arXiv subjects

Sergey A. Pavluchenko

Publications and source records attributed to Sergey A. Pavluchenko.

18 recordsLinked to original sources

arXiv2021

Exponential cosmological solutions in Einstein-Gauss-Bonnet gravity with two subspaces: general approach

In this paper we perform systematic investigation of all possible exponential solutions in Einstein-Gauss-Bonnet gravity with the spatial section being a product of two subspaces. We describe a scheme which always allow to find solution for a given $\{p, q\} > 2$ (number of dimensions of two subspaces) and $ζ$ (ratio of the expansion rates of these two subspaces). Depending on the parameters, for given $\{α, Λ\}$ (Gauss-Bonnet coupling and cosmological constant) there could be up to four distinct solutions (with different $ζ$'s). Stability requirement introduces relation between $ζ$, $\{p, q\}$ and sign of the expansion rate. Nevertheless, for any $\{p, q\} > 2$ we can always choose sign for expansion rates so that the resulting solution would be stable. The scheme for finding solutions is described and the bounds on the parameters are drawn. Specific cases with $\{p, q\} = \{1, 2\}$ are also considered. Finally, we separately described physically sensible case with one of the subspaces being three-dimensional and expanding (resembling our Universe) while another to be contracting (resembling extra dimensions), describing successful compactification; for this case we also drawn bounds on the parameters where such regime occurs.

gr-qc↗

arXiv2021

Some aspects of the cosmological dynamics in Einstein-Gauss-Bonnet gravity

We study some aspects of dynamical compactification scenario where stabilisation of extra dimensions occurs due to presence the Gauss-Bonnet term and non-zero spatial curvature. In the framework of the model under consideration there exists two-stages scenario of evolution of a Universe: on the first stage, the space evolves from a totally anisotropic state to the state with 3-dimensional (corresponding to our "real", world) expanding and $D$-dimensional contracting isotropic subspaces; on the second stage, constant curvature of extra dimensions begins to play role and provide compactification of extra dimensions. It is already known that such a scenario is realizable when constant curvature of extra dimensions is negative. Here we show that a range of coupling constants for which exponential solutions with 3-dimensional expanding and $D$-dimensional contracting isotropic subspaces are stable is located in a zone where compactification solutions with positively curved extra space are unstable, so that two-stage scenario analogous to the one described above is \emph{not} realizable. Also we study "nearly-Friedmann", regime for the case of arbitrary constant curvature of extra dimensions and describe new parametrization of the general solution for the model under consideration which provide elegant way of describing areas of existence over parameters space.

gr-qc↗

arXiv2020

Cosmological solutions in Einstein-Gauss-Bonnet gravity with static curved extra dimensions

In this paper we perform systematic investigation of all possible solutions with static compact extra dimensions and expanding three-dimensional subspace (``our Universe''). Unlike previous papers, we consider extra-dimensional subspace to be constant-curvature manifold with both signs of spatial curvature. We provide a scheme how to build solutions in all possible number of extra dimensions and perform stability analysis for the solutions found. Our study suggests that the solutions with negative spatial curvature of extra dimensions are always stable while those with positive curvature are stable for a narrow range of the parameters and the width of this range shrinks with growth of the number of extra dimensions. This explains why in the previous papers we detected compactification in the case of negative curvature but the case of positive curvature remained undiscovered. Another interesting feature which distinguish cases with positive and negative curvatures is that the latter do not coexist with maximally-symmetric solutions (leading to ``geometric frustration'' of a sort) while the former could -- this difference is noted and discussed.

gr-qc↗

arXiv2018

Dynamics of the cosmological models with perfect fluid in Einstein-Gauss-Bonnet gravity: low-dimensional case

In this paper we performed investigation of the spatially-flat cosmological models whose spatial section is product of three- ("our Universe") and extra-dimensional parts. The matter source chosen to be the perfect fluid which exists in the entire space. We described all physically sensible cases for the entire range of possible initial conditions and parameters as well as brought the connections with vacuum and $Λ$-term regimes described earlier. In the present paper we limit ourselves with $D=1, 2$ (number of extra dimensions). The results suggest that in $D=1$ there are no realistic compactification regimes while in $D=2$ there is if $α> 0$ (the Gauss-Bonnet coupling) and the equation of state $ω< 1/3$, the measure of the initial conditions leading to this regime is increasing with growth of $ω$ and reaches its maximum at $ω\to 1/3 - 0$. We also describe some pecularities of the model, distinct to the vacuum and $Λ$-term cases -- existence of the isotropic power-law regime, different role of the constant-volume solution and the presence of the maximal density for $D = 2$, $α< 0$ subcase and associated features.

gr-qc↗

arXiv2018

Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: High-dimensional case

We investigate possible regimes in spatially flat vacuum cosmological models in cubic Lovelock gravity. The spatial section is a product of three- and extra-dimensional isotropic subspaces. This is the second paper of the series and we consider D=5 and general D>=6 cases here. For each D case we found critical values for $α$ (Gauss-Bonnet coupling) and $β$ (cubic Lovelock coupling) which separate different dynamical cases and study the dynamics in each region to find all regimes for all initial conditions and for arbitrary values of $α$ and $β$. The results suggest that for D>=3 there are regimes with realistic compactification originating from `generalized Taub' solution. The endpoint of the compactification regimes is either anisotropic exponential solution (for $α> 0$, $μ\equiv β/α^2 < μ_1$ (including entire $β< 0$)) or standard Kasner regime (for $α> 0$, $μ> μ_1$). For D>=8 there is additional regime which originates from high-energy (cubic Lovelock) Kasner regime and ends as anisotropic exponential solution. It exists in two domains: $α> 0$, $β< 0$, $μ\leqslant μ_4$ and entire $α> 0$, $β> 0$. Let us note that for D>=8 and $α> 0$, $β< 0$, $μ< μ_4$ there are two realistic compactification regimes which exist at the same time and have two different anisotropic exponential solutions as a future asymptotes. For D>=8 and $α> 0$, $β> 0$, $μ< μ_2$ there are two realistic compactification regimes but they lead to the same anisotropic exponential solution. This behavior is quite different from the Einstein-Gauss-Bonnet case. There are two more unexpected observations among the results -- all realistic compactification regimes exist only for $α> 0$ and there is no smooth transition from high-energy Kasner regime to low-energy one with realistic compactification.

hep-th↗

arXiv2018

Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: Low-dimensional case

In this paper we begin to perform systematical investigation of all possible regimes in spatially flat vacuum cosmological models in cubic Lovelock gravity. We consider the spatial section to be a product of three- and extra-dimensional isotropic subspaces, with the former considered to be our Universe. As the equations of motion are different for $D=3, 4, 5$ and general $D \geqslant 6$ cases, we considered them all separately. Due to the quite large amount different subcases, in the current paper we consider only $D=3, 4$ cases. For each $D$ case we found values for $α$ (Gauss-Bonnet coupling) and $β$ (cubic Lovelock coupling) which separate different dynamical cases, all isotropic and anisotropic exponential solutions, and study the dynamics in each region to find all possible regimes for all possible initial conditions and any values of $α$ and $β$. The results suggest that in both $D$ cases the regimes with realistic compactification originate from so-called "generalized Taub" solution. The endpoint of the compactification regimes is either anisotropic exponential (for $α> 0$, $μ\equiv β/α^2 < μ_1$ (including entire $β< 0$)) or standard low-energy Kasner regime (for $α> 0$, $μ> μ_1$), as it is compactification regime, both endpoints have expanding three and contracting extra dimensions. There are two unexpected observations among the results -- all realistic compactification regimes exist only for $α> 0$ and there is no smooth transition between high-energy and low-energy Kasner regimes, the latter with realistic compactification.

hep-th↗

arXiv2017

Effects of spatial curvature and anisotropy on the asymptotic regimes in Einstein-Gauss-Bonnet gravity

In this paper we address two important issues which could affect reaching the exponential and Kasner asymptotes in Einstein-Gauss-Bonnet cosmologies -- spatial curvature and anisotropy in both three- and extra-dimensional subspaces. In the first part of the paper we consider cosmological evolution of spaces being the product of two isotropic and spatially curved subspaces. It is demonstrated that the dynamics in $D=2$ (the number of extra dimensions) and $D \geqslant 3$ is different. It was already known that for the $Λ$-term case there is a regime with "stabilization" of extra dimensions, where the expansion rate of the three-dimensional subspace as well as the scale factor (the "size") associated with extra dimensions reach constant value. This regime is achieved if the curvature of the extra dimensions is negative. We demonstrate that it take place only if the number of extra dimensions is $D \geqslant 3$. In the second part of the paper we study the influence of initial anisotropy. Our study reveals that the transition from Gauss-Bonnet Kasner regime to anisotropic exponential expansion (with expanding three and contracting extra dimensions) is stable with respect to breaking the symmetry within both three- and extra-dimensional subspaces. However, the details of the dynamics in $D=2$ and $D \geqslant 3$ are different. Combining the two described affects allows us to construct a scenario in $D \geqslant 3$, where isotropisation of outer and inner subspaces is reached dynamically from rather general anisotropic initial conditions.

gr-qc↗

arXiv2017

Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: High-dimensional $Λ$-term case

In this paper we perform a systematic study of spatially flat $[(3+D)+1]$-dimensional Einstein-Gauss-Bonnet cosmological models with $Λ$-term. We consider models that topologically are the product of two flat isotropic subspaces with different scale factors. One of these subspaces is three-dimensional and represents our space and the other is $D$-dimensional and represents extra dimensions. We consider no {\it ansatz} of the scale factors, which makes our results quite general. With both Einstein-Hilbert and Gauss-Bonnet contributions in play, $D=3$ and the general $D\geqslant 4$ cases have slightly different dynamics due to the different structure of the equations of motion. We analytically study equations of motion in both cases and describe all possible regimes with special interest on the realistic regimes. Our analysis suggests that the only realistic regime is the transition from high-energy (Gauss-Bonnet) Kasner regime, which is the standard cosmological singularity in that case, to the anisotropic exponential regime with expanding three and contracting extra dimensions. Availability of this regime allows us to put constraint on the value of Gauss-Bonnet coupling $α$ and the $Λ$-term -- this regime appears in two regions on $(α, Λ)$ plane: $α< 0$, $Λ> 0$, $αΛ\leqslant 1/2$ and $α> 0$, $αΛ\leqslant (3D^2 - 7D + 6)/(4D(D-1))$, including entire $Λ< 0$ region. The obtained bounds are confronted with the restrictions on $α$ and $Λ$ from other considerations, like causality, entropy-to-viscosity ratio in AdS/CFT and others. Joint analysis constraints ($α$, $Λ$) even further: $α> 0$, $D \geqslant 2$ with $(3D^2 - 7D + 6)/(4D(D-1)) \geqslant αΛ\geqslant - (D+2)(D+3)(D^2 + 5D + 12)/(8(D^2 + 3D + 6)^2)$.

hep-th↗

arXiv2016

Dynamics of gravitating hadron matter in Bianchi-IX cosmological model

We perform an analysis of the Einstein-Skyrme cosmological model in Bianchi-IX background. We analytically describe asymptotic regimes and semi-analytically -- generic regimes. It appears that depending on the product of Newtonian constant $κ$ with Skyrme coupling $K$, in absence of the cosmological term there are three regimes possible -- recollapse with $\kK < 2$ and two power-law regimes -- $\propto t^{1/2}$ for $\kK=2$ and $\propto t$ for $\kK > 2$. In presence of the positive cosmological term, power-law regimes turn to exponential (de Sitter) ones while recollapse regime turn to exponential if the value for $Λ$-term is sufficiently large, otherwise the regime remains recollapse. Negative cosmological term leads to the recollapse regardless of $\kK$. All nonsingular regimes have the squashing coefficient $a(t) \to 1$ at late times, which is associated with restoring symmetry dynamics. Also all nonsingular regimes appear to be linearly stable -- exponential solutions always while power-law for an open region of initial conditions.

gr-qc↗

arXiv2016

Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: Low-dimensional $Λ$-term case

In this paper we perform a systematic study of spatially flat [(3+D)+1]-dimensional Einstein-Gauss-Bonnet cosmological models with $Λ$-term. We consider models that topologically are the product of two flat isotropic subspaces with different scale factors. One of these subspaces is three-dimensional and represents our space and the other is D-dimensional and represents extra dimensions. We consider no {\it Ansatz} on the scale factors, which makes our results quite general. With both Einstein-Hilbert and Gauss-Bonnet contributions in play, the cases with $D=1$ and $D=2$ have different dynamics due to the different structure of the equations of motion. We analytically study equations of motion in both cases and describe all possible regimes. It is demonstrated that $D=1$ case does not have physically viable regimes while $D=2$ has smooth transition from high-energy Kasner to anisotropic exponential regime. This transition occurs for two ranges of $α$ and $Λ$: $α> 0$, $Λ> 0$ with $αΛ\leqslant 1/2$ and $α< 0$, $Λ> 0$ with $αΛ< -3/2$. For the latter case if $αΛ= -3/2$, extra dimensional part has $h\to 0$ and so the size of extra dimensions (in the sense of the scale factor) is reaching constant value. We report substantial differences between $D=1$ and $D=2$ cases and between these cases and their vacuum counterparts, describe features of the cases under study and discuss the origin of the differences.

hep-th↗

arXiv2016

Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions. Vacuum case

In this paper we perform a systematic study of vacuum spatially flat ((3+D)+1)-dimensional Einstein-Gauss-Bonnet cosmological models. We consider models which topologically are the product of two flat isotropic subspaces with different scale factors. One of these subspaces is 3D and represents our space and the other is D-dimensional and represents extra dimensions. We consider no ansatz of the scale factors, which makes our results quite general. With both Einstein-Hilbert and Gauss-Bonnet contributions in play, the cases with D=1, D=2, D=3 and $D\geqslant 4$ have different dynamics due to different structure of the equations of motion. We analytically study equations of motion in all cases and describe all possible regimes. It appears that the only regimes with nonsingular future asymptotes are the Kasner regime in GR as well as exponential regimes. As of the past asymptotes, for a smooth transition only Kasner regime in Gauss-Bonnet is an option. With that at hand, we are down only to two viable regimes -- "pure" Kasner regime (transition from high- to low-energy Kasner regime) and a transition from high-energy Kasner to anisotropic exponential solution. It appears that these regimes take place for different signs of the Gauss-Bonnet coupling $α$: "pure" Kasner regime occur for $α> 0$ at low D and $α< 0$ for high D; anisotropic exponential regime is reached only for $α> 0$. So if we restrain ourselves with $α> 0$ solutions, the only late-time regimes are Kasner for D=1, 2 and anisotropic exponential for $D\geqslant 2$. Also, low-energy Kasner regimes ($a(t)\propto t^p$) have expansion rates for (3+1)-dimensional subspace ("our Universe") ranging from p=0.5 (D=1) to $p=1/\sqrt{3} \approx 0.577$ ($D\to\infty$), which contradicts with dust-dominated Friedmann prediction (p=2/3).

hep-th↗

arXiv2016

Friedmann dynamics recovered from compactified Einstein-Gauss-Bonnet cosmology

In this paper cosmological dynamics in Einstein-Gauss-Bonnet gravity with a perfect fluid source in arbitrary dimension is studied. A systematic analysis is performed for the case that the theory does not admit maximally symmetric solutions. Considering two independent scale factors, namely one for the three dimensional space and one for the extra dimensional space, is found that a regime exists where the two scale factors tend to a constant value via damped oscillations for not too negative pressure of the fluid, so that asymptotically the evolution of the $(3+1)$-dimensional Friedmann model with perfect fluid is recovered. At last, it is worth emphasizing that the present numerical results strongly support a 't Hooft-like interpretation of the parameter $1/D$ (where $D$ is the number of extra dimensions) as a small expansion parameter in very much the same way as it happens in the large $N$ expansion of gauge theories with $1/N$. Indeed, the dependence on $D$ of many of the relevant physical quantities computed here manifests a clear WKB-like pattern, as expected on the basis of large $N$ arguments.

gr-qc↗

arXiv2015

Stability analysis of the exponential solutions in Lovelock cosmologies

In this paper we perform stability analysis for exponential solutions in Einstein-Gauss-Bonnet and cubic Lovelock gravity. We report our findings, provide areas on parameters space and discuss familiarities and differences between cases. Analysis suggests that only several cases out of numerous found solutions could be called stable. In particular, cases with three-dimensional isotropic subspace which could give rise to successful compactification are diminished to one general case and one additional partial solution in the cubic Lovelock case.

gr-qc↗

arXiv2014

Cosmological dynamics in higher-dimensional Einstein-Gauss-Bonnet gravity

In this paper we perform a systematic classification of the regimes of cosmological dynamics in Einstein-Gauss-Bonnet gravity with generic values of the coupling constants. We consider a manifold which is a warped product of a four dimensional Friedmann-Robertson-Walker space-time with a $D$-dimensional Euclidean compact constant curvature space with two independent scale factors. A numerical analysis of the time evolution as function of the coupling constants and of the curvatures of the spatial section and of the extra dimension is performed. We describe the distribution of the regimes over the initial conditions space and the coupling constants. The analysis is performed for two values of the number of extra dimensions ($D\geqslant 6$ both) which allows us to describe the effect of the number of the extra dimensions as well.

gr-qc↗

arXiv2014

Constant volume exponential solutions in Einstein-Gauss-Bonnet flat anisotropic cosmology with a perfect fluid

In this paper we investigate the constant volume exponential solutions (i.e. the solutions with the scale factors change exponentially over time so that the comoving volume remains the same) in the Einstein-Gauss-Bonnet gravity. We find conditions for these solutions to exist and show that they are compatible with any perfect fluid with the equation of state parameter $ω<1/3$ if the matter density of the Universe exceeds some critical value. We write down some exact solutions which generalize ones found in our previous paper for models with a cosmological constant.

gr-qc↗

arXiv2014

Cosmological dynamics of gravitating hadron matter

Anisotropic cosmologies are studied in the case where the matter source is given by the Skyrme model which is an effective description of low energy QCD. The dynamical evolution of the Kantowski-Sachs and Bianchi-I universes are analyzed in depth. In both situations in order for solutions to exist and at the same time to avoid finite time future singularities, bounds on the value of the cosmological constant and on the values of the Skyrme couplings must be set. The upper bound on the cosmological constant, which depends also on the initial conditions is closely related to the fact that the baryons appear below 1 GeV. The upper bound on the cosmological constant is actually 72 orders of magnitudes lower than the standard estimations from quantum field theory. The lower bound on the cosmological constant and the bounds on the Skyrme couplings are due to the peculiar combination of nonlinear terms in the Skyrme model. It is worth to point out that bounds on the Skyrme couplings occur in similar fashion both for the Kantowski-Sachs and for the Bianchi-I models which are topologically completely different. Our results suggest that this behavior is intrinsic to the coupling of the Skyrme field to gravity rather than on a specific cosmological model.

gr-qc↗

arXiv2013

Dynamical compactification in Einstein-Gauss-Bonnet gravity from geometric frustration

In this paper we study dynamical compactification in Einstein-Gauss-Bonnet gravity from arbitrary dimension for generic values of the coupling constants. We showed that, when the curvature of the extra dimensional space is negative, for any value of the spatial curvature of the four dimensional space-time one obtains a realistic behavior in which for asymptotic time both the volume of the extra dimension and expansion rate of the four dimensional space-time tend to a constant. Remarkably, this scenario appears within the open region of parameters space for which the theory does not admit any maximally symmetric (4+D)- dimensional solution, which gives to the dynamical compactification an interpretation as geometric frustration. In particular there is no need to fine-tune the coupling constants of the theory so that the present scenario does not violate "naturalness hypothesis". Moreover we showed that with increase of the number of extra dimensions the stability properties of the solution are increased.

gr-qc↗

arXiv2004

Some constraints on brane inflation models with power-law potentials

We investigate inflation in Randall-Sundrum type II brane scenario with closed Friedman-Robertson-Walker (FRW) brane. We consider only power-law potentials of the scalar field and wide range of powers and parameters for them. For our models we numerically calculate the total number of e-folds, the value of potential at the end of inflation and amplitude and spectral index of scalar perturbations at the epoch when the present Hubble scale leaves the horizon. All these values we calculate for different initial conditions and different values of parameters. Then we compare our theoretical predictions with observation data and set constraints on the parameters of our model.

astro-ph↗