arXiv subjects
Publications and source records attributed to F. Darabi.
We study the black hole thermodynamics and obtain the correction terms for temperature, entropy, and heat capacity of the Schwarzschild black hole, resulting from the commutation relations in the framework of {\it Modified Generalized Uncertainty Principle} suggested by {\it Doubly Special Relativity}.
We study the classical Euclidean wormholes in the context of extended theories of gravity. With no loss of generality, we use the dynamical equivalence between $f(\tilde{R})$ gravity and scalar-tensor theories to construct a point-like Lagrangian in the flat FRW space time. We first show the dynamical equivalence between Palatini $f(\tilde{R})$ gravity and the Brans-Dicke theory with self-interacting potential, and then show the dynamical equivalence between the Brans-Dicke theory with self-interacting potential and the minimally coupled O'Hanlon theory. We show the existence of new Euclidean wormhole solutions for this O'Hanlon theory and, for an special case, find out the corresponding form of $f(\tilde{R})$ having wormhole solution. For small values of the Ricci scalar, this $f(\tilde{R})$ is in agreement with the wormhole solution obtained for higher order gravity theory $\tilde{R}+ε\tilde{R}^2,ε<0$.
We study an special law for the deceleration parameter, recently proposed by Akarsu and Dereli, in the context of $f(R)$, $f(T)$ and $f(\mathcal{G})$ theories of modified gravity. This law covers the law of Berman for obtaining exact cosmological models to account for the current acceleration of the universe, and also gives the opportunity to generalize many of the dark energy models having better consistency with the cosmological observations. Our aim is to reconstruct the $f(R)$, $f(T)$ and $f(\mathcal{G})$ models inspired by this law of variable deceleration parameter. Such models may then exhibit better consistency with the cosmological observations.
We have considered an action of the form $T+f(T)+L_m$ describing Einstein's gravity plus a function of the torsion scalar. By considering an exact power-law solution we have obtained the Friedmann equation as a differential equation for the function $f(T)$ in spatially flat universe and obtained the real valued solutions of this equation for some power-law solutions. We have also studied the power-law solutions when the universe enters a Phantom phase and shown that such solutions may exist for some f(T) solutions.
We study the classical and quantum Euclidean wormholes for an empty (4+1) dimensional Kaluza-Klein universe with a positive cosmological constant and a spatially flat Robertson-Walker type metric. It is shown that classical wormholes do not exist neither for the spacetime sector nor the extra dimensional sector of this model, but two spectrums of quantum wormholes as the solutions of Wheeler-DeWitt equation exist which are consistent with the Hawking-Page conjecture about the necessary boundary conditions. In the spectrum where the external scale factor $R$ shapes the quantum wormholes the internal scale factor $a$ may play the role of effective matter source, and in the spectrum where the internal scale factor $a$ shapes the quantum wormholes the external scale factor $R$ may play the role of effective matter source.
We consider Noether symmetry approach to find out exact cosmological solutions in $f(T)$-gravity. Instead of taking into account phenomenological models, we apply the Noether symmetry to the $f(T)$ gravity. As a result, the presence of such symmetries selects viable models and allow to solve the equations of motion. We show that the generated $f(T)$ leads to a power law expansion for the cosmological scale factor.
Power-law solutions for $f(G)$ gravity coupled with perfect fluid have been studied for spatially flat universe. It is shown that despite the matter dominated and accelerating power-law solutions, the power-law solution exists for an special form of $f(G)$ when this universe enters a Phantom phase.
An speculative solution for the cosmological constant problem is proposed. It is argued that while the true quantum vacuum energy density is of the order of $M_P^4$, the observed classical vacuum energy density may be much smaller due to the huge amount of scattering process in the vacuum state of quantum gravity.
We study the classical Euclidean wormhole solutions for the gravitational systems with minimally coupled pure Phantom field and minimally coupled Phantom field accompanied by perfect fluid. It is shown that such solutions do exist and then the general forms of the Phantom field potential are obtained for which there are classical Euclidean wormhole solutions.
We investigate the necessary condition for the existence of classical Euclidean wormholes in a conformally non-invariant gravitational model minimally coupled to an scalar field. It is shown that while the original Ricci tensor with positive eigenvalues does not allow the Euclidean wormholes to occur, under dynamical conformal transformations the Ricci tensor, with respect to the original metric, is dynamically coupled with the conformal field and its eigenvalues may become negative allowing the Euclidean wormholes to occur. Therefore, it is conjectured that dynamical conformal transformations may provide us with {\it effective} forms of matter sources leading to Euclidean wormholes in conformally non-invariant systems.
Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant. Then, the system of second class constraints is quantized by introducing Dirac brackets in the reduced phase space.
In the framework of noncompact Kaluza-Klein theory, we investigate a $(4+1)$-dimensional universe consisting of a $(4+1)$ dimensional Robertson-Walker type metric coupled to a $(4+1)$ dimensional energy-momentum tensor. The matter part consists of an energy density together with a pressure subject to 4D part of the $(4+1)$ dimensional energy-momentum tensor. The dark part consists of just a dark pressure $\bar{p}$, corresponding to the extra-dimension endowed by a scalar field, with no element of dark energy. It is shown that for a flat universe, coupled with the non-vacuum states of the scalar field, the reduced field equations subject to suitable equations of state for matter and dark part may reveal inflationary behavior at early universe, deceleration for radiation dominant era and then acceleration in matter dominant era.
In this paper, we show the equivalence between a classical static scalar field theory and the (closed) de Sitter cosmological model whose potential represents shape invariance property. Based on this equivalence, we calculate the one-loop quantum cosmological correction to the ground state energy of the kink-like solution in the (closed) de Sitter cosmological model in which the fluctuation potential $V^{\prime\prime}$ has a shape invariance property. It is shown that this type of correction, which yields a renormalized mass in the case of scalar field theory, may be {\it interpreted} as a renormalized gravitational constant in the case of (closed) de Sitter cosmological model. Keywords: One-loop correction; kink energy; shape invariance; zeta function regularization; de Sitter universe.
In this paper, we calculate the one-loop quantum cosmological corrections to the kink energy in the closed Friedmann-Robertson-Walker universe in which the fluctuation potential $V^{\prime\prime}$ has a shape invariance property. We use the generalized zeta function regularization method to implement our setup for describing quantum kink-like states. It is conjectured that the corrections lead to the renormalized gravitational constant.
A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in $f(R)$ metric formalism nor the ones in $f({\cal R})$ Palatini formalism, whereas the modified source terms are {\it formally} equivalent to those of $f({\cal R})=\frac{1}{2}{\cal R}^2$ gravity in Palatini formalism. The correspondence between the present model, the modified gravity theory, and Brans-Dicke theory with $ω=-\frac{3}{2}$ is explicitly shown, provided the dilaton field is condensated to its vacuum state.
In the framework of Kaluza-Klein theory, we investigate a $(4+1)$-dimensional universe consisting of a $(4+1)$ dimensional Robertson-Walker type metric coupled with a $(4+1)$ dimensional energy-momentum tensor. The matter part consists of an energy density together with a pressure subject to 4D part of the $(4+1)$ dimensional energy-momentum tensor. The dark part consists of just a dark pressure $\bar{p}$, corresponding to the extra-dimension endowed by a scalar field, with no element of dark energy. It is shown that the reduced Einstein field equations are free of 4D pressure and are just affected by an effective pressure produced by the 4D energy density and dark pressure. It is then proposed that the expansion of the universe may be controlled by the equation of state in higher dimension rather than four dimensions. This may account for the emergence of unexpected current acceleration in the middle of matter dominant era.
A new interpretation is introduced for MOND based on the Sciama's interpretation of Mach principle and an Unruh like effect, in the context of a generalized equivalence principle. It is argued that in a locally accelerated frame with acceleration $a$ the appearance of a Rindler horizon may give rise to a constant acceleration $a_0$ as the local properties of cosmological horizon or Hubble length. The total gravitational acceleration inside this frame becomes the combination of $a$ with $a_0$. For $a\gg a_0$, the conventional gravitational mass $m_g$ interacts with the dominant acceleration as $m_g a$ and application of Sciama's interpretation leads to the standard Newtonian dynamics. For $a\ll a_0$, however, a reduced gravitational mass $\bar{m}_g$ interacts with the dominant acceleration as $\bar{m}_g a_0$ and the application of Sciama's interpretation on this reduced gravitational mass leads to MOND. This introduces a third proposal for MOND: {\it The modification of gravitational mass}.
We propose a Machian model of gravitational interaction at galactic scales to explain the rotation curves of these large structures without the need for dark matter or MOND.