity.

gr-qc↗

arXiv2016

Photon gas thermodynamics in dS and AdS momentum spaces

In this paper, we study thermostatistical properties of a photon gas in the framework of two deformed special relativity models defined by the cosmological coordinatizations of the de Sitter (dS) and anti-de Sitter (AdS) momentum spaces. The dS model is a doubly special relativity theory in which an ultraviolet length scale is invariant under the deformed Lorentz transformations. For the case of AdS model, however, the Lorentz symmetry breaks at the high energy regime. We show that the existence of a maximal momentum in dS momentum space leads to maximal pressure and temperature at the thermodynamical level while maximal internal energy and entropy arise for the case of the AdS momentum space due to the existence of a maximal kinematical energy. These results show the thermodynamical duality of these models much similar to their well-known kinematical duality.

gr-qc↗

arXiv2016

Scalar perturbation potentials in a homogeneous and isotropic Weitzenböck geometry

We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory, perturbations are the result of small fluctuations in the tetrad field. The tetrad transforms as a vector in both its holonomic and anholonomic indices. As a result, in the gauge invariant formalism, physical degrees of freedom are those combinations of perturbation parameters which remain invariant under a diffeomorphism in the coordinate frame, followed by an arbitrary rotation of the local inertial (Lorentz) frame. We derive these gauge invariant perturbation potentials for scalar perturbations and present the gauge invariant field equations governing their evolution.

gr-qc↗

arXiv2016

Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology

Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and Bohmian interpretation of quantum cosmology.

gr-qc↗

arXiv2016

Early universe thermostatistics in curved momentum spaces

The theories known as doubly special relativity are introduced in order to take into account an observer-independent length scale and the speed of light in the framework of special relativity. These theories can be generally formulated on the de Sitter and also recently proposed anti-de Sitter momentum spaces. In the context of these theories, we study the statistical mechanics and to do this, we consider the natural measure on the corresponding extended phase space. The invariant measure on the space of distinct microstates is obtained by restriction of the natural measure of the extended phase space to the physical phase space through the disintegration theorem. Having the invariant measure, one can study the statistical mechanics in an arbitrary ensemble for any doubly special relativity theory. We use the constructed setup to study the statistical properties of four doubly special relativity models. Applying the results to the case of early universe thermodynamics, we show that one of these models that is defined by the cosmological coordinatization of anti-de Sitter momentum space, implies a finite total number of microstates. Therefore, without attribution to any ensemble density and quite generally, we obtain entropy and internal energy bounds for the early radiation dominated universe. We find that while these results cannot be supported by the standard Friedmann equations, they indeed are in complete agreement with the nonsingular effective Friedmann equations that arise in the context of loop quantum cosmology.

gr-qc↗

arXiv2015

Bounds on quantum gravity parameter from the $SU(2)$ NJL effective model of QCD

Existence of a minimal measurable length, as an effective cutoff in the ultraviolet regime, is a common feature of all approaches to the quantum gravity proposal. It is widely believed that this length scale will be of the order of the Planck length $λ=λ_0\,l_{_{\rm Pl}}$, where $λ_0\sim{\mathcal O}(1)$ is a dimensionless parameter that should be fixed only by the experiments. This issue can be taken into account through the deformed momentum spaces with compact topologies. In this paper, we consider minimum length effects on the physical quantities related to three parameters of the $SU(2)$ Nambu-Jona-Lasinio effective model of QCD by means of the deformed measure which is defined on compact momentum space with ${\mathbf S}^3$ topology. This measure is suggested by the doubly special relativity theories, Snyder deformed spaces, and the deformed algebra that is obtained in the light of the stability theory of Lie algebras. Using the current experimental data of the particle physics collaboration, we constraint quantum gravity parameter $λ_0$ and we compare our results with bounds that are arisen from the other experimental setups.

gr-qc↗

arXiv2015

On the Stability of Einstein Static Universe in Doubly General Relativity Scenario

By presenting a relation between average energy of the ensemble of probe photons and energy density of the Universe, in the context of {\it gravity's rainbow} or {\it doubly general relativity} scenario, we introduce a rainbow FRW Universe model. By analyzing the fixed points in flat FRW model modified by two well known rainbow functions, we find that the finite time singularity avoidance (i.e. Big-Bang) may still remain as a problem. Then, we follow the "Emergent Universe" scenario in which there is no beginning of time and consequently there is no Big-Bang singularity. Moreover, we study the impact of a high energy quantum gravity modifications related to the gravity's rainbow on the stability conditions of an "Einstein static Universe" (ESU). We find that independent of a particular rainbow function, the positive energy condition dictates a positive spatial curvature for the Universe. In fact, without raising a nonphysical energy condition in the quantum gravity regimes, we can address an agreement between gravity's rainbow scenario and basic assumption of modern version of "Emergent Universe". We show that in the absence and presence of an energy-dependent cosmological constant $Λ(ε)$, a stable Einstein static solution is available versus the homogeneous and linear scalar perturbations under the variety of obtained conditions. Also, we explore the stability of ESU against the vector and tensor perturbations.

gr-qc↗

arXiv2015

Braneworld Cosmological Perturbations in Teleparallel Gravity

We describe the fully gauge invariant cosmological perturbation equations in braneworld teleparallel gravity. In this theory, perturbations are the result of small fluctuations in the pentad field. We derive the gauge invariant 'potentials' for both geometric and matter variables. Unlike the metric fluctuations in general relativity, pentad perturbations can only contain scalar and vector modes. As a result, in teleparallel gravity, tensor modes including gravitational waves, come from the contortion tensor.

gr-qc↗

arXiv2015

Noncommutative spaces and covariant formulation of statistical mechanics

We study the statistical mechanics of a general Hamiltonian system in the context of symplectic structure of the corresponding phase space. This covariant formalism reveals some interesting correspondences between properties of the phase space and the associated statistical physics. While topology, as a global property, turns out to be related to the total number of microstates, the invariant measure which assigns {\it a priori} probability distribution over the microstates, is determined by the local form of the symplectic structure. As an example of a model for which the phase space has a nontrivial topology, we apply our formulation on the Snyder noncommutative space-time with de Sitter four-momentum space and analyze the results. Finally, in the framework of such a setup, we examine our formalism by studying the thermodynamical properties of a harmonic oscillator system.

gr-qc↗