arXiv subjects

V. A. Yurov

Publications and source records attributed to V. A. Yurov.

13 recordsLinked to original sources

arXiv2019

What can the anthropic principle tell us about the future of the dark energy universe?

An anthropic explanation for evident smallness of the value of the dark energy implies the existence of a time-dependent component of the scalar field, serving, together with a negative-valued cosmological constant, as one of two components to the overall density of the dark energy. The observers (i.e. us) might then only evolve in those regions of the universe where the sum of those two components (a positive and a negative ones) is sufficiently close to zero. However, according to Vilenkin and Garriga, the scalar field component has to slowly but surely diminish in time. In about a trillion years this process will put a cap to the now-observable accelerated expansion of the universe, leading to a subsequent phase of impending collapse. However, the vanishing scalar field might also produce some rather unexpected singularities for a finite non-zero scale factor. We analyse this possibility on a particular example of Sudden Future Singularities (SFS) and come to a startling conclusion: the time required for SFS to arise must be "comparable" to the lifetime of observable universe.

gr-qc↗

arXiv2018

The Landau-Lifshitz equation, the NLS, and the magnetic rogue wave as a by-product of two colliding regular "positons"

In this article we present a new method for construction of exact solutions of the Landau-Lifshitz-Gilbert equation (LLG) for ferromagnetic nanowires. The method is based on the established relationship between the LLG and the nonlinear Schrödinger equation (NLS), and is aimed at resolving an old problem: how to produce multiple-rogue wave solutions of NLS using just the Darboux-type transformations. The solutions of this type - known as P-breathers - have been proven to exist by Dubard and Matveev, but their technique heavily relied on using the solutions of yet another nonlinear equation, Kadomtsev-Petviashvili I equation (KP-I), and its relationship with NLS. We have shown that in fact one doesn't have to use KP-I but can instead reach the same results just with NLS solutions, but only if they are dressed via the binary Darboux transformation. In particular, our approach allows to construct all the Dubard-Matveev P-breathers. Furthermore, the new method can lead to some completely new, previously unknown solutions. One particular solution that we have constructed describes two positon-like waves, colliding with each other and in the process producing a new, short-lived rogue wave. We called this unusual solution (rogue wave begotten after the impact of two solitons) the "impacton".

nlin.SI↗

arXiv2015

The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation

We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov-Veselov equation. The procedure shown therein utilizes the well-known Airy function $\text{Ai}(ξ)$ which in turn serves as a solution to the ordinary differential equation $\frac{d^2 z}{d ξ^2} = ξz$. In the second part of the article we show that the aforementioned procedure can also work for the $n$-th order generalizations of the Novikov-Veselov equation, provided that one replaces the Airy function with the appropriate solution of the ordinary differential equation $\frac{d^{n-1} z}{d ξ^{n-1}} = ξz$.

nlin.SI↗

arXiv2014

The KdV in Cosmology: a useful tool or a distraction?

The letter is a response to the recent article by J. Lidsey. We demonstrate that the Schwarzian derivative technique developed therein is but a consequence of linearizabiliy of the original cosmological equations. Furthermore, we show the required linearized equation to be nothing else but a Schrödinger equation.

gr-qc↗

arXiv2011

Friedman vs Abel equations: A connection unraveled

We present an interesting connection between Einstein-Friedmann equations for the models of universe filled with scalar field and the special form of Abel equation of the first kind. This connection works in both ways: first, we show how, knowing the general solution of the Abel equation (corresponding to the given scalar field potential) one can obtain the general solution of the Friedman Equation (and use the former for studying such problems as existence of inflation with exit for particular models). On the other hand, one can invert the procedure and construct the Bäcklund auto-transformations for the Abel equation.

hep-th↗

arXiv2008

Quantum Creation of a Universe in Albrecht-Magueijo-Barrow model

In quantum cosmology the closed universe can spontaneously nucleate out of the state with no classical space and time. The semiclassical tunneling nucleation probability can be estimated as $\emph{P}\sim\exp(-α^2/Λ)$ where $α$=const and $Λ$ is the cosmological constant. In classical cosmology with varying speed of light $c(t)$ (VSL) it is possible to solve the horizon problem, the flatness problem and the $Λ$-problem if $c=sa^n$ with $s$=const and $n<-2$. We show that in VSL quantum cosmology with $n<-2$ the semiclassical tunneling nucleation probability is $\emph{P}\sim\exp(-β^2Λ^k)$ with $β$=const and $k>0$. Thus, the semiclassical tunneling nucleation probability in VSL quantum cosmology is very different from that in quantum cosmology with $c$=const. In particular, it can be strongly suppressed for large values of $Λ$. In addition, we propose the instanton which describes the nucleation of closed universes in VSL models. This solution is akin to the Hawking-Turok instanton in the means of O(4) invariance but, unlike to it, is non-singular. Moreover, using this solution we can obtain the probability of nucleation which is suppressed for large value of $Λ$ too.

hep-th↗

arXiv2007

The dressing procedure for the cosmological equations and the indefinite future of the universe

In this paper we present a new simple method of construction of infinite number of solutions of Freidmann equations from the already known ones, which allows for a startling conclusion of practical impossibility of correct predictions on the universe's future dynamics which are based solely on astronomical observations on the value of a scale factor. In addition, we present particular examples of newly constructed solutions, such as the ones, describing the smooth dynamical (de)-phantomization, and the models lacking the events horizons (both in classical and brane world cases). The generalization of the method to the simplest anisotropic universes are presented as well.

astro-ph↗

arXiv2005

One more observational consequence of many-worlds quantum theory

Using new cosmological doomsday argument Page predicts that the maximal lifetime of de Sitter universe should be $t_{max}=10^{60}$ yr which is way too small in comparison with strings predictions ($t_f>$googleplex). However, since this prediction is dependant on the total number of human observations, we show that Page arguments results instead in astounding conclusion that this number is the quantum variable and is therefore much greater then Page's estimation. Identifying it with the number of coarse-grained histories in de Sitter universe we get the lifetime of the universe comparable with strings predictions. Moreover, it seems that this result can be considered as another one of the observational evidences of validity of the many-worlds quantum theory. Finally, we show that for the universe filled with phantom energy $t_{max}\sim t_f$ up to very high precision.

hep-th↗

arXiv2005

The nonsingular brane solutions via the Darboux transformation

We consider the Darboux transformation as a method of construction of exact nonsingular solutions describing the three-dimensional brane that interacts with five-dimensional gravity and the bulk scalar field. To make it work, the five-dimensional Einstein's equations and the Israel's conditions are being reduced to the Schrödinger equation with the jump-like potential and the wave functions sewing conditions in jump point correspondingly. We show further that it is always possible to choose the functions in Crum's determinants in such way, that the five-dimensional Ricci scalar $R$ will always be finite both on brane and in bulk. The new exact solutions being the generalizations of the model with the odd superpotential are presented. Described formalism is also appliable to the cases of more realistic branes with cosmological expansion. As an example, via the usage of the simple orbifold model ($S_1/{\Bbb Z}_2$) and one-time Darboux transformation we construct the models where the cosmological constant on the visible brane is exponentially small.

hep-th↗

arXiv2005

Can we escape from the big rip in the achronal cosmic future?

Recently Pedro F. Gonzalez-Diaz had shown that phantom energy can results in achronal cosmic future where the wormholes become infinite before the occurrence of the big rip singularity. After that, while the phantom energy continues its accretion, any wormhole becomes the Einstein-Rosen bridge. Pedro F. Gonzalez-Diaz has suggested that such objects can be used by an advanced civilization as the means of escape from the big rip. Using the Bekenstein Bound we'll show that it is impossible due to the very strong upper bound laid on the total amount of information which can be sent through this bridge.

astro-ph↗

arXiv2005

Quantum cosmologies with varying speed of light and the $Λ$ problem

In quantum cosmology the closed universe can spontaneously nucleate out of the state with no classical space and time. For the universe filled with a vacuum of constant energy density the semiclassical tunneling nucleation probability can be estimated as $\emph{P}\sim\exp(-α^2/Λ)$ where $α$=const and $Λ$ is the cosmological constant, so once it nucleates, the universe immediately starts the de Sitter inflationary expansion. The probability $\emph{P} $ will be large for values of $Λ$ that are large enough, whereas $Λ$ of our Universe is definitely small. Of course, for the early universe filled with radiation or another ''matter'' the mentioned probability is large nevertheless ($\emph{P}\sim 1$) but in this case we have no inflation which is a standard solution for the flatness and horizon problems. In the other hand, the alternative solution of these problems can be obtained in framework of cosmologies with varying speed of light $c(t)$ (VSL). We show that, as a matter of principle, such quantum VSL cosmologies exist that $\emph{P}\sim 1$, $ρ_{_Λ}/ρ_c\sim 0.7$ ($Λ$-problem) and both horizon and flatness problems are solvable without inflation.

hep-th↗

arXiv2004

A new integrable 3+1 dimensional generalization of the Burgers equation

A new nonlinear 3+1 dimensional evolution equation admitting the Lax pair is presented. In the case of one spatial dimension, the equation reduces to the Burgers equation. A method of construction of exact solutions, based on a class of discrete symmetries of the former equation is developed. These symmetries reduce to the Cole-Hopf transformation in one-dimensional limit. Some exact solutions are analyzed, in the physical context of spatial dissipative structures and shock wave dressing.

nlin.SI↗

arXiv2004

The semiclassical tunneling probability in quantum cosmologies with varying speed of light

In quantum cosmology the closed universe can spontaneously nucleate out of the state with no classical space and time. The semiclassical tunneling nucleation probability can be estimated as $\emph{P}\sim\exp(-α^2/Λ)$ where $α$=const and $Λ$ is the cosmological constant. In classical cosmology with varying speed of light c(t) (VSL) it is possible to solve the horizon problem, the flatness problem and the $Λ$-problem if c=sa^n with s=const and n<-2. We show that in VSL quantum cosmology with n<-2 the semiclassical tunneling nucleation probability is $\emph{P}\sim\exp(-β^2Λ^k)$ with beta=const and k>0. Thus, the semiclassical tunneling nucleation probability in VSL quantum cosmology is very different from this one in quantum cosmology with c=const. In particular, this one is strongly suppressed for large values of $Λ$.

hep-th↗