Designing Cyclic Universe Models

Recent advances in understanding the propagation of perturbations through the transition from big crunch to big bang (esp. Tolley et al. hep-th/0306109) make it possible for the first time to consider the full set of phenomenological constraints on the scalar field potential in cyclic models of the universe. We show that cyclic models require a comparable degree of tuning to that needed for inflationary models. The constraints are reduced to a set of simple design rules including "fast-roll" parameters analogous to the "slow-roll" parameters in inflation.Comment: 4 pages, 2 figures. Minor typos and figure correcte

Ekpyrotic collapse with multiple fields

A scale invariant spectrum of isocurvature perturbations is generated during collapse in the scaling solution in models where two or more fields have steep negative exponential potentials. The scale invariance of the spectrum is realised by a tachyonic instability in the isocurvature field. We show that this instability is due to the fact that the scaling solution is a saddle point in the phase space. The late time attractor is identified with a single field dominated ekpyrotic collapse in which a steep blue spectrum for isocurvature perturbations is found. Although quantum fluctuations do not necessarily to disrupt the classical solution, an additional preceding stage is required to establish classical homogeneity.Comment: 13 pages, 1 figur

Is subdiffusional transport slower than normal?

We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium are characterized by a power-law viscoelastic memory kernel which ultra slow decays in time on the time scale \tau of strong viscoelastic correlations. The subdiffusive transport regime emerges transiently for t<\tau. However, the transport becomes asymptotically normal for t>>\tau. It is shown that even though transiently the mean displacement and the variance both scale sublinearly, i.e. anomalously slow, in time, ~ F t^\alpha, ~ t^\alpha, 0<\alpha<1, the mean displacement at each instant of time is nevertheless always larger than one obtained for normal transport in a purely viscous medium with the same macroscopic viscosity obtained in the Markovian approximation. This can have profound implications for the subdiffusive transport in biological cells as the notion of "ultra-slowness" can be misleading in the context of anomalous diffusion-limited transport and reaction processes occurring on nano- and mesoscales

Topological phase for spin-orbit transformations on a laser beam

We investigate the topological phase associated with the double connectedness of the SO(3) representation in terms of maximally entangled states. An experimental demonstration is provided in the context of polarization and spatial mode transformations of a laser beam carrying orbital angular momentum. The topological phase is evidenced through interferometric measurements and a quantitative relationship between the concurrence and the fringes visibility is derived. Both the quantum and the classical regimes were investigated.Comment: 4 pages, 4 figure

Quantum Fields in a Big Crunch/Big Bang Spacetime

We consider quantum field theory on a spacetime representing the Big Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies. We show via several independent methods that an essentially unique matching rule holds connecting the incoming state, in which a single extra dimension shrinks to zero, to the outgoing state in which it re-expands at the same rate. For free fields in our construction there is no particle production from the incoming adiabatic vacuum. When interactions are included the total particle production for fixed external momentum is finite at tree level. We discuss a formal correspondence between our construction and quantum field theory on de Sitter spacetime.Comment: 30 pages, RevTex file, five postscript figure file

Curvature perturbations from ekpyrotic collapse with multiple fields

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in the ekpyrotic scaling solution in models where multiple fields have steep negative exponential potentials. The scale invariance of the spectrum is realized by a tachyonic instability in the isocurvature field. This instability drives the scaling solution to the late time attractor that is the old ekpyrotic collapse dominated by a single field. We show that the transition from the scaling solution to the single field dominated ekpyrotic collapse automatically converts the initial isocurvature perturbations about the scaling solution to comoving curvature perturbations about the late-time attractor. The final amplitude of the comoving curvature perturbation is determined by the Hubble scale at the transition.Comment: 15 pages, 3 figures, a reference added, to be published in CQG, a remark on the comoving density perturbation correcte