arXiv subjects
Publications and source records attributed to M. R. Setare.
We study the chaotic inflation in the context of a gravity theory where the Friedman equation is modified, inspired by the polytropic gas equation of state. It is seen that in the $n=1$ case for the polytropic index the inflaton field at the end of inflation $ϕ_e$, depends on the Planck mass, while for $n\neq1$ it generally depends on the polytropic constant and mass of the inflaton field.
In a series of papers, Quesne and Tkachuk (J. Phys. A: Math. Gen. \textbf{39}, 10909 (2006); Czech. J. Phys. \textbf{56}, 1269 (2006)) presented a $D+1$-dimensional $(β,β')$-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal measurable length. In this paper, the Lagrangian formulation of electrodynamics in a 3+1-dimensional space-time described by Quesne-Tkachuk algebra is studied in the special case $β'=2β$ up to first order over the deformation parameter $β$. It is demonstrated that at the classical level there is a similarity between electrodynamics in the presence of a minimal measurable length (generalized electrodynamics) and Lee-Wick electrodynamics. We obtain the free space solutions of the inhomogeneous Maxwell's equations in the presence of a minimal length. These solutions describe two vector particles (a massless vector particle and a massive vector particle). We estimate two different upper bounds on the isotropic minimal length. The first upper bound is near to the electroweak length scale $(\ell_{electroweak}\sim 10^{-18}\, m)$, while the second one is near to the length scale for the strong interactions $(\ell_{strong}\sim 10^{-15}\, m)$. The relationship between the Gaete-Spallucci nonlocal electrodynamics (J. Phys. A: Math. Theor. \textbf{45}, 065401 (2012)) and electrodynamics with a minimal length is investigated.
In the 1990s, Kempf and his collaborators Mangano and Mann introduced a $D$-dimensional $(β,β')$-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length $(\triangle X^{i})_{min}=\hbar\sqrt{Dβ+β'}\;,\forall i\in \{1,2, \cdots,D\}$. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions $(D=3)$ described by Kempf algebra is presented in the special case of $β'=2β$ up to the first order over $β$. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee-Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot-Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is $4.42\times10^{-19}m$. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci non-local magnetostatics (J. Phys. A: Math. Theor. \textbf{45}, 065401 (2012)) is investigated.
In this paper we consider the structure of the $AdS_3$ vacua in $R^3$ expansion of the New Massive Gravity ($R^3$-NMG). We obtain the degeneracies of the $AdS_3$ vacua at several points of the parametric space. Additionally, following a specific analysis we show that $AdS_3$ wave solutions are present. Using these wave solutions, we single out two special points of the parametric space for which logarithmic terms appear in the solutions. The first one is a point at which the effective mass of the wave profile which is interpreted as a scalar mode, completely saturates the Breitenlohner-Freedman bound of the $AdS_3$ space in which the wave is propagating. The second special point is a point at which the central charge of the theory vanishes. Furthermore, we investigate the possibility of asymptotically Lifshitz black solutions to be present in the three-dimensional $R^3$-NMG. We derive analytically the Lifshitz vacua considering specific relations between the mass parameters of $R^3$-NMG. A certain polynomial equation arises at the first special point where solutions with logarithmic fall-off in the $AdS_3$ space appear. Solving this polynomial equation, we obtain the values of the dynamical exponent $z$ which correspond to possible asymptotically Lifshitz black hole solutions. However, it is shown that asymptotically Lifshitz black solutions do not exist in the three-dimensional $R^3$-NMG for a specific ansatz of the black hole metric.
In this paper we introduce the "warm vector inflation" scenario. In warm inflation scenario radiation is produced during the inflation epoch and reheating is avoided. Slow-roll and perturbation parameters of this model are presented. We develop our model using intermediate inflation model. In this case, the model is compatible with observational data. We also study the model using another exact cosmological solution, named logamediate scenario. We present slow-roll and Hubble parameters, power spectrum and tensor-scalar ratio in terms of inflaton. The model is compatible with WMAP7 and Planck observational data.
Non-abelian gauge field inflation is studied in the context of warm inflation scenario. We introduce this scenario as a mechanism that gives an end for gauge-flation model. Slow-roll parameters and perturbation parameters are presented for this model. We find the general conditions which are required for this model to be realizable in slow-roll approximation. We also develop our model in the context of intermediate and logamediate scenarios which are exact solutions of inflationary field equation in the Einstein theory. General expressions of slow-roll parameters, tensor-scalar ratio and scalar spectral index are presented in terms of inflaton field for these two cases. Our model is compatible with recent observational data from Planck satellite.
In the present paper we study warm inflationary universe models in the context of a polytropic gas. We derive the characteristics of this model in slow-roll approximation and develop our model in two cases, 1- For a constant dissipative parameter $Γ$. 2- $Γ$ as a function of scalar field $ϕ$. In these cases we will obtain exact solution for the scalar field and Hubble parameter. We will also obtain explicit expressions for the tensor-scalar ratio $R$, scalar spectrum index $n_s$ and its running $α_s$, in slow-roll approximation.
In the present work, we study warm tachyon inflation model in the context of "logamediate inflation" where the cosmological scale factor expands as $a=a_0\exp(A[\ln t]^λ)$. The characteristics of this model in slow-roll approximation are presented in two cases: 1- Dissipative parameter $Γ$ is a function of tachyon field $ϕ$. 2- $Γ$ is a constant parameter. The level of non-Gaussianity of this model is found for these two cases. Scalar and tensor perturbations for this scenario are presented. The parameters appearing in our model are constrained by recent observational data (WMAP7). Harrison-Zeldovich spectrum, i.e. $n_s=1,$ is approximately obtained for large values of $λ$ (i.e. $λ\simeq 50$)and normal value of number of e-folds, i.e. $N\simeq 60$. On the other hand, the scale invariant spectrum (Harrison-Zeldovich spectrum) is given by using two parameters in our model. For intermediate inflation, where the cosmological scale factor expands as $a=a_0\exp(A t^{f}),$ this spectrum has been exactly obtained using one parameter, i.e. $f=2/3$ \cite{2-n}.
We study warm-viscous inflationary universe model on the brane, in a tachyon field theory. We obtain the general conditions which are required for this model to be realizable. In longitudinal gauge, the primoradial perturbation parameters are found in great details, using slow-roll and quasi-stable approximations. The general expressions of the tensor-to-scalar ratio, scalar spectral index and its running are found. We derive the characteristics of the inflationary universe model by using an effective exponential potential in two cases: 1- Dissipative parameter $Γ$ and bulk viscous parameter $ζ$ are constant parameters. 2- Dissipative parameter as a function of tachyon field $ϕ$ and bulk viscous parameter as a function of radiation-matter mixture energy density $ρ$. The parameters of the model are restricted by recent observational data from the seven-year Wilkinson microwave anisotropy probe (WMAP7).
We investigate models of future finite-time singularities in $f(T)$ theory, where $T$ is the torsion scalar. The algebraic function $f(T)$ is put as the teleparallel term $T$ plus an arbitrary function $g(T)$. A suitable expression of the Hubble parameter is assumed and constraints are imposed in order to provide an expanding universe. Two parameters $β$ and $H_s$ that appear in the Hubble parameter are relevant in specifying the types of singularities. Differential equations of $g(T)$ are established and solved, leading to the algebraic $f(T)$ models for each type of future finite time singularity. Moreover, we take into account the viscosity in the fluid and discuss three interesting cases: constant viscosity, viscosity proportional to $\sqrt{-T}$ and the general one where the viscosity is proportional to $(-T)^{n/2}$, where $n$ is a natural number. We see that for the first and second cases, in general, the singularities are robust against the viscous fluid, while for the general case, the Big Rip and the Big Freeze can be avoided from the effects of the viscosity for some values of $n$.
Recently the teleparallel Lagrangian density described by the torsion scalar T has been extended to a function of T. The $f(T)$ modified teleparallel gravity has been proposed as the natural gravitational alternative for dark energy to explain the late time acceleration of the universe. In order to reconstruct the function $f(T)$ by demanding a background $Λ$CDM cosmology we assume that, (i) the background cosmic history provided by the flat $Λ$CDM (the radiation ere with $ω_{eff}=1/3$, matter and de Sitter eras with $ω_{eff}=0$ and $ω_{eff}=-1$, respectively) (ii) the radiation dominate in the radiation era with $Ω_{0r}=1$ and the matter dominate during the matter phases when $Ω_{0m}=1$. We find the cosmological dynamical system which can obey the $Λ$CDM cosmic history. In each era, we find a critical lines that, the radiation dominated and the matter dominated are one points of them in the radiation and matter phases, respectively. Also, we drive the cosmologically viability condition for these models. We investigate the stability condition with respect to the homogeneous scalar perturbations in each era and we obtain the stability conditions for the fixed points in each eras. Finally, we reconstruct the function $f(T)$ which mimics cosmic expansion history.
We study particle production aspect in the flat FRW universe in the framework of $f(T)$ gravity. The matter is minimally coupled with the gravity and an exact power-law solution is obtained by solving the Friedmann equations, and matter is assumed to be minimally coupled with gravitation. The torsion scalar $T$ appears to plays the same role as the the curvature (Ricci scalar) in the the General Relativity (GR) and its modified theories $f(R)$. Specially in phantom phase, we observe that the vacuum state corresponds to a vanishing torsion scalar and particle production becomes important as the torsion scalar diverges. This aspect, not only provides the equivalence between the teleparallel gravity and the GR, but also between their respective modified versions, f(T) and f(R), in the view of massless particle production phenomenon when the matter is minimally coupled with the gravity. However, when the gravitational and scalar fields are not minimally coupled, it appears that this similarity between the teleparallel and GR may break down, due to the fact that the torsion scalar has no longer the same time dependent expression as the Ricci scalar.
In this work we study the analytical properties of a 2+1 dimensional magnetically charged holographic superconductor in $AdS_4$. We obtain the critical chemical potential $μ_c$ analytically, using the Sturm-Liouville variational approach. Also, the obtained analytic result can be used to back up the numerical computations in the holographic superconductor in the probe limit.
Recently $f(T)$ modified teleparallel gravity where T is the torsion scalar has been proposed as the natural gravitational alternative for dark energy. We perform a detailed dynamical analysis of these models and find conditions for the cosmological viability of $f(T)$ dark energy models as geometrical constraints on the derivatives of these models. We show that in the phase space exists two cosmologically viable trajectory which (i) The universe would start from an unstable radiation point, then pass a saddle standard matter point which is followed by accelerated expansion de sitter point. (ii) The universe starts from a saddle radiation epoch, then falls onto the stable matter era and the system can not evolve to the dark energy dominated epoch. Finally, for a number of $f(T)$ dark energy models were proposed in the more literature, the viability conditions are investigated.
We consider tachyonic warm-inflationary models in the context of intermediate inflation. We derive the characteristics of this model in slow-roll approximation and develop our model in two cases, 1- For a constant dissipative parameter $Γ$. 2- $Γ$ as a function of tachyon field $ϕ$. We also describe scalar and tensor perturbations for this scenario. The parameters appearing in our model are constrained by recent observational data. We find that the level of non-Gaussianity for this model is comparable with non-tachyonic model.
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.
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) on manifolds with a boundary. We can use conformal symmetry to constrain correlation functions of conformal invariant fields. We compute two-point and three-point functions of conformal invariant fields which live in semi-infinite space. For a situation with a boundary condition in surface $z=\bar{z}$ ($t=0$), the results agree with gravity dual results. We also explore representations of conformal group in two dimensions.
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) in semi-infinite space-time. In non-relativistic limit ($x\rightarrowεx, t\rightarrow t, ε\rightarrow 0$), boundary conformal algebra changes to boundary Galilean conformal algebra (BGCA). In this work, some aspects of AdS/BCFT in non-relatvistic limit were explored. We constrain correlation functions of Galilean conformal invariant fields with BGCA generators. For a situation with a boundary condition at surface $x=0$ ($z=\bar{z}$), our result is agree with non-relativistic limit of BCFT two-point function. We also, introduce holographic dual of boundary Galilean conformal field theory.