Brane-world cosmology

Brane-world models, where observers are restricted to a brane in a higher-dimensional spacetime, offer a novel perspective on cosmology. I discuss some approaches to cosmology in extra dimensions and some interesting aspects of gravity and cosmology in brane-world models.Comment: 16 pages, 4 figures, to appear in proceedings of ERE2005, the XXVIII Spanish Relativity Meeting, Oviedo, Spai

Cosmological perturbations through the big bang

Several scenarios have been proposed in which primordial perturbations could originate from quantum vacuum fluctuations in a phase corresponding to a collapse phase (in an Einstein frame) preceding the Big Bang. I briefly review three models which could produce scale-invariant spectra during collapse: (1) curvature perturbations during pressureless collapse, (2) axion field perturbations in a pre big bang scenario, and (3) tachyonic fields during multiple-field ekpyrotic collapse. In the separate universes picture one can derive generalised perturbation equations to describe the evolution of large scale perturbations through a semi-classical bounce, assuming a large-scale limit in which inhomogeneous perturbations can be described by locally homogeneous patches. For adiabatic perturbations there exists a conserved curvature perturbation on large scales, but isocurvature perturbations can change the curvature perturbation through the non-adiabatic pressure perturbation on large scales. Different models for the origin of large scale structure lead to different observational predictions, including gravitational waves and non-Gaussianity.Comment: 13 pages, latex, no figures. To appear in Adv Sci Lett, special issue on Quantum Gravity, Cosmology amd Black Hole

Primordial non-Gaussianity from mixed inflaton-curvaton perturbations

We characterise the primordial perturbations produced due to both inflaton and curvaton fluctuations in models where the curvaton has a quadratic, cosine or hyperbolic potential, and the inflaton potential is characterised by the usual slow-roll parameters. Isocurvature curvaton field perturbations can produce significant non-Gaussianity in the primordial density field, in contrast with adiabatic inflaton field perturbations which produce negligible non-Gaussianity for canonical scalar fields. A non-self-interacting curvaton with quadratic potential produces a local-type non-Gaussianity that is well described by the non-linearity parameter fNL, which may be scale-dependent when the inflaton perturbations dominate the power spectrum. We show how observational bounds on non-linearity parameters and the tensor-scalar ratio can be used to constrain curvaton and inflaton parameters. We find a consistency relation between the bispectrum and trispectrum parameters in a mixed inflaton-curvaton model for a quadratic curvaton potential. Self-interaction terms in the curvaton potential can lead to both a large trispectrum parameter, gNL, and scale-dependence of the non-linearity parameters.Comment: 17 pages, 8 figures, (v2 references added

Tilted Ekpyrosis

We consider a simple model of cosmological collapse driven by canonical fields with exponential potentials. We generalise the two-field ekpyrotic collapse to consider non-orthogonal or tilted potentials and give the general condition for isocurvature field fluctuations to have a scale-invariant spectrum in this model. In particular we show that tilted potentials allow for a slightly red spectrum of perturbations as required by current observations. However a red spectrum of fluctuations implies that the two-field ekpyrotic phase must have a finite duration and requires a preceding phase which sets the initial conditions for what otherwise appears to be a fine-tuned trajectory in the phase space.Comment: 5 pages, references adde

Cosmological matching conditions

We investigate the evolution of scalar metric perturbations across a sudden cosmological transition, allowing for an inhomogeneous surface stress at the transition leading to a discontinuity in the local expansion rate, such as might be expected in a big crunch/big bang event. We assume that the transition occurs when some function of local matter variables reaches a critical value, and that the surface stress is also a function of local matter variables. In particular we consider the case of a single scalar field and show that a necessary condition for the surface stress tensor to be perturbed at the transition is the presence of a non-zero intrinsic entropy perturbation of the scalar field. We present the matching conditions in terms of gauge-invariant variables assuming a sudden transition to a fluid-dominated universe with barotropic equation of state. For adiabatic perturbations the comoving curvature perturbation is continuous at the transition, while the Newtonian potential may be discontinuous if there is a discontinuity in the background Hubble expansion.Comment: 12 pages, no figure

Cosmological perturbations

We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear and curvature of constant-time hypersurfaces and the orthogonal timelike vector field. We give the gauge transformation rules for metric and matter variables at first and second order. We show how gauge invariant variables are constructed by identifying geometric or matter variables in physically-defined coordinate systems, and give the relations between many commonly used gauge-invariant variables. In particular we show how the Einstein equations or energy-momentum conservation can be used to obtain simple evolution equations at linear order, and discuss extensions to non-linear order. We present evolution equations for systems with multiple interacting fluids and scalar fields, identifying adiabatic and entropy perturbations. As an application we consider the origin of primordial curvature and isocurvature perturbations from field perturbations during inflation in the very early universe.Comment: 96 pages, submitted to Phys. Rep; v2: minor changes, typos corrected, references added, 1 figure added, corresponds to published versio