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On the Creation of the Universe out of Nothing

We explain how the Universe was created with no expenditure of energy or initial mass.Comment: To be presented at IWARA 2009 (4th International Workshop on Astronomy and Relativistic Astrophysics), to be held in Brazil, October 200

Oscillating universes as eigensolutions of cosmological Schr\"odinger equation

We propose a cosmological model which could explain, in a very natural way, the apparently periodic structures of the universe, as revealed in a series of recent observations. Our point of view is to reduce the cosmological Friedman--Einstein dynamical system to a sort of Schr\"odinger equation whose bound eigensolutions are oscillating functions. Taking into account the cosmological expansion, the large scale periodic structure could be easily recovered considering the amplitudes and the correlation lengths of the galaxy clusters.Comment: 12 pages, Latex, submitted to Int. Jou. of Theor. Phy

Scenario of inflationary cosmology from the phenomenological Λ\Lambda models

Choosing the three phenomenological models of the dynamical cosmological term $\Lambda$, viz., $\Lambda \sim (\dot a/a)^2$, $\Lambda \sim {\ddot a/a}$ and $\Lambda \sim \rho$ where $a$ is the cosmic scale factor, it has been shown by the method of numerical analysis that the three models are equivalent for the flat Universe $k=0$. The evolution plots for dynamical cosmological term $\Lambda$ vs. time $t$ and also the cosmic scale factor $a$ vs. $t$ are drawn here for $k=0, +1$. A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.Comment: 12 latex pages with 12 figures; Replaced with the revised version; Accepeted for `J. Non-lin. Frac. Phen. Sci. Engg.

General Solutions for Tunneling of Scalar Fields with Quartic Potentials

For the theory of a single scalar field $\varphi$ with a quartic potential $V(\varphi)$, we find semi-analytic expressions for the Euclidean action in both four and three dimensions. The action in four dimensions determines the quantum tunneling rate at zero temperature from a false vacuum state to the true vacuum state; similarly, the action in three dimensions determines the thermal tunneling rate for a finite temperature theory. We show that for all quartic potentials, the action can be obtained from a one parameter family of instanton solutions corresponding to a one parameter family of differential equations. We find the solutions numerically and use polynomial fitting formulae to obtain expressions for the Euclidean action. These results allow one to calculate tunneling rates for the entire possible range of quartic potentials, from the thin-wall (nearly degenerate) limit to the opposite limit of vanishing barrier height. We also present a similar calculation for potentials containing $\varphi^4 \ln \varphi^2$ terms, which arise in the one-loop approximation to the effective potential in electroweak theory.Comment: 17 pages, 6 figures not included but available upon request, UM AC 93-

Non-topological solitons as nucleation sites for cosmological phase transitions

I consider quantum field theories that admit charged non-topological solitons of the Q-ball type, and use the fact that in a first-order cosmological phase transition, below the critical temperature, there is a value of the soliton charge above which the soliton becomes unstable and expands, converting space to the true vacuum, much like a critical bubble in the case of ordinary tunneling. Using a simple model for the production rate of Q-balls through charge accretion during a random walk out of equilibrium, I calculate the probability for the formation of critical charge solitons and estimate the amount of supercooling needed for the phase transition to be completed.Comment: 20 pages, 2 figures, some comments and references adde

Closed Trapped Surfaces in Cosmology

The existence of closed trapped surfaces need not imply a cosmological singularity when the spatial hypersurfaces are compact. This is illustrated by a variety of examples, in particular de Sitter spacetime admits many closed trapped surfaces and obeys the null convergence condition but is non-singular in the k=+1 frame.Comment: 11 pages. To appear in GRG, Vol 35 (August issue

Double Field Inflation

We present an inflationary universe model which utilizes two coupled real scalar fields. The inflation field $\phi$ experiences a first order phase transition and its potential dominates the energy density of the Universe during the inflationary epoch. This field $\phi$ is initially trapped in its metastable minimum and must tunnel through a potential barrier to reach the true vacuum. The second auxiliary field $\psi$ couples to the inflaton field and serves as a catalyst to provide an abrupt end to the inflationary epoch; i.e., the $\psi$ field produces a time-dependent nucleation rate for bubbles of true $\phi$ vacuum. In this model, we find that bubbles of true vacuum can indeed percolate and we argue that thermalization of the interiors can more easily take place. The required degree of flatness (i.e., the fine tuning) in the potential of the $\psi$ field is comparable to that of other models which invoke slowly rolling fields. Pseudo Nambu-Goldstone bosons may naturally provide the flat potential for the rolling field.Comment: 18 pages, 2 figures, This early paper is being placed on the archive to make it more easily accessible in light of recent interest in reviving tunneling inflationary models and as its results are used in an accompanying submissio

Inflationary spacetimes are not past-complete

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.Comment: We improve the basic argument to apply to a wider class of spacetimes, use a better title and add a discussion of cyclic models. 4 pages, 1 figure, RevTe

Non-Equilibrium Evolution of Scalar Fields in FRW Cosmologies I

We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies.The calculation is performed both to one-loop and in a non-perturbative, self-consistent Hartree approximation.The method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. The renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. We investigate the high temperature expansion and show that it breaks down at long times. We also obtain the time evolution of the initial Boltzmann distribution functions, and argue that to one-loop order or in the Hartree approximation, the time evolved state is a ``squeezed'' state. We illustrate the departure from thermal equilibrium by numerically studying the case of a free massive scalar field in de Sitter and radiation dominated cosmologies. It is found that a suitably defined non-equilibrium entropy per mode increases linearly with comoving time in a de Sitter cosmology, whereas it is {\it not} a monotonically increasing function in the radiation dominated case.Comment: 29 pages, revtex 3.0, 11 figures available upon request, PITT-93-6; LPTHE-93-52; CMU-HEP-93-2