George Lavrelashvili

Regular and black hole solutions of Einstein-Yang-Mills dilaton theory

Abstract We present numerical and analytical results on static spherically symmetric solutions of an SU(2) Yang-Mills field coupled to the gravitational field and to a dilaton. For any value of the dilaton coupling constant we find a discrete family of globally regular solutions of finite mass. In addition our analysis indicates the existence of a similar discrete family of black hole solutions for any given radius rh of their horizon. All these solutions turn out to be unstable in linearized perturbation theory.

Faraday rotation of the Cosmic Microwave Background polarization by a stochastic magnetic field

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 arc minute 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.

CMB temperature anisotropy from broken spatial isotropy due to a homogeneous cosmological magnetic field

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.

Static spherically symmetric solutions of a Yang-Mills field coupled to a dilaton

Abstract We have performed a detailed numerical and analytical study of static spherically symmetric solutions of an SU (2) Yang-Mills field coupled to a scalar graviton (dilaton). The results show a striking similarity to those obtained for the Einstein-Yang-Mills theory by Bartnik and McKinnon. We find a discrete family of globally regular solutions of finite energy. All these solutions are shown to be unstable in linearized perturbation theory.

A REMARK ON THE INSTABILITY OF THE BARTNIK-McKINNON SOLUTIONS

Abstract 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 th Bartnik-McKinnon solution has exactly 2 n unstable modes, n of either type.

Particle creation and destruction of quantum coherence by topological change

Abstract The possibility is considered that changes of spatial topology occur as tunneling events in quantum gravity. Creation of scalar and spinor particles during these tunneling transitions is studied. The relevant formalism based on the euclidean Schrodinger equation and coherent state representation is developed. This formalism is illustrated in a two-dimensional example. It is argued that the particle creation during the topological changes induces the loss of quantum coherence. The particle creation is calculated in the case of O(4)-invariant background euclidean four-dimensional metrics. This calculation is used for estimating the loss of quantum coherence. An upper limit on the rate of the topological changes, A ⪅10 −17 M Pl 4 , is derived from the observation of K 0 − K 0 oscillations.

One loop corrections to the metastable vacuum decay

We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self-interacting scalar field in

Tunneling transitions with gravitation: Breakdown of the quasiclassical approximation

3+1

Negative mode problem in false vacuum decay with gravity

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 show in particular that the quantum corrections strongly increase when one approaches the thin-wall case. In the thin-wall limit the numerical results are found to join into those obtained by a gradient expansion.

Negative Modes of Oscillating Instantons

Abstract We discuss the perturbations around the O(4)-invariant bounce describing the tunneling process leading to the materialization of a bubble of a new phase in metastable vacuum. We find that for some range of parameters, the gravitational effects lead to the existence of a huge number of negative modes. We argue that this implies the breakdown of the quasiclassical approximation and speculate on a possible alternative to the quasiclassical tunneling. We point out that the possibility of non-quasiclassical tunneling makes the quasiclassical description of tunneling questionable even in models with stable classical euclidean configurations.