arXiv subjects
Publications and source records attributed to George Lavrelashvili.
We derive the cosmic microwave background temperature anisotropy two-point correlation function (including off-diagonal correlations) from broken spatial isotropy due to an arbitrarily oriented homogeneous cosmological magnetic field.
The spectrum of small perturbations about oscillating bounce solutions recently discussed in the literature is investigated. Our study supports quite intuitive and expected result: the bounce with N nodes has exactly N homogeneous negative modes. Existence of more than one negative modes makes obscure the relation of these oscillating bounce solutions to the false vacuum decay processes.
A primordial cosmological magnetic field induces Faraday rotation of the cosmic microwave background polarization. This rotation produces a curl-type polarization component even when the unrotated polarization possesses only gradient-type polarization, as expected from scalar density perturbations. We compute the angular power spectrum of curl-type polarization arising from small Faraday rotation due to a weak stochastic primordial magnetic field with a power-law power spectrum. The induced polarization power spectrum peaks at arcminute angular scales. Faraday rotation is one of the few cosmological sources of curl-type polarization, along with primordial tensor perturbations, gravitational lensing, and the vector and tensor perturbations induced by magnetic fields; the Faraday rotation signal peaks on significantly smaller angular scales than any of these, with a power spectrum amplitude which can be comparable to that from gravitational lensing. Prospects for detection are briefly discussed.
We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self interacting scalar field in 3+1 dimensions. We use a numerical method, established some time ago, which is based on a well-known theorem on functional determinants. The proper handling of zero modes and of renormalization is discussed. The numerical results in particular show that quantum corrections become smaller away from the thin-wall case. In the thin-wall limit the numerical results are found to join into those obtained by a gradient expansion.
Static, spherically symmetric solutions with regular origin are investigated of the Einstein-Yang-Mills theory with a negative cosmological constant $Λ$. A combination of numerical and analytical methods leads to a clear picture of the `moduli space' of the solutions. Some issues discussed in the existing literature on the subject are reconsidered and clarified. In particular the stability of the asymptotically AdS solutions is studied. Like for the Bartnik-McKinnon (BK) solutions obtained for $Λ=0$ there are two different types of instabilities -- `topological' and `gravitational'. Regions with any number of these instabilities are identified in the moduli space. While for BK solutions there is always a non-vanishing equal number of instabilities of both types, this degeneracy is lifted and there exist stable solutions, genuine sphalerons with exactly one unstable mode and so on. The boundaries of these regions are determined.
The unconstrained reduced action corresponding to the dynamics of scalar fluctuations about the Friedmann-Robertson-Walker (FRW) background is derived using Dirac's method of description of singular Lagrangian systems. The results are applied to so-called negative mode problem in description of tunneling transitions with gravity. With our special choice of physical variable, the kinetic term of the reduced action has a conventional signature for a wide class of models. In this representation, the existence of a negative mode justifying the false vacuum decay picture turns out to be manifest. We also explain how the present result becomes consistent with the previously proved ``no negative mode (supercritical supercurvature mode) theorem''.
There is a single negative mode in the spectrum of small perturbations about the tunneling solutions describing a metastable vacuum decay in flat spacetime. This mode is needed for consistent description of decay processes. When gravity is included the situation is more complicated. An approach based on elimination of scalar field perturbations shows no negative mode, whereas the recent approach based on elimination of gravitational perturbations indicates presence of a negative mode. In this contribution we analyse and compare the present approaches to the negative mode problem in false vacuum decay with gravity.
Positive definiteness of the quadratic part of the action of the Hawking-Turok instanton is investigated. The Euclidean quadratic action for scalar perturbations is expressed in terms of a single gauge invariant quantity $q$. The mode functions satisfy a Schrödinger type equation with a potential $U$. It is shown that the potential $U$ tends to a positive constant at the regular end of the instanton. The detailed shape of $U$ depends on the initial data of the instanton, on parameters of the background scalar field potential $V$ and on a positive integer, $p$, labeling different spherical harmonics. For certain well behaved scalar field potentials it is proven analytically that for $p>1$ quadratic action is non-negative. For the lowest $p=1$ (homogeneous) harmonic numerical solution of the Schrödinger equation for different scalar field potentials $V$ and different initial data show that in some cases the potential $U$ is negative in the intermediate region. We investigated the monotonously growing potentials and a potential with a false vacuum. For the monotonous potentials no negative modes are found about the Hawking-Turok instanton. For a potential with the false vacuum the HT instanton is shown to have a negative mode for certain initial data.
The interior geometry of static, spherically symmetric black holes of the Einstein-Yang-Mills-Higgs theory is analyzed. It is found that in contrast to the Abelian case generically no inner (Cauchy) horizon is formed inside non-Abelian black holes. Instead the solutions come close to a Cauchy horizon but then undergo an enormous growth of the mass function, a phenomenon which can be termed `mass inflation' in analogy to what is observed for perturbations of the Reissner-Nordstrøm solution. A significant difference between the theories with and without a Higgs field is observed. Without a Higgs field the YM field induces repeated cycles of massinflation -- taking the form of violent `explosions' -- interrupted by quiescent periods and subsequent approaches to an almost Cauchy horizon. With the Higgs field no such cycles occur. Besides the generic solutions there are non-generic families with a Schwarzschild, Reissner-Nordstrøm and a pseudo Reissner-Nordstrøm type singularity at $r=0$.
We analyze the interior geometry of static, spherically symmetric black holes of the Einstein-Yang-Mills-Higgs theory. Generically the solutions exhibit a behaviour that may be described as ``mass inflation'', although with a remarkable difference between the cases with and without a Higgs field. Without Higgs field the YM field induces a kind of cyclic behaviour leading to repeated cycles of mass inflation - taking the form of violent explosions - interrupted by quiescent periods and subsequent approaches to an almost Cauchy horizon. With the Higgs field no such cycles occur. In addition there are non-generic families with a Schwarzschild resp. Reissner-Nordstrøm type singularity at r=0.
We present a brief review of some recent results on non-abelian solitons and black holes in different theories. Lecture given at the Simi-96, Tbilisi, Georgia, September 22-28, 1996.
This is a brief review of the main properties of sphalerons in various theories with a Yang--Mills field. Talk given at the Heat Kernel Techniques and Quantum Gravity, Winnipeg, Canada, August 2-6, 1994.
Talk given at the 7th Marcel Grossmann Meeting on General Relativity, Stanford University, July 24-30, 1994.
We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills-dilaton theory. This sequence is parametrized by the number $n$ of zeros of a component of the gauge field potential. It is demonstrated that solutions with odd $n$ posses all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analysed.
The aim of the present letter is to critically review the stability of the Bartnik-McKinnon solutions of the Einstein-Yang-Mills theory. The stability question was already studied by several authors, but there seems to be some confusion about the nature and the number of unstable modes. We suggest to distinguish two different kind of instabilities, which we call `gravitational' respectively `sphaleron' instabilities. We claim that the $n^{\rm th}$ Bartnik-McKinnon solution has exactly $2n$ unstable modes, $n$ of either type.
We discuss properties and interpretation of recently found globally regular and black hole solutions of a Einstein-Yang-Mills-dilaton theory. Talk given at the 15th annual MRST meeting on High Energy Physics, Syracuse University, NY, May 14-15, 1993.