STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY

In Brans-Dicke theory the Universe becomes divided after inflation into many exponentially large domains with different values of the effective gravitational constant. Such a process can be described by diffusion equations for the probability of finding a certain value of the inflaton and dilaton fields in a physical volume of the Universe. For a typical chaotic inflation potential, the solutions for the probability distribution never become stationary but grow forever towards larger values of the fields. We show here that a non-minimal conformal coupling of the inflaton to the curvature scalar, as well as radiative corrections to the effective potential, may provide a dynamical cutoff and generate stationary solutions. We also analyze the possibility of large nonperturbative jumps of the fluctuating inflaton scalar field, which was recently revealed in the context of the Einstein theory. We find that in the Brans--Dicke theory the amplitude of such jumps is strongly suppressed.Comment: 19 pages, LaTe

Open inflation and the singular boundary

The singularity in Hawking and Turok's model (hep-th/9802030) of open inflation has some appealing properties. We suggest that this singularity should be regularized with matter. The singular instanton can then be obtained as the limit of a family of ``no-boundary'' solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking boundary term. Unrelated to this question, we also point out that gravitational backreaction improves the behaviour of scalar perturbations near the singularity. As a result, the problem of quantizing scalar perturbations and gravity waves seems to be very well posed.Comment: 7 page

Quantum Creation of an Open Inflationary Universe

We discuss a dramatic difference between the description of the quantum creation of an open universe using the Hartle-Hawking wave function and the tunneling wave function. Recently Hawking and Turok have found that the Hartle-Hawking wave function leads to a universe with Omega = 0.01, which is much smaller that the observed value of Omega > 0.3. Galaxies in such a universe would be about $10^{10^8}$ light years away from each other, so the universe would be practically structureless. We will argue that the Hartle-Hawking wave function does not describe the probability of the universe creation. If one uses the tunneling wave function for the description of creation of the universe, then in most inflationary models the universe should have Omega = 1, which agrees with the standard expectation that inflation makes the universe flat. The same result can be obtained in the theory of a self-reproducing inflationary universe, independently of the issue of initial conditions. However, there exist two classes of models where Omega may take any value, from Omega > 1 to Omega << 1.Comment: 23 pages, 4 figures. New materials are added. In particular, we show that boundary terms do not help to solve the problem of unacceptably small Omega in the new model proposed by Hawking and Turok in hep-th/9803156. A possibility to solve the cosmological constant problem in this model using the tunneling wave function is discusse

Relaxation of the cosmological constant at inflation?

We suggest that the cosmological constant has been relaxed to its present, very small value during the inflationary stage of the evolution of the Universe. This requires relatively low scale, very long duration and unconventional source of inflation. We present a concrete mechanism of the cosmological constant relaxation at the inflationary epoch.Comment: 11 page

Cosmological Consequences of String-forming Open Inflation Models

We present a study of open inflation cosmological scenarios in which cosmic strings form betwen the two inflationary epochs. It is shown that in these models strings are stretched outside the horizon due to the inflationary expansion but must necessarily re-enter the horizon before the epoch of equal matter and radiation densities. We determine the power spectrum of cold dark matter perturbations in these hybrid models, finding good agreement with observations for values of $\Gamma=\Omega_0h\sim0.3$ and comparable contributions from the active and passive sources to the CMB. Finally, we briefly discuss other cosmological consequences of these models.Comment: 11 LaTeX pages with 3 eps figure

Glass Transition of Hard Sphere Systems: Molecular Dynamics and Density Functional Theory

The glass transition of a hard sphere system is investigated within the framework of the density functional theory (DFT). Molecular dynamics (MD) simulations are performed to study dynamical behavior of the system on the one hand and to provide the data to produce the density field for the DFT on the other hand. Energy landscape analysis based on the DFT shows that there appears a metastable (local) free energy minimum representing an amorphous state as the density is increased. This state turns out to become stable, compared with the uniform liquid, at some density, around which we also observe sharp slowing down of the $alpha$ relaxation in MD simulations.Comment: 5 pages, 5 figure

Inflationary models inducing non-Gaussian metric fluctuations

We construct explicit models of multi-field inflation in which the primordial metric fluctuations do not necessarily obey Gaussian statistics. These models are realizations of mechanisms in which non-Gaussianity is first generated by a light scalar field and then transferred into curvature fluctuations. The probability distribution functions of the metric perturbation at the end of inflation are computed. This provides a guideline for designing strategies to search for non-Gaussian signals in future CMB and large scale structure surveys.Comment: 4 pages, 7 figure

Wall fluctuation modes and tensor CMB anisotropy in open inflation models

We calculate the spectrum of large angle cosmic microwave background (CMB) anisotropies due to quantum fluctuations of the gravitational wave modes in one-bubble open inflation models. We find the bubble-wall fluctuation modes, which had been thought to exist discretely in previous analyses, are actually contained in the continuous spectrum of gravitational wave modes when the gravitational coupling is correctly taken into account. Then we find that the spectrum of the tensor CMB anisotropy can be decomposed into the part due to the wall fluctuation modes and that due to the usual gravitational wave modes in a way which is almost model-independent, even when the gravitational coupling is strong. We also discuss observational constraints on the model parameters. We find that an appreciable portion of the parameter space is excluded but the remaining allowable region is still wide enough to leave the one-bubble scenario viable.Comment: 12 pages revtex file, 9 postscript figure

Oscillations During Inflation and the Cosmological Density Perturbations

Adiabatic (curvature) perturbations are produced during a period of cosmological inflation that is driven by a single scalar field, the inflaton. On particle physics grounds -- though -- it is natural to expect that this scalar field is coupled to other scalar degrees of freedom. This gives rise to oscillations between the perturbation of the inflaton field and the perturbations of the other scalar degrees of freedom, similar to the phenomenon of neutrino oscillations. Since the degree of the mixing is governed by the squared mass matrix of the scalar fields, the oscillations can occur even if the energy density of the extra scalar fields is much smaller than the energy density of the inflaton field. The probability of oscillation is resonantly amplified when perturbations cross the horizon and the perturbations in the inflaton field may disappear at horizon crossing giving rise to perturbations in scalar fields other than the inflaton. Adiabatic and isocurvature perturbations are inevitably correlated at the end of inflation and we provide a simple expression for the cross-correlation in terms of the slow-roll parameters.Comment: 23 pages, uses LaTeX, added few reference