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

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

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

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

Issues Concerning Loop Corrections to the Primordial Power Spectra

We expound ten principles in an attempt to clarify the debate over infrared loop corrections to the primordial scalar and tensor power spectra from inflation. Among other things we note that existing proposals for nonlinear extensions of the scalar fluctuation field $\zeta$ introduce new ultraviolet divergences which no one understands how to renormalize. Loop corrections and higher correlators of these putative observables would also be enhanced by inverse powers of the slow roll parameter $\epsilon$. We propose an extension which should be better behaved.Comment: 36 pages, uses LaTeX2e, version 3 revised for publication with a much expanded section 4, proving that our proposed extension of the zeta-zeta correlator absorbs the one loop infrared divergences from graviton

Signatures of Planck-scale interactions in the cosmic microwave background?

Based on a rather general low-energy effective action (interacting quantum fields in classical curved space-times), we calculate potential signatures of new physics (such as quantum gravity) at ultra-high energies (presumably the Planck scale) in the anisotropies of the cosmic microwave background. These Planck-scale interactions create non-Gaussian contributions, where special emphasis is laid on the three-point function as the most promising observable, which also allows the discrimination between models violating and those obeying Lorentz invariance. PACS: 98.80.Cq, 04.62.+v, 98.70.Vc, 98.80.Qc.Comment: 4 page

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

Gravitational Wave Background and Non-Gaussianity as a Probe of the Curvaton Scenario

We study observational implications of the stochastic gravitational wave background and a non-Gaussian feature of scalar perturbations on the curvaton mechanism of the generation of density/curvature fluctuations, and show that they can determine the properties of the curvaton in a complementary manner to each other. Therefore even if Planck could not detect any non-Gaussianity, future space-based laser interferometers such as DECIGO or BBO could practically exhaust its parameter space.Comment: 16 pages, 2 figure