Transport equations for the inflationary trispectrum

We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, tauNL and gNL, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, and obtain its third-order part for the first time. We clarify how the 'backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.Comment: 24 pages, plus references and appendix. v2: matches version published in JCAP; typo fixed in Eq. (54

de Sitter limit of inflation and nonlinear perturbation theory

We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.Comment: 14 pages, 1 figure; typos corrected and discussion of tensor modes adde

Dominance of gauge artifact in the consistency relation for the primordial bispectrum

The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because observable portion of the universe is limited. To give a theoretical prediction to the observable fluctuations, gauge-invariant observables should be composed of the information in our local observable universe with finite volume. From this point of view, we reexamine the primordial non-Gaussianity in single field models, focusing on the bispectrum in the squeezed limit. A conventional prediction states that the bispectrum in this limit is related to the power spectrum through the so-called consistency relation. However, it turns out that, if we adopt a genuine gauge invariant variable which is naturally composed purely of the information in our local universe, the leading term for the bispectrum in the squeezed limit predicted by the consistency relation vanishes.Comment: 12 pages; v2: accepted version in JCA

Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model

We investigate the primordial trispectra of the general multifield DBI inflationary model. In contrast with the single field model, the entropic modes can source the curvature perturbations on the super horizon scales, so we calculate the contributions from the interaction of four entropic modes mediating one adiabatic mode to the trispectra, at the large transfer limit ($T_{RS}\gg1$). We obtained the general form of the 4-point correlation functions, plotted the shape diagrams in two specific momenta configurations, "equilateral configuration" and "specialized configuration". Our figures showed that we can easily distinguish the two different momenta configurations.Comment: 17pages, 7 figures, version to appear in JCA

Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Bispectrum

The methods of effective field theory are used to study generic theories of inflation with a single inflaton field and to perform a general analysis of the associated non-Gaussianities. We investigate the amplitudes and shapes of the various generic three-point correlators, the bispectra, which may be generated by different classes of single-field inflationary models. Besides the well-known results for the DBI-like models and the ghost inflationary theories, we point out that curvature-related interactions may give rise to large non-Gaussianities in the form of bispectra characterized by a flat shape which, quite interestingly, is independently produced by several interaction terms. In a subsequent work, we will perform a similar general analysis for the non-Gaussianities generated by the generic four-point correlator, the trispectrum.Comment: Version matching the one published in JCAP, 2 typos fixed, references added. 30 pages, 20 figure

A parton picture of de Sitter space during slow-roll inflation

It is well-known that expectation values in de Sitter space are afflicted by infra-red divergences. Long ago, Starobinsky proposed that infra-red effects in de Sitter space could be accommodated by evolving the long-wavelength part of the field according to the classical field equations plus a stochastic source term. I argue that--when quantum-mechanical loop corrections are taken into account--the separate-universe picture of superhorizon evolution in de Sitter space is equivalent, in a certain leading-logarithm approximation, to Starobinsky's stochastic approach. In particular, the time evolution of a box of de Sitter space can be understood in exact analogy with the DGLAP evolution of partons within a hadron, which describes a slow logarithmic evolution in the distribution of the hadron's constituent partons with the energy scale at which they are probed.Comment: 36 pages; uses iopart.cls and feynmp.sty. v2: Minor typos corrected. Matches version published in JCA

Infrared effects in inflationary correlation functions

In this article, I briefly review the status of infrared effects which occur when using inflationary models to calculate initial conditions for a subsequent hot, dense plasma phase. Three types of divergence have been identified in the literature: secular, "time-dependent" logarithms, which grow with time spent outside the horizon; "box-cutoff" logarithms, which encode a dependence on the infrared cutoff when calculating in a finite-sized box; and "quantum" logarithms, which depend on the ratio of a scale characterizing new physics to the scale of whatever process is under consideration, and whose interpretation is the same as conventional field theory. I review the calculations in which these divergences appear, and discuss the methods which have been developed to deal with them.Comment: Invited review for focus section of Classical & Quantum Gravity on nonlinear and nongaussian perturbation theory. Some improvements compared to version which will appear in CQG, especially in Sec. 2.3. 30 pages + references

Large slow-roll corrections to the bispectrum of noncanonical inflation

Nongaussian statistics are a powerful discriminant between inflationary models, particularly those with noncanonical kinetic terms. Focusing on theories where the Lagrangian is an arbitrary Lorentz-invariant function of a scalar field and its first derivatives, we review and extend the calculation of the observable three-point function. We compute the "next-order" slow-roll corrections to the bispectrum in closed form, and obtain quantitative estimates of their magnitude in DBI and power-law k-inflation. In the DBI case our results enable us to estimate corrections from the shape of the potential and the warp factor: these can be of order several tens of percent. We track the possible sources of large logarithms which can spoil ordinary perturbation theory, and use them to obtain a general formula for the scale dependence of the bispectrum. Our result satisfies the next-order version of Maldacena's consistency condition and an equivalent consistency condition for the scale dependence. We identify a new bispectrum shape available at next-order, which is similar to a shape encountered in Galileon models. If fNL is sufficiently large this shape may be independently detectable.Comment: v1: 37 pages, plus tables, figures and appendices. v2: supersedes version published in JCAP; some clarifications and more detailed comparison with earlier literature. All results unchanged. v3:improvements to some plots; text unchange

On the Physical Significance of Infra-red Corrections to Inflationary Observables

Inflationary observables, like the power spectrum, computed at one- and higher-order loop level seem to be plagued by large infra-red corrections. In this short note, we point out that these large infra-red corrections appear only in quantities which are not directly observable. This is in agreement with general expectations concerning infra-red effects.Comment: 11 pages; LateX file; 5 figures. Some coefficients in Eq.(A6) corrected; References adde

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 f_NL 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.Comment: 16 pages, uses iopart.sty. v2: replaced with version accepted by JCAP; minor changes of wording only. v3: supersedes version published by journal; typo fixed in Eq. (20) and updated references. v4: sign errors in Eqs. (32) and (38) correcte