David Seery

Primordial non-Gaussianities in single-field inflation

We calculate the three-point function for primordial scalar fluctuations in a single-field inflationary scenario where the scalar field Lagrangian is a completely general function of the field and its first derivative. We obtain an explicit expression for the three-point correlation function in a self-consistent approximation scheme where the expansion rate varies slowly, analogous to the slow-roll limit in standard, single-field inflation. The three-point function can be written in terms of the familiar slow-roll parameters and three new parameters which measure the non-trivial kinetic structure of the scalar field, the departure of the speed of sound from the speed of light, and the rate of change of the speed of sound.

Primordial non-Gaussianities from multiple-field inflation

We calculate the three-point correlation function evaluated at horizon crossing for a set of interacting scalar fields coupled to gravity during inflation. This provides the initial condition for the three-point function of the curvature perturbation in the Sasaki-Stewart delta N formulation. We find that the effect is small, of the order of a slow-roll parameter, and that the non-Gaussianity can be determined on large scales once the unperturbed background evolution is known. As an example of the use of our formalism, we calculate the primordial non-Gaussianity arising in a model of assisted inflation.

Inflationary trispectrum from graviton exchange

We compute the connected four-point correlation function of the primordial curvature perturbation generated during inflation with standard kinetic terms, where the correlation is established via exchange of a graviton between two pairs of scalar fluctuations. Any such correlation yields a contribution to the scalar trispectrum of the order of the tensor to scalar ratio r. This contribution is numerically one order of magnitude larger than the one previously calculated on the basis of scalar perturbations interacting at a point and satisfies a simple relation in the limit where the momentum of the graviton which is exchanged becomes much smaller than the external momenta. We conclude that the total non-linearity parameter generated by single-field models of slow-roll inflation is at maximum |tNL| ~ r.

The inflationary trispectrum

We calculate the trispectrum of the primordial curvature perturbation generated by an epoch of slow-roll in. ation in the early universe, and demonstrate that the non-Gaussian signature imprinted at horizon crossing is unobservably small, of order lambda NL less than or similar to r/50, where r < 1 is the tensor-to-scalar ratio. Therefore any primordial non-Gaussianity observed in future microwave background experiments is likely to have been synthesized by gravitational effects on superhorizon scales. We discuss the application of Maldacenas consistency condition to the trispectrum.

One-loop corrections to a scalar field during inflation

The leading quantum correction to the power spectrum of a gravitationally coupled light scalar field is calculated, assuming that it is generated during a phase of single-field, slow-roll inflation.

Non-Gaussianity from the inflationary trispectrum

We present an estimate for the non-linear parameter τNL, which measures the non-Gaussianity imprinted in the trispectrum of the comoving curvature perturbation, ζ. Our estimate is valid throughout the inflationary era, until the slow-roll approximation breaks down, and takes into account the evolution of perturbations on superhorizon scales. We find that the non-Gaussianity is always small if the field values at the end of inflation are negligible when compared to their values at horizon crossing. Under the same assumption, we show that in N-flation-type scenarios, where the potential is a sum of monomials, the non-Gaussianity measured by τNL is independent of the couplings and initial conditions.

One-loop corrections to the curvature perturbation from inflation

An estimate of the one-loop correction to the power spectrum of the primordial curvature perturbation is given, assuming it is generated during a phase of single-field, slow-roll inflation. The loop correction splits into two parts, which can be calculated separately: a purely quantum-mechanical contribution which is generated from the interference among quantized field modes around the time when they cross the horizon, and a classical contribution which comes from integrating the effect of field modes which have already passed far beyond the horizon. The loop correction contains logarithms which may invalidate the use of naive perturbation theory for cosmic microwave background (CMB) predictions when the scale associated with the CMB is exponentially different from the scale at which the fundamental theory governing inflation is formulated. This may have important consequences for the comparison of chaotic inflationary models with forthcoming high-precision satellite data

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.

Non-Gaussian inflationary perturbations from the dS/CFT correspondence

We use the dS/CFT correspondence and bulk gravity to predict the form of the renormalized holographic three-point correlation function of the operator which is dual to the inflaton field perturbation during single-field, slow-roll inflation. Using Maldcaenas formulation of the correspondence, this correlator can be related to the three-point function of the curvature perturbation generated during single-field inflation, and we find exact agreement with previous bulk QFT calculations. This provides a consistency check on existing derivations of the non-Gaussianity from single-field inflation and also yields insight into the nature of the dS/CFT correspondence. As a result of our calculation, we obtain the properly renormalized dS/CFT one-point function, including boundary contributions where derivative interactions are present in the bulk. In principle, our method may be employed to derive the n-point correlators of the inflationary curvature perturbation within the context of (n-1)th-order perturbation theory, rather than nth-order theory as in conventional approaches.

Non-Gaussianity of inflationary field perturbations from the field equation

We calculate the tree-level bispectrum of the inflaton field perturbation directly from the field equations, and construct the corresponding fNL parameter. Our results agree with previous ones derived from the Lagrangian. We argue that quantum theory should only be used to calculate the correlators when they first become classical a few Hubble times after horizon exit, the classical evolution taking over thereafter.