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

Slow-roll corrections to inflaton fluctuations on a brane

Quantum fluctuations of an inflaton field, slow-rolling during inflation are coupled to metric fluctuations. In conventional four dimensional cosmology one can calculate the effect of scalar metric perturbations as slow-roll corrections to the evolution of a massless free field in de Sitter spacetime. This gives the well-known first-order corrections to the field perturbations after horizon-exit. If inflaton fluctuations on a four dimensional brane embedded in a five dimensional bulk spacetime are studied to first-order in slow-roll then we recover the usual conserved curvature perturbation on super-horizon scales. But on small scales, at high energies, we find that the coupling to the bulk metric perturbations cannot be neglected, leading to a modified amplitude of vacuum oscillations on small scales. This is a large effect which casts doubt on the reliability of the usual calculation of inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure

Slow-roll corrections to inflaton fluctuations on a brane

Quantum fluctuations of an inflaton field, slow-rolling during inflation are coupled to metric fluctuations. In conventional four dimensional cosmology one can calculate the effect of scalar metric perturbations as slow-roll corrections to the evolution of a massless free field in de Sitter spacetime. This gives the well-known first-order corrections to the field perturbations after horizon-exit. If inflaton fluctuations on a four dimensional brane embedded in a five dimensional bulk spacetime are studied to first-order in slow-roll then we recover the usual conserved curvature perturbation on super-horizon scales. But on small scales, at high energies, we find that the coupling to the bulk metric perturbations cannot be neglected, leading to a modified amplitude of vacuum oscillations on small scales. This is a large effect which casts doubt on the reliability of the usual calculation of inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure

Scalar perturbations in braneworld cosmology

We study the behaviour of scalar perturbations in the radiation-dominated era of Randall-Sundrum braneworld cosmology by numerically solving the coupled bulk and brane master wave equations. We find that density perturbations with wavelengths less than a critical value (set by the bulk curvature length) are amplified during horizon re-entry. This means that the radiation era matter power spectrum will be at least an order of magnitude larger than the predictions of general relativity (GR) on small scales. Conversely, we explicitly confirm from simulations that the spectrum is identical to GR on large scales. Although this magnification is not relevant for the cosmic microwave background or measurements of large scale structure, it will have some bearing on the formation of primordial black holes in Randall-Sundrum models.Comment: 17 pages, 7 figure

Primordial perturbations from slow-roll inflation on a brane

In this paper we quantise scalar perturbations in a Randall-Sundrum-type model of inflation where the inflaton field is confined to a single brane embedded in five-dimensional anti-de Sitter space-time. In the high energy regime, small-scale inflaton fluctuations are strongly coupled to metric perturbations in the bulk and gravitational back-reaction has a dramatic effect on the behaviour of inflaton perturbations on sub-horizon scales. This is in contrast to the standard four-dimensional result where gravitational back-reaction can be neglected on small scales. Nevertheless, this does not give rise to significant particle production, and the correction to the power spectrum of the curvature perturbations on super-horizon scales is shown to be suppressed by a slow-roll parameter. We calculate the complete first order slow-roll corrections to the spectrum of primordial curvature perturbations

Fully relativistic predictions in Horndeski gravity from standard Newtonian N-body simulations

The N-body gauge allows the introduction of relativistic effects in Newtonian cosmological simulations. Here we extend this framework to general Horndeski gravity theories, and investigate the relativistic effects that the scalar field introduces in the matter power spectrum at intermediate and large scales. In particular, we show that the kineticity function at these scales enhances the amplitude of the signal of contributions coming from the extra degree of freedom. Using the Quasi-Static Approximation (QSA), we separate modified gravity effects into two parts: one that only affects small-scale physics, and one that is due to relativistic effects. This allows our formalism to be readily implemented in modified gravity N-body codes in a straightforward manner, e.g., relativistic effects can be included as an additional linear density field in simulations. We identify the emergence of gravity acoustic oscillations (GAOs) in the matter power spectrum at large scales, $k \sim 10^{-3}-10^{-2}$ Mpc$^{-1}$. GAO features have a purely relativistic origin, coming from the dynamical nature of the scalar field. GAOs may be enhanced to detectable levels by the rapid evolution of the dark energy sound horizon in certain modified gravity models and can be seen as a new test of gravity at scales probed by future galaxy and intensity-mapping surveys

Primordial perturbations from slow-roll inflation on a brane

In this paper we quantise scalar perturbations in a Randall-Sundrum-type model of inflation where the inflaton field is confined to a single brane embedded in five-dimensional anti-de Sitter space-time. In the high energy regime, small-scale inflaton fluctuations are strongly coupled to metric perturbations in the bulk and gravitational back-reaction has a dramatic effect on the behaviour of inflaton perturbations on sub-horizon scales. This is in contrast to the standard four-dimensional result where gravitational back-reaction can be neglected on small scales. Nevertheless, this does not give rise to significant particle production, and the correction to the power spectrum of the curvature perturbations on super-horizon scales is shown to be suppressed by a slow-roll parameter. We calculate the complete first order slow-roll corrections to the spectrum of primordial curvature perturbations.Comment: 23 pages, 10 figure

Living on a dS brane: Effects of KK modes on inflation

We develop a formalism to study non-local higher-dimensional effects in braneworld scenarios from a four-dimensional effective theory point of view and check it against the well-known Garriga-Tanaka result in the appropriate limit. We then use this formalism to study the spectrum of density perturbations during inflation as seen from the lower-dimensional effective theory. In particular, we find that the gravitational potential is greatly enhanced at short wavelengths. The consequences to the curvature perturbations are nonetheless very weak and will lead to no characteristic signatures on the power spectrum.Comment: 21 pages, no figure

Density perturbations in the brane-world

In Randall-Sundrum-type brane-world cosmologies, density perturbations generate Weyl curvature in the bulk, which in turn backreacts on the brane via stress-energy perturbations. On large scales, the perturbation equations contain a closed system on the brane, which may be solved without solving for the bulk perturbations. Bulk effects produce a non-adiabatic mode, even when the matter perturbations are adiabatic, and alter the background dynamics. As a consequence, the standard evolution of large-scale fluctuations in general relativity is modified. The metric perturbation on large-scales is not constant during high-energy inflation. It is constant during the radiation era, except at most during the very beginning, if the energy is high enough.Comment: Additional arguments and minor corrections; version accepted by Phys. Rev.