David J. Mulryne

Evolution of fNL to the adiabatic limit

We study inflationary perturbations in multiple-field models, for which ζ typically evolves until all isocurvature modes decay — the adiabatic limit. We use numerical methods to explore the sensitivity of the local-shape bispectrum to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of fNL to be large. Other examples can be constructed using a waterfall field to terminate inflation while fNL is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak fNL.

Oscillatory universes in loop quantum cosmology and initial conditions for inflation

Positively curved oscillatory universes are studied within the context of loop quantum cosmology subject to a consistent semiclassical treatment. The semiclassical effects are reformulated in terms of an effective phantom fluid with a variable equation of state. In cosmologies sourced by a massless scalar field, these effects lead to a universe that undergoes ever-repeating cycles of expansion and contraction. The presence of a self-interaction potential for the field breaks the symmetry of the cycles and can enable the oscillations to establish the initial conditions for successful slow-roll inflation, even when the field is initially at the minimum of its potential with a small kinetic energy. The displacement of the field from its minimum is enhanced for lower and more natural values of the parameter that sets the effective quantum gravity scale. For sufficiently small values of this parameter, the universe can enter a stage of eternal self-reproduction.

Diffusing nonlocal inflation: Solving the field equations as an initial value problem

There has been considerable recent interest in solving nonlocal equations of motion which contain an infinite number of derivatives. Here, focusing on inflation, we review how the problem can be reformulated as the question of finding solutions to a diffusionlike partial differential equation with nonlinear boundary conditions. Moreover, we show that this diffusionlike equation, and hence the nonlocal equations, can be solved as an initial value problem once nontrivial initial data consistent with the boundary conditions is found. This is done by considering linearized equations about any field value, for which we show that obtaining solutions using the diffusionlike equation is equivalent to solving a local but infinite field cosmology. These local fields are shown to consist of at most two canonically normalized or phantom fields together with an infinite number of quintoms. We then numerically solve the diffusionlike equation for the full nonlinear case for two string field theory motivated models.

Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity

In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate the conditions that subsequently lead to slow-roll inflation. The consequences for this mechanism of various quantization ambiguities arising within loop quantum cosmology are considered. For the case of a quadratic potential, it is found that some quantization procedures are more likely to generate a phase of slow--roll inflation. In general, however, loop quantum cosmology is robust to ambiguities in the quantization and extends the range of initial conditions for inflation.

Moment transport equations for the primordial curvature perturbation

In a recent publication, we proposed that inflationary perturbation theory can be reformulated in terms of a probability transport equation, whose moments determine the correlation properties of the primordial curvature perturbation. In this paper we generalize this formulation to an arbitrary number of fields. We deduce ordinary differential equations for the evolution of the moments of ζ on superhorizon scales, which can be used to obtain an evolution equation for the dimensionless bispectrum, fNL. Our equations are covariant in field space and allow identification of the source terms responsible for evolution of fNL. In a model with M scalar fields, the number of numerical integrations required to obtain solutions of these equations scales like O(M3). The performance of the moment transport algorithm means that numerical calculations with M 1 fields are straightforward. We illustrate this performance with a numerical calculation of fNL in Nflation models containing M ~ 102 fields, finding agreement with existing analytic calculations. We comment briefly on extensions of the method beyond the slow-roll approximation, or to calculate higher order parameters such as gNL.

Superinflation in loop quantum cosmology

We investigate the dynamics of superinflation in two versions of loop quantum cosmology, one in which the Friedmann equation is modified by the presence of inverse volume corrections, and one in which quadratic corrections are important. Computing the tilt of the power spectrum of the perturbed scalar field in terms of fast-roll parameters, we conclude that the first case leads to a power spectrum that is scale invariant for steep power law negative potentials and for the second case, scale invariance is obtained for positive potentials that asymptote to a constant value for large values of the scalar field. It is found that in both cases, the horizon problem is solved with only a few e-folds of superinflationary evolution.

Moment transport equations for non-Gaussianity

We present a novel method for calculating the primordial non-Gaussianity produced by super-horizon evolution during inflation. Our method evolves the distribution of coarse-grained inflationary field values using a transport equation. We present simple evolution equations for the moments of this distribution, such as the variance and skewness. This method possesses some advantages over existing techniques. Among them, it cleanly separates multiple sources of primordial non-Gaussianity, and is computationally efficient when compared with popular alternatives, such as the δN framework. We adduce numerical calculations demonstrating that our new method offers good agreement with those already in the literature. We focus on two fields and the fnl parameter, but we expect our method will generalize to multiple scalar fields and to moments of arbitrarily high order. We present our expressions in a field-space covariant form which we postulate to be valid for any number of fields.

Non-Gaussianity from the hybrid potential

We study the hybrid inflationary potential in a regime where the defect field is light, and more than 60 e-folds of accelerated expansion occur after the symmetry breaking transition. Using analytic and numerical techniques, we then identify parameter values within this regime for which the statistics of the primordial curvature perturbation are significantly non-Gaussian. Focusing on this range of parameters, we provide a specific example which leads to an observationally consistent power spectrum, and a level of non-Gaussianity within current WMAP bounds and in reach of the Planck satellite. An interesting feature of this example is that the initial conditions at horizon crossing appear quite natural.

Gravitational wave background from superinflation in loop quantum cosmology

We investigate the behavior of tensor fluctuations in Loop Quantum Cosmology, focusing on a class of scaling solutions which admit a near scale-invariant scalar field power spectrum. We obtain the spectral index of the gravitational field perturbations, and find a strong blue tilt in the power spectrum with n{sub t}{approx_equal}2. The amplitude of tensor modes are, therefore, suppressed by many orders of magnitude on large scales compared to those predicted by the standard inflationary scenario where n{sub t}{approx_equal}0.

Non‐linear non‐local Cosmology

Non‐local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion‐like equation with non‐linear boundary conditions. Moreover, we show that this equation can be solved as an initial value problem once a set of non‐trivial initial conditions that satisfy the boundary conditions is found. We find these initial conditions by looking at the linear approximation to the boundary conditions. We then numerically solve the diffusion‐like equation, and hence the non‐local equations, as an initial value problem for the full non‐linear potential and subsequently identify the cases when inflation is attained.