arXiv subjects

K. Atazadeh

Publications and source records attributed to K. Atazadeh.

At least 19 recordsLinked to original sources

arXiv2026

Exact solutions of the FLRW cosmological model via invariants of the Hamilton-Jacobi method

In this study, we proceed to solve the field equations of the spatially flat Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological model in the presence of the cosmological constant $\Lambda$ by making use of the Invariants of Hamilton-Jacobi method (IHJM). This method enables us to extract systematically two independent first integrals such as $l_{\rm HJ,1}(a,\dot{a})=c_{1}$ and $l_{\rm HJ,2}(t,a,\dot{a})=c_{2}$ associated to the transformations group keeping the form of the Hamilton's canonical equations (HCEs) of the cosmological model invariant. Extracting these invariants means not only finding the general solution of the field equations of the model, but also obtaining the Lagrangian and Hamiltonian functions for the model whose dynamics acts like the dynamics of a single particle in a one-dimensional mini-super space $\mathbb{Q}=(a)$. In addition, to obtain the general solution of the model, the IHJM have also solved the inverse problem of calculus of variation (IPCV) without resorting to Helmholtz conditions and whether the necessary conditions for the existence of the Lagrangian function are hold or not. The main part of the IHJM is to find the generating function of the canonical transformation (CT) and then extract two independent invariants for the desired model by using the Hamilton-Jacobi equation (HJE). This study shows that there is a close relationship between the group of the CTs of the Hamiltonian function of the particle and the one-parameter Lie group of transformations keeping invariant the Einstein-Friedmann dynamical equation (EFDE) $\ddot{a}=F(a,\dot{a})$, so that both of them lead to the same result. In this way, having both the IHJM and the invariants of the symmetry groups method (ISGM), a comprehensive integration theory by unifying them can be achieved for studying the desired models.

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arXiv2025

Cosmological solutions in $f(Q)$ gravity via Noether symmetry approach

Symmetry plays a crucial role in theoretical physics, especially Noether symmetry, which is a powerful approach for identifying the models at the fundamental level. The exact solution is provided within the point-like Lagrangian framework. In this work, we study one of the alternative theories of gravity based on the non-metricity scalar $Q$, namely $f(Q)$ gravity, via Noether symmetry. We utilize Noether symmetry within the framework of $f(Q)$ gravity to derive the functional expression for $f(Q)$, which is given by $f(Q)=c(Q-nQ)^{\frac{3}{2-2n}}$. To confirm the exact solution of the model through Noether symmetry, we continue to consider the Friedmann-Robertson-Walker (FRW) cosmology with the dynamical solution of the system using dimensionless variables and show that the accelerated expansion of the universe follows a power law scale factor. In the following, we show that the quantities corresponding to the exact solution for $n<1$ lead to an accelerated expansion universe. Finally, in the framework of $f(Q)$ scalar-tensor cosmology, we apply the Noether symmetry approach to find the cosmological models consistent with the Noether symmetry.

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arXiv2025

Energy conditions and gravitational baryogenesis in $f(R, {\cal R})$ gravity

In this work, first we examine the energy conditions in the context of the generalized metric-Palatini hybrid gravity, known as $f(R, {\cal R})$ gravity. We show that for the proposed model in this study, {\it i.e.} $ f(R, {\cal R})= R +\alpha{\cal R}^{n} $, one of the four fundamental energy conditions, specifically the strong energy condition, does not hold for some values of $n$. Therefore, it seems that hybrid gravity can provide a model for the accelerated expansion of the universe. In continuation of completing our study in this work, we try to analyze the impact of hybrid metric-Palatini gravity on the gravitational baryogenesis process. The hybrid metric-Palatini model combines two gravitational theories that allow for a more detailed examination of the behavior of space-time and its interaction with matter. This combination is critical in the early radiation-dominant universe, where unusual gravitational effects may play a key role in generating baryonic asymmetry and the production of baryons and anti-baryons.

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arXiv2024

Linear independence of field equations in the Brans-Dicke theory

In solving the Brans-Dicke (BD) equations in the BD theory of gravity, their linear independence is important. This is due to fact that in solving these equations in cosmology, if the number of unknown quantities is equal to the number of independent equations, then the unknowns can be uniquely determined. In the BD theory, the tensor field $g_{\mu \nu}$ and the BD scalar field $\varphi$ are not two separate fields, but they are coupled together. The reason behind this is a corollary that proposed by V. B. Johri and D. Kalyani in cosmology, which states that the cosmic scale factor of the universe, $a$, and the BD scalar field $\varphi$ are related by a power law. Therefore, when the principle of least action is used to derive the BD equations, the variations $\delta g^{\mu \nu}$ and $\delta \varphi$ should not be considered as two independent dynamical variables. So, there is a constraint on $\delta g^{\mu \nu}$ and $\delta \varphi$ that causes the number of independent BD equations to decrease by one unit, in such a way that in the equations that have been known as BD equations, one of them is redundant. In this paper, we prove this issue, that is, we show that one of these equations, which we choose as the modified Klein-Gordon equation, is not an independent equation, but a result establishing other BD equations, the law of conservation of energy-momentum of matter and Bianchi's identity. Therefore, we should not look at the modified Klein-Gordon equation as an independent field equation in the BD theory, but rather it is included in the other BD equations and should not be mentioned separately as one of the BD equations once again.

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arXiv2024

Cosmological solutions in the Brans-Dicke theory via invariants of symmetry groups

We proceed to obtain an exact analytical solution of the Brans-Dicke (BD) equations for the spatially flat ($k=0$) Friedmann-Lamaitre-Robertson-Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the "invariants of symmetry groups method" (ISG-method). This method is based on the extended Prelle-Singer (PS) method and it employs the Lie point symmetry, $\lambda$-symmetry, and Darboux polynomials (DPs). Indeed, the ISG-method tries to provide two independent first-order invariants associated to the one-parameter Lie groups of transformations keeping ordinary differential equations (ODEs) invariant, as solutions. It should be noted for integrable ODEs, the ISG-method guarantees the extraction of these two invariants. In this work for the BD equations in FLRW cosmological model, we find the Lie point symmetries, $\lambda$-symmetries and DPs, and obtain the basic quantities of the extended PS method (which are the null forms and the integrating factors). By making use of the extended PS method we find two independent first-order invariants, in such a way appropriate cosmological solutions from solving these invariants as a system of algebraic equations are simultaneously obtained. These solutions are wealthy so that they include many known special solutions, such as O'Hanlon-Tupper vacuum solutions, Nariai's solutions, Brans-Dicke dust solutions, inflationary solutions, and etc.

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arXiv2024

Quantum cosmology in teleparallel gravity with a boundary term

We quantize a homogeneous and isotropic universe for two models of modified teleparallel gravity, wherein an arbitrary function of the boundary term, namely $B$, is present in the action and in the other model a scalar field that is non-minimally coupled to both the torsion and boundary term. In this regard, we study exact solutions of both the classical and quantum frameworks by utilizing the corresponding Wheeler-DeWitt (WDW) equations of the models. To correspond to the comprehensive classical and quantum levels, in the second model, we propose an appropriate initial condition for the wave packets and observe that they closely adhere to the classical trajectories and reach their peak. We quantify this correspondence using the de-Broglie Bohm interpretation of quantum mechanics. According to this proposal, the classical and Bohmian trajectories coincide when the quantum potential vanishes along the Bohmian paths. Furthermore, we apply the de-parameterization technique to our model in the realm of the problem of time in quantum cosmological models based on the WDW equation, utilizing the global internal time denoted as $\chi$, which represents a scalar field.

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arXiv2023

Source of black bounces in Rastall gravity

In this study, we explore the black bounce solution in Rastall gravity and its potential source field, which can be described as a black hole or wormhole solution depending on certain parameters. We focus on the Bardeen-Type black bounce and Simpson-Visser solution and aim to identify an appropriate source field for these solutions. Our findings suggest that in Rastall gravity, a source for the black bounce solution with non-linear electromagnetic can be found. However, in the presence of a non-linear electromagnetic source, it is impossible to identify an appropriate source for the black bounce solution without a scalar field. We also investigate the energy conditions outside the event horizon for two types of black bounce solutions: Simpson-Visser and Bardeen. We find that these solutions do not satisfy the null energy condition, but we also reveal that Rastall gravity has more flexibility for maintaining some of the energy conditions by selecting an appropriate value for the Rastall parameter $\gamma$.

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arXiv2023

Geodesic deviation equation in generalized hybrid Metric-Palatini gravity

In the context of general relativity, the geodesic deviation equation (GDE) relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics. In this paper, we consider the GDE for the generalized hybrid Metric-Palatini gravity and apply it in this model to investigate the structure of time-like, space-like, and null geodesics in the homogeneous and isotropic universe. We propose a particular case $f(R,{\cal R})=R+{\cal R}$ to study the numerical behavior of the deviation vector $\eta(z)$ and the observer area-distance $r_{0}(z)$ with respect to redshift $z$. Also, we consider the GDE in the framework of the scalar-tensor representation of the generalized hybrid Metric-Palatini gravity i.e. $f(R, {\cal R} )$, in which the model can be considered as dynamically equivalent to a gravitational theory with two scalar fields. Finally, we extend our calculations to obtain the modification of the Mattig relation in this model.

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arXiv2023

Exact FLRW cosmological solutions via invariants of the symmetry groups

Until now, various methods have been demonstrated to solve the Friedmann-Lama\'{\i}tre-Robertson-Walker (FLRW) equations in the spatially flat $(k=0)$ cosmological model. In this study, in order to solve the field equations of the spatially flat FLRW cosmological model in the presence of $\Lambda$, a new method based on the invariants of the symmetry groups which we called ISG-method, is presented. This method is based on the extended Prelle-Singer (PS) method and it uses the Lie point symmetry, $\lambda$-symmetry and Darboux polynomials (DPs). We employ this method to extract systematically the two independent first integrals (or invariants) such as $I_1 (a,\dot{a})=c_1$ and $I_2 (t,a,\dot{a})=c_2$ associated to the group of the Lie point transformations keeping the Friedmann-Einstein dynamical equation (DE), $\ddot{a}=\phi(t,a,\dot{a})$, invariant. The obtained solutions from solving the DEs of the FLRW cosmological model by the ISG-method are explicitly written, so that they are suitable for cosmological applications. Finally, as an application of the solutions we look at the age of universe in the presence of cosmological constant where the dominant matter of the universe is considered to be fluid with the state parameter $w$. In this regard, we calculate the age of universe when the dominant matter is dust.

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arXiv2022

Quantum time dilation in the near-horizon region of a black hole

In this work, we obtain a relation for average quantum time dilation between two clocks A and B in the near-horizon region of a black hole supported by the Rindler metric and conformal tortoise coordinate. It is indicated that this relation is identified with time dilation in classical and flat background limits.

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arXiv2022

Quantum time in near-horizon region of a black hole

The understanding of time and dynamics can be elucidated by examining the concept of entanglement in quantum theory. This particular perspective on time is referred to as the timeless approach, which posits that the universe exists in a fixed state where two separate subsystems, namely the "clock" and the "rest," are entangled. By selecting an appropriate observable for the clock, the state of the rest of the universe evolves unitarily in relation to the variable that labels the clock observable's eigenstates, which is then interpreted as time. This intriguing model, initially introduced by Page and Wootters, has also been applied to the context of curved spacetime. In this study, we explore various uncertainties pertaining to the dynamics of the rest of the universe within a curved spacetime, including ambiguities related to the clock, the system's time evolution, the flow of time, and the recording of its history. Our investigation is primarily focused on the near horizon region of a black hole, as the peculiar behavior of quantum effects in this area allows for a thorough examination of the timeless depiction proposed by Page and Wootters in describing the system's dynamics within curved spacetime. This analysis may be valuable for quantum gravity projects that align with the approach put forth by Page and Wootters. It is worth noting that the application of the Page and Wootters approach in this particular region results in a distinct clock without any ambiguity. However, the other aforementioned issues, unlike those resolved in the realm of quantum mechanics, persist in this region.

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arXiv2022

Cosmological future singularities in massive gravity and massive bigravity

We study the future cosmological singularities in the framework of massive gravity and minimal massive bigravity theory. In this regards, we consider the possible classes of finite-time future singularities such as sudden, big rip, big freeze and big brake singularities in the massive universe. In dRGT model with an open expanding universe we obtain the sudden singularity in the future at a finite-time which generally without taking account of any particular realistic equation of state, is not avoidable and except the fluid density, all dynamical physical quantities such as pressure approach to infinity. To complete our study, we search the future cosmological singularities in the context of minimal massive bigravity theory and we find that the cosmology of this theory suffers from the sudden and big brake singularities, in which we can see that the parameters of the model approaches to zero the sudden singularity can be removed.

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arXiv2021

Maximum force conjecture in Kiselev, $4$D-EGB and Barrow corrected-entropy black holes

The classical maximum force bound in the general relativity (GR) is defined between two black holes with touching horizons. We consider the maximum force conjecture for Kiselev solution that the black holes surrounded by quintessential matter, $w=-2/3$. We show that the maximum force bound is independent of black hole masses in this solution and we also indicate that when two black holes surrounded by static quintessence, the maximum force between them can approach to zero. In continue, we also study the maximum force bound for $4$D Einstein-Gauss-Bonnet ($4$D-EGB) black holes and we obtain that in this theory the maximum force bound exists and the force is bigger than the maximum force in GR. Finally, we consider the Barrow entropy in the framework of the entropic force theories and find that the maximum force only holds when the exponent of the corrected-entropy, namely $Δ$, goes to zero and for other ranges of $Δ$ it does not hold in which the mass dependence in the maximum force bound may cause the formation of naked singularities.

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arXiv2020

Gravitational baryogenesis in DGP brane cosmology

We consider the imbalance of matter and antimatter by using a gravitational baryogenesis mechanism in the background of Dvali-Gabadadze-Porrati (DGP) brane cosmology. By taking into account a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric in the DGP brane model, we find that for a radiation dominated universe, $w = 1/3$, the ratio of baryon number density to entropy from the gravitational baryogenesis is not zero, contrary to ordinary general relativity. Also, we study the ratio of baryon number density to entropy against the observational constraints in DGP cosmology.

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arXiv2020

D-bound and Bekenstein Bound for the Surrounded Vaidya Black Hole

We study the Vaidya black hole surrounded by the exotic quintessence-like, phantom-like and cosmological constant-like fields by means of entropic considerations. Explicitly, we show that for this thermodynamical system, the requirement for the identification of D-bound and Bekenstein entropy bound can be considered as a thermodynamical criterion by which one can rule out the quintessence-like and phantom-like fields, and prefer the cosmological constant as a viþable cosmological field.

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arXiv2020

D-bound and Bekenstein bound for McVittie solution surrounded by dark energy cosmological fields

The cosmological candidate fields for dark energy as quintessence, phantom and cosmological constant, are studied in terms of an entropic hypothesis imposed on the McVittie solution surrounded by dark energy. We certify this hypothesis as "$D$-bound-Bekenstein bound identification" for dilute systems and use it as a criterion to determine which candidate of dark energy can satisfy this criterion for a dilute McVittie solution. It turns out that only the cosmological constant can pass this criterion successfully while the quintessence and phantom fields fail, as non-viable dark energy fields for this particular black hole solution. Moreover, assuming this black hole to possess the saturated entropy, the entropy-area law and the holographic principle can put two constraints on the radius $R$ of the cosmological horizon. The first one shows that the Hubble radius is discrete such that for any arbitrary value of the black hole mass $m_{0}$, the value of $R$ is determined up to an integer number. The latter one shows that when a black hole is immersed in a cosmological background, the radius of the cosmological horizon is constrained as $R<\frac{1}{H}$.

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arXiv2019

Bounding f(R,T) gravity by particle creation

We consider the possibility of the quantum vacuum states in f(R,T) gravity. Particularly, we study the Bogoliubov transformations associated to different vacuum states for some f(R,T) models. The method consists of fixing the f(R,T) free parameters by requiring the Bogoliubov coefficients to be minimized. In such a way, the particle production is related to the value of the Hubble parameter and also the given f(R,T) model.

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arXiv2019

f(T) Quantum Cosmology

We quantize a flat cosmological model in the context of $f(T)$ theory of modified gravity using the Dirac's quantization approach for Hamiltonian constraint systems. In this regard, first we obtain the Wheeler-DeWitt equation as the operator equation of the Hamiltonian constraint and solve it for some typical cosmological models of $f(T)=T-2Λ$, $f(T)= β\sqrt{-2T}$ and $f(T)= γT^2$. Then, in the context of classical-quantum correspondence, we interpret the obtained wavefunctions of the universe to describe an accelerating de Sitter universe which is found to be in good agreement with $f(T)=T-2Λ$ model. Finally, we study Bohm--de Broglie interpretation of the quantum model for $f(T)=T-2Λ$ model.

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