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

Must Cosmological Perturbations Remain Non-Adiabatic After Multi-Field Inflation?

Even if non-adiabatic perturbations are generated in multi-field inflation, the perturbations will become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities, and will remain adiabatic as long as the wavelength is outside the horizon, even when local thermal equilibrium no longer applies. Small initial non-adiabatic perturbations associated with imperfect local thermal equilibrium remain small when baryons are created from out-of-equilibrium decay of massive particles, or when dark matter particles go out of local thermal equilibrium.Comment: 12 pages, typographical errors corrected, acknowledgment added. Article accepted for publication in Physical Review

Anisotropic Pressures at Ultra-stiff Singularities and the Stability of Cyclic Universes

We show that the inclusion of simple anisotropic pressures stops the isotropic Friedmann universe being a stable attractor as an initial or final singularity is approached when pressures can exceed the energy density. This shows that the situation with isotropic pressures, studied earlier in the context of cyclic and ekpyrotic cosmologies, is not generic, and Kasner-like behaviour occurs when simple pressure anisotropies are present. We find all the asymptotic behaviours and determine the dynamics when the anisotropic principal pressures are proportional to the density. We expect distortions and anisotropies to be significantly amplified through a simple cosmological bounce in cyclic or ekpyrotic cosmologies when ultra-stiff pressures are present.Comment: 18 pages, 2 figure

Phase-plane analysis of Friedmann-Robertson-Walker cosmologies in Brans-Dicke gravity

We present an autonomous phase-plane describing the evolution of Friedmann-Robertson-Walker models containing a perfect fluid (with barotropic index gamma) in Brans-Dicke gravity (with Brans-Dicke parameter omega). We find self-similar fixed points corresponding to Nariai's power-law solutions for spatially flat models and curvature-scaling solutions for curved models. At infinite values of the phase-plane variables we recover O'Hanlon and Tupper's vacuum solutions for spatially flat models and the Milne universe for negative spatial curvature. We find conditions for the existence and stability of these critical points and describe the qualitative evolution in all regions of the (omega,gamma) parameter space for 0-3/2. We show that the condition for inflation in Brans-Dicke gravity is always stronger than the general relativistic condition, gamma<2/3.Comment: 24 pages, including 9 figures, LaTe

Exponential potentials and cosmological scaling solutions

We present a phase-plane analysis of cosmologies containing a barotropic fluid with equation of state $p_\gamma = (\gamma-1) \rho_\gamma$, plus a scalar field $\phi$ with an exponential potential $V \propto \exp(-\lambda \kappa \phi)$ where $\kappa^2 = 8\pi G$. In addition to the well-known inflationary solutions for $\lambda^2 3\gamma$ in which the scalar field energy density tracks that of the barotropic fluid (which for example might be radiation or dust). We show that the scaling solutions are the unique late-time attractors whenever they exist. The fluid-dominated solutions, where $V(\phi)/\rho_\gamma \to 0$ at late times, are always unstable (except for the cosmological constant case $\gamma = 0$). The relative energy density of the fluid and scalar field depends on the steepness of the exponential potential, which is constrained by nucleosynthesis to $\lambda^2 > 20$. We show that standard inflation models are unable to solve this `relic density' problem.Comment: 6 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Matches published versio

Cosmologies with Energy Exchange

We provide a simple mathematical description of the exchange of energy between two fluids in an expanding Friedmann universe with zero spatial curvature. The evolution can be reduced to a single non-linear differential equation which we solve in physically relevant cases and provide an analysis of all the possible evolutions. Particular power-law solutions exist for the expansion scale factor and are attractors at late times under particular conditions. We show how a number of problems studied in the literature, such as cosmological vacuum energy decay, particle annihilation, and the evolution of a population of evaporating black holes, correspond to simple particular cases of our model. In all cases we can determine the effects of the energy transfer on the expansion scale factor. We also consider the situation in the presence of anti-decaying fluids and so called phantom fluids which violate the dominant energy conditions.Comment: 12 pages, 1 figur

Preheating after N-flation

We study preheating in N-flation, assuming the Mar\v{c}enko-Pastur mass distribution, equal energy initial conditions at the beginning of inflation and equal axion-matter couplings, where matter is taken to be a single, massless bosonic field. By numerical analysis we find that preheating via parametric resonance is suppressed, indicating that the old theory of perturbative preheating is applicable. While the tensor-to-scalar ratio, the non-Gaussianity parameters and the scalar spectral index computed for N-flation are similar to those in single field inflation (at least within an observationally viable parameter region), our results suggest that the physics of preheating can differ significantly from the single field case.Comment: 14 pages, 14 figures, references added, fixed typo

Dynamics of Assisted Inflation

We investigate the dynamics of the recently proposed model of assisted inflation. In this model an arbitrary number of scalar fields with exponential potentials evolve towards an inflationary scaling solution, even if each of the individual potentials is too steep to support inflation on its own. By choosing an appropriate rotation in field space we can write down explicitly the potential for the weighted mean field along the scaling solution and for fields orthogonal to it. This demonstrates that the potential has a global minimum along the scaling solution. We show that the potential close to this attractor in the rotated field space is analogous to a hybrid inflation model, but with the vacuum energy having an exponential dependence upon a dilaton field. We present analytic solutions describing homogeneous and inhomogeneous perturbations about the attractor solution without resorting to slow-roll approximations. We discuss the curvature and isocurvature perturbation spectra produced from vacuum fluctuations during assisted inflation.Comment: 9 pages, 2 figures, latex with revtex and eps