Quantum State During and after O(4)O(4)-Symmetric Bubble Nucleation with Gravitaional Effects

We extend our previous analysis of the quantum state during and after $O(4)$-symmetric bubble nucleation to the case including gravitational effects. We find that there exists a simple relationship between the case with and without gravitational effects. In a special case of a conformally coupled scalar field which is massless except on the bubble wall, the state is found to be conformally equivalent to the case without gravity.Comment: 31 pages plain Tex file, uuencoded postscript figure file is available from [email protected] upon request, KUNS126

General Solutions for Tunneling of Scalar Fields with Quartic Potentials in de Sitter Space

The tunneling rates for scalar fields with quartic potentials in de Sitter space in the limit of no gravitational back reaction are calculated numerically and the results are fitted by analytic formulae.Comment: (Contours in Figure 1 corrected, two-dimensional fitting coefficient corrected, references added.), 16 pages, KUNS 124

More varieties of hybrid inflation

It is pointed out that hybrid inflation can be implemented with the inflaton field rolling away from the origin instead of towards it. This `inverted' hybrid inflation has a spectral index $n < 1$, in contrast with ordinary hybrid inflation which has $n \gtrsim 1$, so a measured value of $n$ substantially different from 1 would distinguish the two. Other generalisations of hybrid inflation are also considered.Comment: 9 page

Comments on Noncommutative Sigma Models

We review the derivation of a noncommutative version of the nonlinear sigma model on \CPn and it's soliton solutions for finite $\theta$ emphasizing the similarities it bears to the GMS scalar field theory. It is also shown that unlike the scalar theory, some care needs to be taken in defining the topological charge of BPS solitons of the theory due to nonvanishing surface terms in the energy functional. Finally it is shown that, like its commutative analogue, the noncommutative \CPn-model also exhibits a non-BPS sector. Unlike the commutative case however, there are some surprises in the noncommutative case that merit further study.Comment: 22 pages, 4 figures, LaTeX (JHEP3), Minor changes, Discussion expanded and references adde

Inflationary models with a flat potential enforced by non-abelian discrete gauge symmetries

Non-abelian discrete gauge symmetries can provide the inflaton with a flat potential even when one takes into account gravitational strength effects. The discreteness of the symmetries also provide special field values where inflation can end via a hybrid type mechanism. An interesting feature of this method is that it can naturally lead to extremely flat potentials and so, in principle, to inflation at unusually low energy scales. Two examples of effective field theories with this mechanism are given, one with a hybrid exit and one with a mutated hybrid exit. They include an explicit example in which the single field consistency condition is violated.Comment: 24 pages, uses revtex.sty, submitted to PRD (Nov. 1999) Final version to appear in PRD. Background information on supergravity expande

Metric perturbations in two-field inflation

We study the metric perturbations produced during inflation in models with two scalar fields evolving simultaneously. In particular, we emphasize how the large-scale curvature perturbation $\zeta$ on fixed energy density hypersurfaces may not be conserved in general for multiple field inflation due to the presence of entropy as well as adiabatic fluctuations. We show that the usual method of solving the linearized perturbation equations is equivalent to the recently proposed analysis of Sasaki and Stewart in terms of the perturbed expansion along neighboring trajectories in field-space. In the case of a separable potential it is possible to compute in the slow-roll approximation the spectrum of density perturbations and gravitational waves at the end of inflation. In general there is an inequality between the ratio of tensor to scalar perturbations and the tilt of the gravitational wave spectrum, which becomes an equality when only adiabatic perturbations are possible and $\zeta$ is conserved.Comment: RevTex, 9 pages, 1 uuencoded figure appended, also available on WWW via http://star.maps.susx.ac.uk/index.htm

Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases

Possible Origin of Antimatter Regions in the Baryon Dominated Universe

We discuss the evolution of U(1) symmetric scalar field at the inflation epoch with a pseudo Nambu-Goldstone tilt revealing after the end of exponential expansion of the Universe. The U(1) symmetry is supposed to be associated with baryon charge. It is shown that quantum fluctuations lead in natural way to baryon dominated Universe with antibaryon excess regions. The range of parameters is calculated at which the fraction of Universe occupied by antimatter and the size of antimatter regions satisfy the observational constraints, survive to the modern time and lead to effects, accessible to experimental search for antimatter.Comment: 10 pages, 1 figur

Thermal photons in QGP and non-ideal effects

We investigate the thermal photon production-rates using one dimensional boost-invariant second order relativistic hydrodynamics to find proper time evolution of the energy density and the temperature. The effect of bulk-viscosity and non-ideal equation of state are taken into account in a manner consistent with recent lattice QCD estimates. It is shown that the \textit{non-ideal} gas equation of state i.e $\epsilon-3\,P\,\neq 0$ behaviour of the expanding plasma, which is important near the phase-transition point, can significantly slow down the hydrodynamic expansion and thereby increase the photon production-rates. Inclusion of the bulk viscosity may also have similar effect on the hydrodynamic evolution. However the effect of bulk viscosity is shown to be significantly lower than the \textit{non-ideal} gas equation of state. We also analyze the interesting phenomenon of bulk viscosity induced cavitation making the hydrodynamical description invalid. We include the viscous corrections to the distribution functions while calculating the photon spectra. It is shown that ignoring the cavitation phenomenon can lead to erroneous estimation of the photon flux.Comment: 11 pages, 13 figures; accepted for publication in JHE

The Spin Structure of the Nucleon

We present an overview of recent experimental and theoretical advances in our understanding of the spin structure of protons and neutrons.Comment: 84 pages, 29 figure