arXiv subjects
Publications and source records attributed to A. Toporensky.
We revisit the cyclic Universe scenario in scalar field FRW cosmology and check its applicability for a nonminimally coupled scalar field. We show that for the most popular case of a quartic potential and the standard nonminimal coupling this scenario does work. On the other hand, we identify certain cases where cyclic model fails to work and present corresponding reasons for this.
We demonstrate that the latest constraints on inflationary observables, namely the tensor-to-scalar ratio $r$ and the scalar spectral index $n_{_S}$, from the Cosmic Background Radiation (CMB) observations are already strong enough to rule out the model of a scalar field with a power law potential even in the presence of kinetic coupling to gravity with a positive coupling constant. The case for a negative coupling constant needs special treatment.
We consider general radially moving frames realized in the background of nonextremal black holes having causal structure similar to that of the Schwarzschild metric. In doing so, we generalize the Lema\^ıtre approach, constructing free-falling frames which are built from the reference particles with an arbitrary specific energy $e_{0}$ including $e_{0}<0$ and a special case $e_{0}=0$. The general formula of 3-velocity of a freely falling particle with the specific energy $e$ with respect to a frame with $% e_{0}$ is presented. We point out the relation between the properties of considered frames near a horizon and the Banados-Silk-West effect of an indefinite growth of energy of particle collisions. Using our radially moving frames, we consider also nonradial motion of test particles including the regions near the horizon and singularity. We also point out the properties of the Lema\^ıtre time at horizons depending on the frame and sign of particle energy.
In this methodological paper we consider geodesic motion of particles in a spherically symmetric black hole space-times. We develop an approach based on splitting the velocity of a freely falling particle to the flow velocity, which depends only on a metric, and deviation from it (a peculiar velocity). It applies to a wide class of spherically symmetric metrics and is exploited under the horizon of the Schwarzschild black hole. The present work generalizes previous results obtained for pure radial motion. Now, the motion is, in general, nonradial, so that an observer can have a nonzero angular momentum. This approach enables us to give simple physical interpretation of redshift (blueshift) inside the horizon including the region near the singularity and agrees with the recent results obtained by direct calculations.
We consider initial conditions for inflation in non-minimal kinetic coupling theory. If inflation is driven solely by kinetic term with no potential, the resulting number of e-folds depends only upon initial velocity of the scalar field $\dot ϕ$. We write down the expression for the number of e-folds explicitly, and show that for physically reasonable values of the coupling constant, we can get 60 e-folds only for exponentially big initial $\dot ϕ$. When the scalar field potential is taken into account, on the other hand, we need not very large $\dot ϕ$ to start with for 60 e-folds, on the other hand, some initial condition lead to physically inadmissible eternal inflation. We show numerically that in the measure used in the present paper only smaller part of initial conditions lead to eternal inflation for reasonable values of the coupling constant.
In this paper we study cosmological perturbations in teleparallel gravity. We discuss problems which appear in standard approach to $f(T)$ gravity, and find that these problems may be solved within covariant formulation of teleparallel gravity, which take into account spin connection. We calculate spin connection which symmetrize equation for perturbation and split diagonal and non-diagonal part of equation of motion. We demonstrate that there is minimal solution for spin connection, which lead to zero slip, however, in this case one additional equation appears, so the system may become over-determined. After that, we show that a more general solution exists, which is incompatible with zero slip, but allows to write down the equations of motion for cosmological perturbation in a self-consistent way without additional equations to be satisfied.
Usually, interpretation of redshift in static spacetimes (for example, near black holes) is opposed to that in cosmology. In this methodological note we show that both explanations are unified in a natural picture. This is achieved if considering the static spacetime one (i) makes a transition to a synchronous frame, (ii) returns to the original frame by means of local Lorentz boost. To reach our goal, we consider a rather general class of spherically symmetric spacetimes. In doing so, we construct frames that generalize the well-known Lemaitre and Painlevé--Gullstand ones and elucidate the relation between them. This helps to understanding in an unifying approach, how gravitation reveals itself in different branches of general relativity. This can be useful for general relativity university courses.
In this work we derive some general features of the redshift measured by radially moving observers in the black hole background. Let observer 1 cross the black hole horizon emitting of a photon while observer 2 crossing the same horizon later receives it. We show that if (i) the horizon is the outer one (event horizon) and (ii) it is nonextremal, received frequency is redshifted. This generalizes previous recent results in literature. For the inner horizon (like in the Reissner-Nordström metric) the frequency is blueshifted. If the horizon is extremal, the frequency does not change. We derive explicit formulas describing the frequency shift in generalized Kruskal- and Lemaitre-like coordinates.
We consider dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described -- the Kasner anisotropic solution and an isotropic "vacuum radiation" solution which has three sub cases depending on whether the equation of state parameter $w$ is bigger, smaller or equals to $1/3$. Initial conditions for numerical integrations have been chosen near General Relativity anisotropic solution with matter (Jacobs solution). We have found that for such initial conditions there is a range of values of coupling constants so that the resulting cosmological singularity is isotropic.
We study some properties of exact cosmological solutions for a flat multidimensional anisotropic Universe in Lovelock gravity. A particular attention is paid to some features of solution in a general Lovelock gravity which have no their counterparts in analogous solution of General Relativity. We consider exponential solutions and so called generalized Milne solution and discuss reasons for these solution to exist in Lovelock gravity and do not exist in General Relativity.
We investigate the cosmological dynamics of non-minimally coupled scalar field system described by $F(ϕ)R$ coupling with $F(ϕ)=(1-ξϕ^N)R$($N\ge2$) and the field potential, $V(ϕ)=V_0ϕ^n$. We use a generic set of dynamical variables to bring out new asymptotic regimes of the underlying dynamics. However, our dynamical variables miss the most important fixed point$-$ the de Sitter solution. We make use of the original form of system of equations to investigate the issues related to this important solution. In particular, we show that the de-Sitter solution which is a dynamical attractor of the system lies in the region of negative effective gravitational constant $G_N$ thereby leading to a ghost dominated universe in future and a transient quintessence(phantom) phase with $G_N>0 $ around the present epoch (however, as demonstrated by Starobinsky in 1981, the ghost dominated universe, if exists, can not be accessed from the Universe we live in, we shall say more about this important result in the last section). We also carry out comparison of the model with other competing models of dark energy such as galileon modified gravity and others.
We consider cosmological dynamics in generalized modified gravity theory with the $R\Box R$ term added to the action of the form $R+R^N$. Influence of $R \Box R$ term to the known solutions of modified gravity is described. We show that in particular case of $N=3$ these two non-Einstein terms are equally important on power-law solutions. These solutions and their stability have been studied using dynamical system approach. Some results for the case of $N \ne 3$ (including stability of de Sitter solution in the theory under investigation) have been found using other methods.
We write down an anisotropic solution for a flat 5+1 dimensional Universe in Gauss-Bonnet gravity. In the model under investigation this solution replaces the generalized Kasner solution near a cosmological singularity.
We consider dynamics of the FRW Universe with a scalar field. Using Maupertuis principle we find a curvature of geodesics flow and show that zones of positive curvature exist for all considered types of scalar field potential. Usually, phase space of systems with the positive curvature contains islands of regular motion. We find these islands numerically for shallow scalar field potentials. It is shown also that beyond the physical domain the islands of regularity exist for quadratic potentials as well.
We study cosmological dynamics of a flat Randall-Sundrum brane with a scalar field and a negative "dark radiation" term. It is shown that in some situations the "dark radiation" can mimic spatial curvature and cause a chaotic behavior which is similar to chaotic dynamics in closed Universe with a scalar field.
The Einstein-Gauss-Bonnet equations projected from the bulk to brane lead to a complicated Friedmann equation which simplifies to $H^2 \sim ρ^q$ in the asymptotic regimes. The Randall-Sundrum (RS) scenario corresponds to $q=2$ whereas $q=2/3$ $&$ $q=1$ give rise to high energy Gauss-Bonnet (GB) regime and the standard GR respectively. Amazingly, while evolving from RS regime to high energy GB limit, one passes through a GR like region which has important implications for brane world inflation. For tachyon GB inflation with potentials $V(ϕ) \sim ϕ^p$ investigated in this paper, the scalar to tensor ratio of perturbations $R$ is maximum around the RS region and is generally suppressed in the high energy regime for the positive values of $p$. The ratio is very low for $p>0$ at all energy scales relative to GB inflation with ordinary scalar field. The models based upon tachyon inflation with polynomial type of potentials with generic positive values of $p$ turn out to be in the $1 σ$ observational contour bound at all energy scales varying from GR to high energy GB limit. The spectral index $n_S$ improves for the lower values of $p$ and approaches its scale invariant limit for $p=-2$ in the high energy GB regime. The ratio $R$ also remains small for large negative values of $p$, however, difference arises for models close to scale invariance limit. In this case, the tensor to scale ratio is large in the GB regime whereas it is suppressed in the intermediate region between RS and GB. Within the frame work of patch cosmologies governed by $H^2 \sim ρ^q$, the behavior of ordinary scalar field near cosmological singularity and the nature of scaling solutions are distinguished for the values of $q < 1$ and $q > 1$.
We investigate Bianchi I cosmological model in the theory of a dilatonM field coupled to gravity through a Gauss-Bonnet term. Two type ofM cosmological singularity are distinguished. The former is analogous toM the Einstein gravity singularity, the latter (which does not appear inM classical General Relativity) occurs when the main determinant of theM system of field equations vanishes. An analogy between the latterM cosmological singularity and the singularity inside a black hole withM a dilatonic hair is discussed. Initial conditions, leading to theseM two types of cosmological singularity are found via numericalM integration of the equation of motion.