What can the observation of nonzero curvature tell us?

The eternally inflating multiverse provides a consistent framework to understand coincidences and fine-tuning in the universe. As such, it provides the possibility of finding another coincidence: if the amount of slow-roll inflation was only slightly more than the anthropic threshold, then spatial curvature might be measurable. We study this issue in detail, particularly focusing on the question: "If future observations reveal nonzero curvature, what can we conclude?" We find that whether an observable signal arises or not depends crucially on three issues: the cosmic history just before the observable inflation, the measure adopted to define probabilities, and the nature of the correlation between the tunneling and slow-roll parts of the potential. We find that if future measurements find positive curvature at \Omega_k < -10^-4, then the framework of the eternally inflating multiverse is excluded with high significance. If the measurements instead reveal negative curvature at \Omega_k > 10^-4, then we can conclude (1) diffusive (new or chaotic) eternal inflation did not occur in our immediate past; (2) our universe was born by a bubble nucleation; (3) the probability measure does not reward volume increase; and (4) the origin of the observed slow-roll inflation is an accidental feature of the potential, not due to a theoretical mechanism. Discovery of \Omega_k > 10^-4 would also give us nontrivial information about the correlation between tunneling and slow-roll; e.g. a strong correlation favoring large N would be excluded in certain measures. We also ask whether the current constraint on \Omega_k is consistent with multiverse expectations, finding that the answer is yes, except for certain cases. In the course of this work we were led to consider vacuum decay branching ratios, and found that it is more likely than one might guess that the decays are dominated by a single channel.Comment: 46 pages, 5 figures; reference updates and typo corrections arising from final Phys. Rev. D copy editin

Domain Walls in SU(5)

We consider the Grand Unified SU(5) model with a small or vanishing cubic term in the adjoint scalar field in the potential. This gives the model an approximate or exact Z$_2$ symmetry whose breaking leads to domain walls. The simplest domain wall has the structure of a kink across which the Higgs field changes sign ($\Phi \to -\Phi$) and inside which the full SU(5) is restored. The kink is shown to be perturbatively unstable for all parameters. We then construct a domain wall solution that is lighter than the kink and show it to be perturbatively stable for a range of parameters. The symmetry in the core of this domain wall is smaller than that outside. The interactions of the domain wall with magnetic monopole is discussed and it is shown that magnetic monopoles with certain internal space orientations relative to the wall pass through the domain wall. Magnetic monopoles in other relative internal space orientations are likely to be swept away on collision with the domain walls, suggesting a scenario where the domain walls might act like optical polarization filters, allowing certain monopole ``polarizations'' to pass through but not others. As SU(5) domain walls will also be formed at small values of the cubic coupling, this leads to a very complicated picture of the evolution of defects after the Grand Unified phase transition.Comment: 6 pages, 1 figure. Animations can be viewed at http://theory4.phys.cwru.edu/~levon/figures.htm

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

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

Inflation and squeezed quantum states

The inflationary cosmology is analyzed from the point of view of squeezed quantum states. As noted by Grishchuk and Sidorov, the amplification of quantum fluctuations into macroscopic perturbations which occurs during cosmic inflation is a process of quantum squeezing. We carefully develop the squeezed state formalism and derive the equations that govern the evolution of a gaussian initial state. We derive the power spectrum of density perturbations for a simple inflationary model and discuss its features. We conclude that the squeezed state formalism provides an interesting framework within which to study the amplification process, but,in disagreement with the claims of Grishchuk and Sidorov, that it does {\em not} provide us with any new physical results.Comment: 33 pages, one section added, significant revisions, 6 figures (in uuencoded file), Imperial/TP/92-93/2

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

Relic Gravitons, Dominant Energy Condition and Bulk Viscous Stresses

If the energy momentum tensor contains bulk viscous stresses violating the dominant energy condition (DOC) the energy spectra of the relic gravitons (produced at the time of the DOC's violation) increase in frequency in a calculable way. In a general relativistic context we give examples where the DOC is only violated for a limited amount of time after which the ordinary (radiation dominated) evolution takes place. We connect our discussion to some recent remarks of Grishchuk concerning the detectability of the stochastic gravitational wave background by the forthcoming interferometric detectors.Comment: 7 pages in LaTex style. Accepted for publication in Phys. Rev. D (Rapid Comm.

Quantum Effects In Cosmology

Contents: Introduction. The Present State of the Universe. What Can We Expect From a Complete Cosmological Theory? An Overview of Quantum Effects in Cosmology. Parametric (Superadiabatic) Amplification of Classical Waves. Graviton Creation in the Inflationary Universe. Quantum States of a Harmonic Oscillator. Squeezed Quantum States of Relic Gravitons and Primordial Density Perturbations. Quantum Cosmology, Minisuperspace Models and Inflation. From the Space of Classical Solutions to the Space of Wave Functions. On the Probability of Quantum Tunneling From "Nothing". Duration of InflationComment: (43 pages, to be published in "The Origin of Structure in the Universe", ed. P.Nardone

On the observational determination of squeezing in relic gravitational waves and primordial density perturbations

We develop a theory in which relic gravitational waves and primordial density perturbations are generated by strong variable gravitational field of the early Universe. The generating mechanism is the superadiabatic (parametric) amplification of the zero-point quantum oscillations. The generated fields have specific statistical properties of squeezed vacuum quantum states. Macroscopically, squeezing manifests itself in a non-stationary character of variances and correlation functions of the fields, the periodic structures of the metric power spectra, and, as a consequence, in oscillatory behavior of the higher order multipoles C_l of the cosmic microwave background anisotropy. We start with the gravitational wave background and then apply the theory to primordial density perturbations. We derive an analytical formula for the positions of peaks and dips in the angular power spectrum l(l+1)C_l as a function of l. This formula shows that the values of l at the peak positions are ordered in the proportion 1:3:5:..., whereas at the dips they are ordered as 1:2:3:.... We compare the derived positions with the actually observed features, and find them to be in reasonably good agreement. It appears that the observed structure is better described by our analytical formula based on the (squeezed) metric perturbations associated with the primordial density perturbations, rather than by the acoustic peaks reflecting the existence of plasma sound waves at the last scattering surface. We formulate a forecast for other features in the angular power spectrum, that may be detected by the advanced observational missions, such as MAP and PLANCK. We tentatively conclude that the observed structure is a macroscopic manifestation of squeezing in the primordial metric perturbations.Comment: 34 pages, 3 figures; to appear in Phys. Rev. D66, 0435XX (2002); includes Note Added in Proofs: "The latest CBI observations (T.J.Pearson et al., astro-ph/0205388) have detected four peaks, at l ~ 550, 800, 1150, 1500, and four dips, at l ~ 400, 700, 1050, 1400. These positions are in a very good agreement with the theoretical formula (6.35) of the present paper. We interpret this data as confirmation of our conclusion that it is gravity, and not acoustics, that is responsible for the observed structure.

Large Scale Inhomogeneities from the QCD Phase Transition

We examine the first-order cosmological QCD phase transition for a large class of parameter values, previously considered unlikely. We find that the hadron bubbles can nucleate at very large distance scales, they can grow as detonations as well as deflagrations, and that the phase transition may be completed without reheating to the critical temperature. For a subset of the parameter values studied, the inhomogeneities generated at the QCD phase transition might have a noticeable effect on nucleosynthesis.Comment: 15 LaTeX pages + 6 PostScript figures appended at the end of the file, HU-TFT-94-1