arXiv subjects
Publications and source records attributed to R. Myrzakulov.
In this paper, we investigate coupled quintessence with scaling potential assuming specific forms of the coupling as $A$ namely, $α\dot{ρ_m}$, $β\dot{ρ_ϕ}$ and $σ(\dot{ρ_m}+\dot{ρ_ϕ})$, and present phase space analysis for three different interacting models. We focus on the attractor solutions that can give rise to late time acceleration with $Ω_{DE}/Ω_{DM}$ of order unity in order to alleviate the coincidence problem.
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schrödinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schrödinger--Hirota--Maxwell--Bloch equations, along with their Lax pairs.
We briefly review the problems and prospects of the standard lore of dark energy and notice that the cosmological constant problems are often over emphasized. In order to keep the discussion pedagogical aimed at a wider audience, we have avoided technical complications in several places and resorted to heuristic arguments based on physical perceptions. We presented underlying ideas of modified theories based upon chameleon mechanism and Vainshtein screening. We have given a lucid illustration of recently investigated ghost free non linear massive gravity. Again we have sacrificed rigor and confined to the basic ideas that led to the formulation of $dRGT$. The review ends with a brief discussion on the difficulties of the theory applied to cosmology with an optimism that a consistent solution of the problem is round the corner.
We have been studied the model of light Galileon with translational shift symmetry $ϕ\to ϕ+c$. The matter Lagrangian is presented in the form $\mathcal{L}_ϕ= -η(\partial ϕ)^2+βG^{μν}\partial_μϕ\partial_νϕ$. We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of $f(R,R^{μν}T_{μν}^m)$. Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at $r=0$ in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon's field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of $ϕ=t$, which it is remembered by us dilaton field.
We propose a generalised de Sitter scale factor for the cosmology of early and late time universe, including single scalar field is called as inflaton. This form of scale factor has a free parameter $q$ is called as nonextensivity parameter. When $q=1$, the scale factor is de Sitter. This scale factor is an intermediate form between power-law and de Sitter. We study cosmology of such families. We show that both kinds of dark components, dark energy and dark matter simultaneously are described by this family of solutions. As a motivated idea, we investigate inflation in the framework of $q$-de Sitter. We consider three types of scenarios for inflation. In a single inflation scenario, we observe that, inflation ended without any specific ending inflation $ϕ_{end}$, the spectral index and the associated running of the spectral index are %$ n_\mathrm{s} - 1 \sim -2ε, \quad α_\mathrm{s} \equiv 0 $. To end the inflation: we should have $q=\frac{3}{4}$. We deduce that the inflation ends when the evolution of the scale factor is $a (t) =e_ {3/4} (t) $. With this scale factor there is no need to specify $ϕ_{end}$. As an alternative to have inflation with ending point, We will study q-inflation model in the context of warm inflation. We propose two forms of damping term $Γ$. In the first case when $Γ=Γ_0$, we show the scale invariant spectrum, (Harrison-Zeldovich spectrum, i.e. $n_s=1$) may be approximately presented by ($q=\frac{9}{10},~~N=70$). Also there is a range of values of $R$ and $n_s$ which is compatible with the BICEP2 data where $q=\frac{9}{10}$. In case $Γ=Γ_1V(ϕ)$, it is observed that small values of a number of e-folds are assured for small values of $q$ parameter. For $q=\frac{9}{10}$ a range of values of $R$ and $n_s$ is compatible with the BICEP2 data.
We investigate two classes of models of quintessential inflation, based upon canonical as well as noncanonical scalar fields. In particular, introducing potentials steeper than the standard exponential, we construct models that can give rise to a successful inflationary phase, with signatures consistent with Planck 2015 results. Additionally, using nonminimal coupling of the scalar field with massive neutrino matter, we obtain the standard thermal history of the Universe, with late-time cosmic acceleration as the last stage of evolution. In both cases, inflation and late-time acceleration are connected by a tracker solution.
We study Galileon scalar field model by considering the lowest order Galileon term in the lagrangian, $(\partial_μ ϕ)^2 \Boxϕ$ by invoking a field potential. We use Statefinder hierarchy to distinguish the light mass galileon models with different potentials amongst themselves and from the $Λ$CDM behaviour. The $Om$ diagnostic is applied to cosmological dynamics and observational constraints on the model parameters are studied using SN+Hubble+BAO data.
Extended $f(R)$ theories of gravity have been investigated from the symmetry point of view. We briefly has been investigated Noether symmetry of two types of extended $f(R)$ theories: $f(R,T)$ theory, in which curvature is coupled non minimally to the trace of energy momentum tensor $T_{μν}$ and mimetic $f (R) $ gravity, a theory with a scalar field degree of freedom, but ghost-free and with internal conformal symmetry. In both cases we write point -like Lagrangian for flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological background in the presence of ordinary matter. We have been shown that some classes of models existed with Noether symmetry in these viable extensions of $f(R)$ gravity. As a motivated idea, we have been investigating the stability of the solutions and the bouncing and $Λ$CDM models using the Noether symmetries. We have been shown that in mimetic $f(R)$ gravity bouncing and $Λ$CDM solutions are possible. Also a class of solutions with future singularities has been investigated.
This paper is devoted to study the possibility of forming anisotropic compact stars in modified Gauss-Bonnet, namely called as $f(G)$ theory of gravity which is one of the strong candidates,responsible for the accelerated expansion of the universe. For this purpose, we have used analytical solution of Krori and Barua metric to the Einstein field equations with anisotropic form of matter and power law model of $f(G)$ gravity. To determine the unknown constants in Krori and Barua metric, we have used the sample of compact stars, 4$U$1820-30, Her X-1, SAX J 1808-3658. The physical behavior of these stars have been analyzed with the observational data. In this setting, we have checked all the regularity conditions and stability of the compact stars 4$U$1820-30, Her X-1, SAX J1808-3658.
We investigate the turbulence effect in dark fluid universe with linear inhomogeneous equation of state. Attention is attached to two physical situations. First, we perform the perturbative analysis of turbulence and check its effects around the Big Rip. Later, treating the turbulence energy density as a part of total dark fluid, we study the stability of the system. The result shows that the stability is achieving as the energy density of turbulence decreases, changing into heat (the radiation), in perfect agreement with the avoidance of the Big Rip.
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters $H_0$ (Hubble constant) and $q$ (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of $Λ$CDM. We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on $ $ and $ $ i.e. $H_0$ average and $q$ average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard $Λ$CDM model as $q\rightarrow -1$. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.
This pedagogical review is devoted to quintessential inflation, which refers to unification of inflation and dark energy using a single scalar field. We present a brief but concise description of the concepts needed to join the two ends, which include discussion on scalar field dynamic, conformal coupling, instant preheating and relic gravitational waves. Models of quintessential inflation broadly fall into two classes, depending upon the early and late time behavior of the field potential. In the first type we include models in which the field potential is steep for most of the history of the Universe but turn shallow at late times, whereas in the second type the potential is shallow at early times followed by a steep behavior thereafter. In models of the first category inflation can be realized by invoking high-energy brane-induced damping, which is needed to facilitate slow roll along a steep potential. In models of second type one may invoke a non-minimal coupling of the scalar field with massive neutrino matter, which might induce a minimum in the potential at late times as neutrinos turn non-relativistic. In this category we review a class of models with non-canonical kinetic term in the Lagrangian, which can comply with recent B mode polarization measurements. The scenario under consideration is distinguished by the presence of a kinetic phase, which precedes the radiative regime, giving rise to blue spectrum of gravity waves generated during inflation. We highlight the generic features of quintessential inflation and also discuss on issues related to Lyth bound.
In this letter we study aspects of the holographic superconductors analytically in the presence of a constant external magnetic field. We show that the critical temperature and critical magnetic field can be calculated at nonzero temperature. We detect the Meissner effect in such superconductors. A universal relation between black hole mass $ M$ and critical magnetic field $H_c$ is proposed as $\frac{H_c}{M^{2/3}}\leq 0.687365$. We discuss some aspects of phase transition in terms of black hole entropy and the Bekenstein's entropy to energy upper bound.
We study thermodynamic of strange quark matter (SQM) using the analytic expressions of free and internal energies. We investigate two regimes of the high density and low density separately. As a vital program, in the case of a massless gluon and massless quarks at finite temperature, we also present a geometry of thermodynamics for the gluon and Bosons using a Legendre invariance metric, it is so called as geometrothermodynamic (GTD) to better understanding of the phase transition. The GTD metric and its second order scalar invariant have been obtained, and we clarify the phase transition by study the singularities of the scalar curvature of this Riemannian metric. This method is ensemble dependence and to complete the phase transition. Meanwhile, we also investigate enthalpy and entropy and internal energy representations. Our work exposes new pictures of the nature of phase transitions in SQM.
In this paper, we study two different models of dark energy based on Chaplygin gas equation of state. The first model is the variable modified Chaplygin gas while the second one is the extended Chaplygin gas. Both models are considered in the framework of higher order $f(R)$ modified gravity. We also consider the case of time varying gravitational constant $G$ and $Λ$ for both models. We investigate some cosmological parameters such as the Hubble, the deceleration and the equation of state parameters. Then we showed that the model that we considered, extended Chaplygin gas with time-dependent $G$ and $Λ$, is consistent with the observational data. Finally we conclude with the discussion of cosmological perturbations of our model.
In this paper, we consider an effective quintessence scalar field with a power-law potential interacting with a $P_{b}=ξqρ_{b}$ barotropic fluid as a first model, where $q$ is a deceleration parameter. For the second model we assume viscous polytropic gas interacting with the scalar field. We investigate problem numerically and analyze behavior of different cosmological parameter concerning to components and behavior of Universe. We also compare our results with observational data to fix parameters of the models. We find some instabilities in the first model which may disappear in the second model for the appropriate parameters. Therefore, we can propose interacting quintessence dark energy with viscous polytropic gas as a successful model to describe Universe.
Based on a stringy inspired Gauss-Bonnet (GB) modification of classical gravity, we constructed a model for neutron stars. We derived the modified forms of Tolman-Oppenheimer-Volkoff (TOV) equations for a generic function of $f(G)$ gravity. The hydrostatic equations remained unchanged but the dynamical equations for metric functions are modified due to the effects of GB term.
We present the analytic Lifshitz solutions for a scalar field model minimally coupled with the abelian gauge field in $N$ dimensions. We also consider the presence of cosmological constant $Λ$. The Lifshitz parameter $z$ appearing in the solution plays the role of the Lorentz breaking parameter of the model. We investigate the thermodynamical properties of the solutions and discuss the energy issue. Furthermore, we study the hairy black hole solutions in which the abelian gauge field breaks the symmetry near the horizon. In the holographic picture, it is equivalent to a second order phase transition. Explicitly we show that there exists a critical temperature which is a function of the Lifshitz parameter $z$. The system below the critical temperature becomes superconductor, but the critical exponent of the model remains the same of the usual holographic superconductors without the higher order gravitational corrections, in agreement with Ginzburg-Landau theories.