arXiv subjects
Publications and source records attributed to R. Myrzakulov.
We reconstruct the field potentials in case of (non)phantom fields for different models resulting from parametrization of q(t), a(t) or H(t). In addition we carry out similar procedure for tachyonic field. We also discuss specific form of parametrization for reconstruction of scalar field potential.
An integrable generalization of the continuous classical O$(2,1)$ pseudospin Heisenberg model to the case of the ospu$(1,1/1)$ superalgebra is constructed. The gauge equivalence of the constructed model and the related NLSE is established. We indicate a method of generating classical solutions using the global ospu$(1,1/1)$ supersymmetry. The relationship between solutions of O$(2,1)$ HM and 'superpartners' of NLSE is obtained.
Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. Within this framework, it is possible to provide an unified geometrical explanation for dark matter, the late-time acceleration, and inflation, making it a very attractive theory. In this review, we summarize the main aspects of mimetic gravity, as well as extensions of the minimal formulation of the model. We devote particular focus to the reconstruction technique, which allows the realization of any desired expansionary history of the Universe by an accurate choice of potential, or other functions defined within the theory (as in the case of mimetic $f(R)$ gravity). We briefly discuss cosmological perturbation theory within mimetic gravity. As a case study within which we apply the concepts previously discussed, we study a mimetic Hořava-like theory, of which we explore solutions and cosmological perturbations in detail. Finally, we conclude the review by discussing static spherically symmetric solutions within mimetic gravity, and apply our findings to the problem of galactic rotation curves. Our review provides an introduction to mimetic gravity, as well as a concise but self-contained summary of recent findings, progresses, open questions, and outlooks on future research directions.
The authors considered the bulk viscous fluid in $f(R, T)$ gravity within the framework of Kaluza-Klein space time. The bulk viscous coefficient $(ξ)$ expressed as $ξ=ξ_0+ξ_1\frac{\dot{a}}{a}+ξ_2\frac{\ddot{a}}{\dot{a}}$, where $ξ_0$, $ξ_1$ and $ξ_2$ are positive constants. We take $p=(γ-1)ρ$, where $0\leγ\le2$ as an equation of state for perfect fluid. The exact solutions to the corresponding field equations are given by assuming a particular model of the form of $f(R, T)=R+2f(T)$, where $f(T)=λT$, $λ$ is constant. We studied the cosmological model in two stages, in first stage: we studied the model with no viscosity, and in second stage: we studied the model involve with viscosity. The cosmological model involve with viscosity is studied by five possible scenarios for bulk viscous fluid coefficient $(ξ)$. The total bulk viscous coefficient seems to be negative, when the bulk viscous coefficient is proportional to $ξ_2\frac{\ddot{a}}{\dot{a}}$, hence the second law of thermodynamics is not valid, however, it is valid with the generalized second law of thermodynamics. The total bulk viscous coefficient seems to be positive, when, the bulk viscous coefficient is proportional to $ξ=ξ_1\frac{\dot{a}}{a}$, $ξ=ξ_1\frac{\dot{a}}{a}+ξ_2\frac{\ddot{a}}{\dot{a}}$ and $ξ=ξ_0+ξ_1\frac{\dot{a}}{a}+ξ_2\frac{\ddot{a}}{\dot{a}}$, so the second law of thermodynamics and the generalized second law of thermodynamics is satisfied throughout the evolution. We calculate statefinder parameters of the model and observed that, it is different from the $\wedge$CDM model. Finally, some physical and geometrical properties of the models are discussed.
In this article, we considered the bulk viscous fluid in the formalism of modified gravity in which the general form of a gravitational action is $f(R, T)$ function, where $R$ is the curvature scalar and $T$ is the trace of the energy momentum tensor within the frame of flat FRW space time. The cosmological model dominated by bulk viscous matter with total bulk viscous coefficient expressed as a linear combination of the velocity and acceleration of the expansion of the universe in such a way that $ξ=ξ_0+ξ_1\frac{\dot{a}}{a}+ξ_2\frac{\ddot{a}}{\dot{a}}$, where $ξ_0$, $ξ_1$ and $ξ_2$ are constants. We take $p=(γ-1)ρ$, where $0\leγ\le2$ as an equation of state for perfect fluid. The exact solutions to the corresponding field equations are obtained by assuming a particular model of the form of $f(R, T)=R+2f(T)$, where $f(T)=λT$, $λ$ is constant. We studied the four possible scenarios for different values of $γ$, such as $γ=0$, $γ=\frac{2}{3}$, $γ=1$ and $γ=\frac{4}{3}$ with the possible positive and negative ranges of $λ$ to observe the accelerated expansion history of the universe. Finally, a big-rip singularity is observed.
In this paper, we propose a simple parametrization of the Hubble parameter H in order to explain the late time cosmic acceleration. We show that our proposal covers many models obtained in different schemes of parametrization under one umbrella. We demonstrate that a simple modification in the functional form of Hubble parameter can give rise to interesting cosmological phenomena such as big rip singularity, bounce and others. We have also constrained the model parameters using the latest 28 points of H(z) data for three cases which admit transition from deceleration to acceleration.
In this paper, we consider rolling tachyon, with steep run-away type of potentials non-minimally coupled to massive neutrino matter. The coupling dynamically builds up at late times as neutrino matter turns non-relativistic. In case of scaling and string inspired potentials, we have shown that non-minimal coupling leads to minimum in the field potential. Given a suitable choice of model parameters, it is shown to give rise to late-time acceleration with the desired equation of state.
In this paper we study cosmological dynamics of phantom as well as non-phantom fields with linear potential in presence of Galileon correction $(\partial_μϕ\partial^μϕ) \Box ϕ$. We show that the Big Crunch singularity is delayed compared to the standard case; the delay crucially depends upon the strength of Galileon correction. As for the phantom Galileon, $ρ_ϕ$ is shown to grow more slowly compared to the standard phantom delaying the approach to singularity. In case, $V\sim ϕ^n, n>4$, Big Rip is also delayed, similar phenomenon is shown to take place for potentials steeper than the exponential.
Computing the holographic entanglement entropy proposed by Ryu-Takayanagi shows that thermal energy near boundary region in $AdS_3$ gain maximum of the temperature. The absolute maxima of temperature is $T^{Max}_{E}= \frac{4G_3 ε_{\infty}}{l}$. By simple physical investigations it has become possible to predict a phase transition of first order at critical temperature $T_c\leq T_{E}$. As they predict a tail or root towards which the AdS space ultimately tend, the boundary is considered thermalized. The Phase transitions of this form have received striking theoretical and experimental verifications so far.
We present a study of the generalized second law of thermodynamics in the scope of the f(R,T) theory of gravity, with R and T representing the Ricci scalar and trace of the energy-momentum tensor, respectively. From the energy-momentum tensor equation for the f(R,T) = R + f(T) case, we calculate the form of the geometric entropy in such a theory. Then, the generalized second law of thermodynamics is quantified and some relations for its obedience in f(R,T) gravity are presented. Those relations depend on some cosmological quantities, as the Hubble and deceleration parameters, and on the form of f(T).
We studied entanglement entropy for a time dependent two dimensional holographic superconductor. We showed that the conserved charge of the system plays the role of the critical parameter to have condensation.
We calculate the contribution of the higher-twist Feynman diagrams to the large-$p_T$ inclusive gluon production cross-section in $πp$ collisions in case of the running coupling and frozen coupling approaches within perturbative and holographic QCD. The structure of infrared renormalon singularities of the higher-twist subprocess cross-section is obtained and the resummed higher-twist cross- sections (Borel sum) with the ones obtained in the framework of the frozen coupling approach and leading-twist cross-section are compared and analyzed.
We consider generic models of quintessence and we investigate the influence of massive neutrino matter with field-dependent masses on the matter power spectrum. In case of minimally coupled neutrino matter, we examine the effect in tracker models with inverse power-law and double exponential potentials. We present detailed investigations for the scaling field with a steep exponential potential, non-minimally coupled to massive neutrino matter, and we derive constraints on field-dependent neutrino masses from the observational data.
In literature there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress-energy momentum tensor $T=T_μ^μ$. This type of modified gravity is called as $f(R,T)$ in which $R$ is Ricci scalar $R=R_μ^μ$. We extend manifestly this model to include the higher derivative term $\Box R$. We derived equation of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter solution is unstable for a generic type of $f(R,\Box R, T)$ model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.
We investigate inflation within $f(R,ϕ)$-theories, where a dynamical scalar field is coupled to gravity. A class of models which can support early-time acceleration with the emerging of an effective cosmological constant at high curvature is studied. The dynamics of the field allow for exit from inflation leading to the correct amount of inflation in agreement with cosmological data. Furthermore, the spectral index and tensor-to-scalar ratio of the models are carefully analyzed. A generalization of the theory to incorporate dark matter in the context of mimetic gravity, and further extensions of the latter, are also discussed.
An alternative method of developing the theory of non-equilibrium two dimensional holographic superconductor is to start from the definition of a time dependent $AdS_3$ background. As originally proposed, many of these formulae were cast in exponential form, but the adoption of the numeric method of expression throughout the bulk serves to show more clearly the relationship between the various parameters. The time dependence behaviour of the scalar condensation and Maxwell fields are fitted numerically. A usual value for Maxwell field on AdS horizon is $\exp(-bt)$, and the exponential $\log$ ratio is therefore $10^{-8} s^{-1}$. The coefficient $b$ of the time in the exponential term $\exp(-bt)$ can be interpreted as a tool to measure the degree of dynamical instability, its reciprocal $\frac{1}{b}$ is the time in which the disturbance is multiplied in the ratio. A discussion of some of the exponential formulae is given by the scalar field $ψ(z,t)$ near the AdS boundary. It might be possible that a long interval would elapse the system which tends to the equilibrium state when the normal mass and conformal dimensions emerged. A somewhat curious calculation has been made, to illustrate the holographic entanglement entropy for this system. The foundation of all this calculation is, of course, a knowledge of multiple (connected and disconnected) extremal surfaces. There are several cases in which exact and approximate solutions are jointly used, a variable numerical quantity is represented by a graph, and the principles of approximation are then applied to determine related numerical quantities. In the case of the disconnected phase with a finite extremal are, we find a discontinuity in the first derivative of the entanglement entropy as the conserved charge $J$ is increased.
Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equation and are integrable. In this paper, the Darboux transformation of the M-XCIX equation is constructed. Using the DT, a 1-soliton solution of the M-XCIX equation is presented.
The goal of this paper is to discuss phase space analysis of some interacting Chaplygin gas models in General Relativity. Chaplygin gas is one of the fluids actively considered in modern cosmology due to the fact that it is a joint model of dark energy and dark matter. In this paper we have considered various forms of interaction term Q including linear and non linear sign changeable interactions. For each case late time attractors for the field equations are found.