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

A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration

Increasing evidence suggests that most of the energy density of the universe consists of a dark energy component with negative pressure, a ``cosmological constant" that causes the cosmic expansion to accelerate. In this paper, we address the puzzle of why this component comes to dominate the universe only recently rather than at some much earlier epoch. We present a class of theories based on an evolving scalar field where the explanation is based entirely on internal dynamical properties of the solutions. In the theories we consider, the dynamics causes the scalar field to lock automatically into a negative pressure state at the onset of matter-domination such that the present epoch is the earliest possible time, consistent with nucleosynthesis restrictions, when it can start to dominate.Comment: 5 pages, 3 figure

Langevin Analysis of Eternal Inflation

It has been widely claimed that inflation is generically eternal to the future, even in models where the inflaton potential monotonically increases away from its minimum. The idea is that quantum fluctuations allow the field to jump uphill, thereby continually revitalizing the inflationary process in some regions. In this paper we investigate a simple model of this process, pertaining to inflation with a quartic potential, in which analytic progress may be made. We calculate several quantities of interest, such as the expected number of inflationary efolds, first without and then with various selection effects. With no additional weighting, the stochastic noise has little impact on the total number of inflationary efoldings even if the inflaton starts with a Planckian energy density. A "rolling" volume factor, i.e. weighting in proportion to the volume at that time, also leads to a monotonically decreasing Hubble constant and hence no eternal inflation. We show how stronger selection effects including a constraint on the initial and final states and weighting with the final volume factor can lead to a picture similar to that usually associated with eternal inflation.Comment: 22 pages, 2 figure

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

Holography and Variable Cosmological Constant

An effective local quantum field theory with UV and IR cutoffs correlated in accordance with holographic entropy bounds is capable of rendering the cosmological constant (CC) stable against quantum corrections. By setting an IR cutoff to length scales relevant to cosmology, one easily obtains the currently observed rho_Lambda ~ 10^{-47} GeV^4, thus alleviating the CC problem. It is argued that scaling behavior of the CC in these scenarios implies an interaction of the CC with matter sector or a time-dependent gravitational constant, to accommodate the observational data.Comment: 7 pages, final version accepted by PR

Cosmological models from quintessence

A generalized quintessence model is presented which corresponds to a richer vacuum structure that, besides a time-dependent, slowly varying scalar field, contains a varying cosmological term. From first principles we determine a number of scalar-field potentials that satisfy the constraints imposed by the field equations and conservations laws, both in the conventional and generalized quintessence models. Besides inverse-power law solutions, these potentials are given in terms of hyperbolic functions or the twelve Jacobian elliptic functions, and are all related to the luminosity distance by means of an integral equation. Integration of this equation for the different solutions leads to a large family of cosmological models characterized by luminosity distance-redshift relations. Out of such models, only four appear to be able to predict a required accelerating universe conforming to observations on supernova Ia, at large or moderate redshifts.Comment: 9 pages, RevTex, to appear in Phys. Rev.

Quantum effects and superquintessence in the new age of precision cosmology

Recent observations of Type Ia supernova at high redshifts establish that the dark energy component of the universe has (a probably constant) ratio between pressure and energy density $w=p/\rho=-1.02(^{+0.13}_{-0.19})$. The conventional quintessence models for dark energy are restricted to the range $-1\le w < 0$, with the cosmological constant corresponding to $w=-1$. Conformally coupled quintessence models are the simplest ones compatible with the marginally allowed superaccelerated regime ($w<-1$). However, they are known to be plagued with anisotropic singularities. We argue here that the extension of the classical approach to the semiclassical one, with the inclusion of quantum counterterms necessary to ensure the renormalization, can eliminate the anisotropic singularities preserving the isotropic behavior of conformally coupled superquintessence models. Hence, besides of having other interesting properties, they are consistent candidates to describe the superaccelerated phases of the universe compatible with the present experimental data.Comment: 7 pages. Essay selected for "Honorable Mention" in the 2004 Awards for Essays on Gravitation, Gravity Research Foundatio

Identifying and Indexing Icosahedral Quasicrystals from Powder Diffraction Patterns

We present a scheme to identify quasicrystals based on powder diffraction data and to provide a standardized indexing. We apply our scheme to a large catalog of powder diffraction patterns, including natural minerals, to look for new quasicrystals. Based on our tests, we have found promising candidates worthy of further exploration.Comment: 4 pages, 1 figur

Phenomenology of a realistic accelerating universe using only Planck-scale physics

Modern data is showing increasing evidence that the Universe is accelerating. So far, all attempts to account for the acceleration have required some fundamental dimensionless quantities to be extremely small. We show how a class of scalar field models (which may emerge naturally from superstring theory) can account for acceleration which starts in the present epoch with all the potential parameters O(1) in Planck units.Comment: 4 pages including 4 figures. Final version accepted for publication in PRL with expanded discussion of the relationship to other quintessence research. No changes to our own wor

Scale-invariance in expanding and contracting universes from two-field models

We study cosmological perturbations produced by the most general two-derivative actions involving two scalar fields, coupled to Einstein gravity, with an arbitrary field space metric, that admit scaling solutions. For contracting universes, we show that scale-invariant adiabatic perturbations can be produced continuously as modes leave the horizon for any equation of state parameter $w \ge 0$. The corresponding background solutions are unstable, which we argue is a universal feature of contracting models that yield scale-invariant spectra. For expanding universes, we find that nearly scale-invariant adiabatic perturbation spectra can only be produced for $w \approx -1$, and that the corresponding scaling solutions are attractors. The presence of a nontrivial metric on field space is a crucial ingredient in our results.Comment: 23 pages, oversight in perturbations calculation corrected, conclusions for expanding models modifie