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R. Myrzakulov

Publications and source records attributed to R. Myrzakulov.

At least 91 records · Page 5Linked to original sources
arXiv2014

Nearly Starobinsky inflation from modified gravity

We study inflation induced by (power-low) scalar curvature corrections to General Relativity. The class of inflationary scalar potentials $V(σ)\sim\exp[n\,σ]$, $n$ general parameter, is investigated in the Einsein frame and the corresponding actions in the Jordan frame are derived. We found the conditions for which these potentials are able to reproduce viable inflation according with the last cosmological data and lead to large scalar curvature corrections which emerge only at a mass scale larger than the Planck mass. Cosmological constant may appear or be set equal to zero in the Jordan frame action without changing the behaviour of the model during inflation. Moreover, polynomial corrections to General Relativity are analyzed in detail. When de Sitter space-time emerges as an exact solution of the models, it is necessary to use perturbative equations in the Jordan framework to study their dynamics during the inflation. In this case, we demonstrate that the Ricci scalar decreases after a correct amount of inflation, making the models consistent with the observable evolution of the universe.

gr-qc↗
arXiv2014

Evading Lyth bound in models of quintessential inflation

Quintessential inflation refers to an attempt to unify inflation and late-time cosmic acceleration using a single scalar field. In this letter we consider two different classes of quintessential inflation, one of which is based upon a Lagrangian with non-canonical kinetic term $k^2(ϕ)\partial^μϕ\partial_μϕ$ and a steep exponential potential while the second class uses the concept of steep brane world inflation. We show that in both cases the Lyth bound can be evaded, despite the large tensor-to-scalar ratio of perturbations. The post-inflationary dynamics is consistent with nucleosynthesis constraint in these cases.

gr-qc↗
arXiv2014

Interacting quintessence dark energy models in Lyra manifold

In this paper, we consider two-component dark energy models in Lyra manifold. The first component is assumed as a quintessence field while the second model may be a viscous polytropic gas, a viscous Van der Waals gas or a viscous modified Chaplygin gas. We also consider the possibility of interaction between components. By using numerical analysis, we study some cosmological parameters of the models and compare them with observational data.

gr-qc↗
arXiv2014

Trace-anomaly driven inflation in modified gravity and the BICEP2 result

We explore conformal-anomaly driven inflation in $F(R)$ gravity without invoking the scalar-tensor representation. We derive the stress-energy tensor of the quantum anomaly in the flat homogeneous and isotropic universe. We investigate a suitable toy model of exponential gravity plus the quantum contribution due to the conformal anomaly, which leads to the de Sitter solution. It is shown that in $F(R)$ gravity model, the curvature perturbations with its enough amplitude consistent with the observations are generated during inflation. We also evaluate the number of $e$-folds at the inflationary stage and the spectral index $n_\mathrm{s}$ of scalar modes of the curvature perturbations by analogy with scalar tensor theories, and compare them with the observational data. As a result, it is found that the Ricci scalar decreases during inflation and the standard evolution history of the universe is recovered at the small curvature regime. Furthermore, it is demonstrated that in our model, the tensor-to-scalar ratio of the curvature perturbations can be a finite value within the $68\%\,\mathrm{CL}$ error of the very recent result found by the BICEP2 experiment.

hep-th↗
arXiv2014

Observational constraints on models of the Universe with time variable Gravitational and Cosmological constants along MOG

The subject of this paper is to investigate the weak regime covariant scalar-tensor-vector gravity (STVG) theory, known as the MOdified gravity (MOG) theory of gravity. First, we show that the MOG in the absence of scalar fields is converted into $Λ(t),G(t)$ models. Time evolution of the cosmological parameters for a family of viable models have been investigated. Numerical results with the cosmological data have been adjusted. We've introduced a model for dark energy (DE) density and cosmological constant which involves first order derivatives of Hubble parameter. To extend this model, correction terms including the gravitational constant are added. In our scenario, the cosmological constant is a function of time. To complete the model,interaction terms between dark energy and dark matter (DM) manually entered in phenomenological form. Instead of using the dust model for DM, we have proposed DM equivalent to a barotropic fluid. Time evolution of DM is a function of other cosmological parameters. Using sophisticated algorithms, the behavior of various quantities including the densities, Hubble parameter, etc. have been investigated graphically. The statefinder parameters have been used for the classification of DE models. Consistency of the numerical results with experimental data of $SneIa+BAO+CMB$ are studied by numerical analysis with high accuracy.

gr-qc↗
arXiv2014

Variable gravity: A suitable framework for quintessential inflation

In this paper, we investigate a scenario of variable gravity and apply it to the unified description of inflation and late time cosmic acceleration dubbed quintessential inflation. The scalar field called "cosmon" which in this model unifies both the concepts reduces to inflaton at early epochs. We calculate the slow-roll parameters, the Hubble parameter at the end of inflation, the reheating temperature,the tensor-to-scalar ration and demonstrate the agreement of the model with observations and the Planck data.As for the post inflationary dynamics, cosmon tracks the background before it exits the scaling regime at late times. The scenario gives rise to correct epoch sequence of standard cosmology, namely, radiative regime, matter phase and dark-energy. We show that the long kinetic regime after inflation gives rise to enhancement of relic gravity wave amplitude resulting into violation of nucleosynthesis constraint at the commencement of radiative regime in case of an inefficient reheating mechanism such as gravitational particle production. Instant preheating is implemented to successfully circumvent the problem. As a generic feature, the scenario gives rise to a blue spectrum for gravity waves on scales smaller than the comoving horizon scale at the commencement of the radiative regime.

gr-qc↗
arXiv2014

A class of quintessential inflation models with parameter space consistent with BICEP2

In this paper, we focus on general features of quintessential inflation which is an effort to unify inflation and dark energy using a single scalar field. We describe a class of models of quintessential inflation which can give rise to the tensor to scalar ratio of perturbations consistent with recent BICEP2 measurements. The scale of inflation in the model is around the GUT scale and there is large parameter space consistent with the recent findings.

gr-qc↗
arXiv2014

Darboux Transformation and Exact Solutions of the Myrzakulov-Lakshmanan-II Equation

The Myrzakulov-Lakshmanan-II (ML-II) equation is one of a (2+1)-dimensional generalizations of the Heisenberg ferromagnetic equation. It is integrable and has a non-isospectral Lax representation. In this paper, the Darboux transformation (DT) for the ML-II equation is constructed. Using the DT, the 1-soliton and 2-soliton solutions of the ML-II equation are presented.

nlin.SI↗
arXiv2014

Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations

Motion of curves and surfaces in $\R^3$ lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self consistent vector potentials can lead to interesting generalized spin systems with self consistent potentials or soliton equations with self consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota-Maxwell-Bloch equations, all in the presence of self consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability.

nlin.PS↗
arXiv2014

FRW cosmology of the generalized model of LQG

In this paper, we study the main cosmological properties of the classical Friedmann equations in the case of homogeneous and isotropic Friedmann-Robertson-Walker Universe and we also generalized the expression of the Friedmann equation in the case of Loop Quantum Cosmology (LQC). Considering the $M_{35}$-model, we found the solutions of the equations considered for two particular cases, i.e. $Q=0$ (i.e., the de Sitter solution) and $Q>0$. Moreover, we considered and studied two exact cosmological solutions of the $M_{35}$-model, in particular the power-law and the exponential ones. Futhermore, we also considered a third more complicated case and we derived the solution for an arbitrary function of the time $f\left(t\right)$. A scalar field description of the model is presented by constructing its self-interacting potential.

gr-qc↗
arXiv2014

Cosmological investigations of (extended) nonlinear massive gravity schemes with non-minimal coupling

In this paper we investigate the case of non-minimal coupling in the (extended) nonlinear massive gravity theories. We first consider massive gravity in the Brans-Dicke background such that the graviton mass is replaced by $A^2(σ)m$ where $σ$ is the Brans-Dicke field and $A(σ)$ is conformal coupling and show that there is no viable thermal history of the universe in this case. We then invoke a cubic galileon term as nonlinear completion of the $σ$ Lagrangian and show that there is a stable de Sitter solution in this case. However, the de Sitter is blocked by the matter phase which is also a simultaneous attractor of the dynamics. The de Sitter phase can, however, be realized by invoking unnatural fine tunings. We next investigate cosmology of quasi-dilaton nonlinear massive gravity with non-minimal coupling. As a generic feature of the non-minimal coupling, we show that the model exhibits a transient phantom phase which is otherwise impossible. While performing the observational data analysis on the models, we find that a small value of coupling constant is allowed for quasi-dilaton nonlinear massive gravity. For both the cases under consideration, it is observed that we have an effective pressure of matter which comes from the constraint equation. For mass-varying nonlinear massive gravity in the Brans-Dicke background, the effective pressure of matter is non zero which affects the evolution of the Hubble parameter thereby spoiling consistency of the model with data. As for, quasi-dilaton nonlinear massive gravity, the effective pressure of matter can be kept around zero by controlling the coupling constant, the model is shown to be fit well with observations.

hep-th↗
arXiv2014

Interacting Ricci dark energy models with an effective $Λ$-term in Lyra manifold

In this paper we consider a universe filled with barotropic dark matter and Ricci dark energy in Lyra geometry with varying Lambda. We assume two different kinds of interactions between dark matter and dark energy. Then, by using numerical analysis, we investigate some cosmological parameters of the models such as equation of state, Hubble and deceleration parameters.

gr-qc↗
arXiv2014

Interaction between modified Chaplygin gas and ghost dark energy in presence of extra dimensions

In this paper, we consider three different models of dark energy in higher dimensional space-time and discuss about some cosmological parameters numerically. The first model is a single component universe including viscous varying modified Chaplygin gas. In the second model, we consider two-component universe including viscous varying modified Chaplygin gas and ghost dark energy. In the third model, we consider another two-component universe including viscous modified cosmic Chaplygin gas and ghost dark energy. In the cases of two-component fluids we also consider possibility of interaction between components.

gr-qc↗
arXiv2014

Cosmology with hybrid expansion law: scalar field reconstruction of cosmic history and observational constraints

In this paper, we consider a simple form of expansion history of Universe referred to as the hybrid expansion law - a product of power-law and exponential type of functions. The ansatz by construction mimics the power-law and de Sitter cosmologies as special cases but also provides an elegant description of the transition from deceleration to cosmic acceleration. We point out the Brans-Dicke realization of the cosmic history under consideration. We construct potentials for quintessence, phantom and tachyon fields, which can give rise to the hybrid expansion law in general relativity. We investigate observational constraints on the model with hybrid expansion law applied to late time acceleration as well as to early universe a la nucleosynthesis.

gr-qc↗
arXiv2013

The instabilities and (anti)-evaporation of Schwarzschild-de Sitter black holes in modified gravity

We investigate the future evolution of Nariai black hole which is extremal limit of Schwarzschild-de Sitter one in modified gravity. The perturbations equations around Nariai black hole are derived in static and cosmological patches for general $F(R)$-gravity. The analytical and numerical study of several realistic $F(R)$-models shows the occurence of rich variety of scenarios: instabilities, celebrated Hawking evaporation and anti-evaporation of black hole. The realization of specific scenario depends on the model under consideration. It is remarkable that the presence of such primordial black holes at current universe may indicate towards the modified gravity which supports the anti-evaporation as preferrable model. As some generalization we extend the study of Nariai black hole evolution to modified Gauss-Bonnet gravity. The corresponding perturbations equations turn out to be much more complicated than in the case of $F(R)$ gravity. For specific example of modified Gauss-Bonnet gravity we demonstrate that Nariai solution maybe stable.

gr-qc↗
arXiv2013

Charged Black Holes in Generalized Teleparallel Gravity

In this paper we investigate charged static black holes in 4D for generalized teleparallel models of gravity, based on torsion as the geometric object for describing gravity according to the equivalence principle. As a motivated idea, we introduce a set of non-diagonal tetrads and derive the full system of non linear differential equations. We prove that the common Schwarzschild gauge is applicable only when we study linear f(T) case. We reobtain the Reissner-Nordstrom-de Sitter (or RN-AdS) solution for the linear case of f(T) and perform a parametric cosmological reconstruction for two nonlinear models. We also study in detail a type of the no-go theorem in the framework of this modified teleparallel gravity.

gr-qc↗
arXiv2013

Looking for empty topological wormhole spacetimes in $F(R)$-modified gravity

Much attention has been recently devoted to modified theories of gravity in the attempt to efficiently describe both early inflation and late-time acceleration of our universe without referring to the cosmological constant or other ad hoc kinds of fluids. The simplest models overcome General Relativity simply by replacing $R$ with $F(R)$ in the Einstein--Hilbert action. Unfortunately, such models typically lack most of the beautiful solutions discovered in Einstein's gravity. Nonetheless, in $F(R)$ gravity, it has been possible to get at least few black holes, but still we do not know any empty wormhole-like spacetime solution. The present paper aims to explain why it is so hard to get such solutions (given that they exist). Few solutions are derived in the simplest cases while only an implicit form has been obtained in the non-trivial case.

gr-qc↗