We compute the 3-point correlation function for a general model of inflation driven by a single, minimally coupled scalar field. Our approach is based on the numerical evaluation of both the perturbation equations and the integrals which contribute to the 3-point function. Consequently, we can analyze models where the potential has a "feature", in the vicinity of which the slow roll parameters may take on large, transient values. This introduces both scale and shape dependent non-Gaussianities into the primordial perturbations. As an example of our methodology, we examine the "step" potentials which have been invoked to improve the fit to the glitch in the T T C ℓ for ℓ ∼ 30, present in both the one and three year WMAP data sets. We show that for the typical parameter values, the non-Gaussianities associated with the step are far larger than those in standard slow roll inflation, and may even be within reach of a next generation CMB experiment such as Planck. More generally, we use this example to explain that while adding features to potential can improve the fit to the 2-point function, these are generically associated with a greatly enhanced signal at the 3-point level. Moreover, this 3-point signal will have a very nontrivial shape and scale dependence, which is correlated with the form of the 2-point function, and may thus lead to a consistency check on the models of inflation with non-smooth potentials.

We use a numerical code to compute the density perturbations generated during an inflationary epoch which includes a spontaneous symmetry breaking phase transition. A sharp step in the inflaton potential generates k dependent oscillations in the spectrum of primordial density perturbations. The amplitude and extent in wavenumber of these oscillations depends on both the magnitude and gradient of the step in the inflaton potential. We show that observations of the cosmic microwave background anisotropy place strong constraints on the step parameters.

Inflation driven by a single, minimally coupled, slowly rolling field generically yields a negligible primordial non-Gaussianity. We discuss two distinct mechanisms by which a nontrivial potential can generate large non-Gaussianities. Firstly, if the inflaton traverses a feature in the potential, or if the inflationary phase is short enough so that initial transient contributions to the background dynamics have not been erased, modes near horizon-crossing can acquire significant non-Gaussianities. Secondly, potentials with small-scale structure may induce significant non-Gaussianities while the relevant modes are deep inside the horizon. The first case includes the "step" potential we previously analyzed while the second "resonance" case is novel. We derive analytic approximations for the 3-point terms generated by both mechanisms written as products of functions of the three individual momenta, permitting the use of efficient analysis algorithms. Finally, we present a significantly improved approach to regularizing and numerically evaluating the integrals that contribute to the 3-point function.

We show that a string-inspired Planck scale modification of general relativity can have observable cosmological effects. Specifically, we present a complete analysis of the inflationary perturbation spectrum produced by a phenomenological Lagrangian that has a standard form on large scales but incorporates a string-inspired short distance cutoff, and find a deviation from the standard result. We use the de Sitter calculation as the basis of a qualitative analysis of other inflationary backgrounds, arguing that in these cases the cutoff could have a more pronounced effect, changing the shape of the spectrum. Moreover, the computational approach developed here can be used to provide unambiguous calculations of the perturbation spectrum in other heuristic models that modify trans-Planckian physics and thereby determine their impact on the inflationary perturbation spectrum. Finally, we argue that this model may provide an exception to constraints, recently proposed by Tanaka and Starobinsky, on the ability of Planck-scale physics to modify the cosmological spectrum.

In many models of inflation, the period of accelerated expansion ends with preheating, a highly non-thermal phase of evolution during which the inflaton pumps energy into a specific set of momentum modes of field(s) to which it is coupled. This necessarily induces large, transient density inhomogeneities which can source a significant spectrum of gravitational waves. In this paper, we consider the generic properties of gravitational waves produced during preheating, perform detailed calculations of the spectrum for several specific inflationary models, and identify problems that require further study. In particular, we argue that if these gravitational waves exist they will necessarily fall within the frequency range that is feasible for direct detection experimentsfrom laboratory through to solar system scales. We extract the gravitational wave spectrum from numerical simulations of preheating after λφ 4 and m 2 φ φ 2 inflation, and find that they lead to a gravitational wave amplitude of around Ωgwh 2 ∼ 10 −10 . This is considerably higher than the amplitude of the primordial gravitational waves produced during inflation. However, the typical wavelength of these gravitational waves is considerably shorter than LIGO scales, although in extreme cases they may be visible at scales accessible to the proposed BBO mission. We survey possible experimental approaches to detecting any gravitational wave background generated during preheating.