Arthur Mezhlumian

From the big bang theory to the theory of a stationary universe.

We consider chaotic inflation in the theories with the effective potentials phi^n and e^{\alpha\phi}. In such theories inflationary domains containing sufficiently large and homogeneous scalar field \phi permanently produce new inflationary domains of a similar type. We show that under certain conditions this process of the self-reproduction of the Universe can be described by a stationary distribution of probability, which means that the fraction of the physical volume of the Universe in a state with given properties (with given values of fields, with a given density of matter, etc.) does not depend on time, both at the stage of inflation and after it. This represents a strong deviation of inflationary cosmology from the standard Big Bang paradigm. We compare our approach with other approaches to quantum cosmology, and illustrate some of the general conclusions mentioned above with the results of a computer simulation of stochastic processes in the inflationary Universe.

Do we live in the center of the world

Abstract We investigate the distribution of energy density in a stationary self-reproducing inflationary universe. We show that the main fraction of the volume of the universe in a state with a given density ϱ at any given moment of time t in synchronous coordinates is concentrated near the centers of deep exponentially wide spherically symmetric holes in the density distribution.

On regularization scheme dependence of predictions in inflationary cosmology

We show that there exists a large class of regularization schemes for probabilistic predictions in the theory of a self-reproducing inflationary univere, all of which eliminate the apparent dependence on the time reparametrization. However, all these schemes lead to different answers for relative probabilities of finding various types of post-inflationary universes. Besides, all these schemes fail to be reparametrization invariant beyond the range of the inflaton field close to end of inflation boundary. Therefore, we argue that at the current level of understanding, the simple regularization schemes associated with cutoffs at equal time hypersurfaces are as good as the recently proposed more complicated procedures which try to fix the time-reparametrization dependence.

Nonperturbative amplification of inhomogeneities in a self-reproducing universe.

We investigate the distribution of energy density in a stationary self-reproducing inflationary universe. We show that the main fraction of volume of the Universe in a state with a given density

String thermalization at a black hole horizon

\ensuremath{\rho}

The classical and quantum cosmology with a complex scalar field

at any given moment of proper time

Infinite-scale percolation in a new type of branching diffusion process

t

TOWARDS THE THEORY OF STATIONARY UNIVERSE.

is concentrated near the centers of deep exponentially wide spherically symmetric wells in the density distribution. Since this statement is very surprising and counterintuitive, we perform our investigation by three different analytical methods to verify our conclusions, and then confirm our analytical results by computer simulations. If one assumes that we are typical observers living in the Universe at a given moment of time, then our results may imply that we should live near the center of a deep and exponentially large void, which we will call an infloid. The validity of this particular interpretation of our results is not quite clear since it depends on the as-yet unsolved problem of measure in quantum cosmology. Therefore, at the moment we would prefer to consider our results simply as a demonstration of nontrivial properties of the hypersurface of a given time in the fractal self-reproducing universe, without making any far-reaching conclusions concerning the structure of our own part of the Universe. Still we believe that our results may be of some importance since they demonstrate that nonperturbative effects in quantum cosmology, at least in principle, may have significant observational consequences, including an apparent violation of the Copernican principle.

Inflation with

Susskind has recently shown that a relativistic string approaching the event horizon of a black hole spreads in both the transverse and longitudinal directions in the reference frame of an outside observer. The transverse spreading can be described as a branching diffusion of wee string bits. This stochastic process provides a mechanism for thermalizing the quantum state of the string as it spreads across the stretched horizon.

\Omega \neq 1

Abstract The standard quantum cosmology as well as the classical inflationary cosmology are based on the Friedmann cosmology in the presence of real scalar fields. At the same time it is evident that a complex scalar field has more physical sense because it corresponds to a matter hydrodynamical field. The present paper can be considered as an introduction to the quantum and classical cosmology with a complex scalar field. The two-dimensional potential which appears in this case in the Wheeler-DeWitt equation hs a region of negative values. Different from the case of real fields [Lavrelashvili et al., Nucl. Phys. B 329 (1990) 98] this region is not convex everywhere and this gives the possibility for quantum creation of universes filled with matter with initial conditions for inflation in classical regions. In the paper of Lavrelashvili et al. it was possible to observe creation only of large but empty universes.