Non-gaussianity for a Two Component Hybrid Model of Inflation

We consider a two component hybrid inflation model, in which two fields drive inflation. Our results show that this model generates an observable non-gaussian contribution to the curvature spectrum, within the limits allowed by the recent WMAP year 3 data. We show that if one field has a mass less than zero, and an initial field value less than 0.06Mpl while the other field has a mass greater than zero, and initial field value ranging between 0.5Mpl and Mpl then the non-gaussianity is observable with 1<fnl<1.5, but that fnl becomes much less than the observable limit should we take both masses to have the same sign, or if we loosened the constraints on the initial field values.Comment: 10 pages and 5 figures. More extensive analysis of model, which shows that observable fnl is possibl

Non-Gaussianities in two-field inflation

We study the bispectrum of the curvature perturbation on uniform energy density hypersurfaces in models of inflation with two scalar fields evolving simultaneously. In the case of a separable potential, it is possible to compute the curvature perturbation up to second order in the perturbations, generated on large scales due to the presence of non-adiabatic perturbations, by employing the $\delta N$-formalism, in the slow-roll approximation. In this case, we provide an analytic formula for the nonlinear parameter $f_{NL}$. We apply this formula to double inflation with two massive fields, showing that it does not generate significant non-Gaussianity; the nonlinear parameter at the end of inflation is slow-roll suppressed. Finally, we develop a numerical method for generic two-field models of inflation, which allows us to go beyond the slow-roll approximation and confirms our analytic results for double inflation.Comment: 29 pages, 6 figures. v2, comparison with previous estimates. v3, JCAP version; Revisions based on Referee's comment, corrected typos, added few eqs and refs, conclusions unchange

Contribution of the hybrid inflation waterfall to the primordial curvature perturbation

A contribution $\zeta_\chi$ to the curvature perturbation will be generated during the waterfall that ends hybrid inflation, that may be significant on small scales. In particular, it may lead to excessive black hole formation. We here consider standard hybrid inflation, where the tachyonic mass of the waterfall field is much bigger than the Hubble parameter. We calculate $\zeta_\chi$ in the simplest case, and see why earlier calculations of $\zeta_\chi$ are incorrect.Comment: Simpler and more complete results, especiallly for delta N approac

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

The inflationary trispectrum

We calculate the trispectrum of the primordial curvature perturbation generated by an epoch of slow-roll inflation in the early universe, and demonstrate that the non-gaussian signature imprinted at horizon crossing is unobservably small, of order tau_NL < 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 Maldacena's consistency condition to the trispectrum.Comment: 23 pages, 2 diagrams drawn with feynmp.sty, uses iopart.cls. v2, replaced with version accepted by JCAP. Estimate of maximal tau_NL refined in Section 5, resulting in smaller numerical value. Sign errors in Eq. (44) and Eq. (48) corrected. Some minor notational change

Non-Gaussian perturbations from multi-field inflation

We show how the primordial bispectrum of density perturbations from inflation may be characterised in terms of manifestly gauge-invariant cosmological perturbations at second order. The primordial metric perturbation, zeta, describing the perturbed expansion of uniform-density hypersurfaces on large scales is related to scalar field perturbations on unperturbed (spatially-flat) hypersurfaces at first- and second-order. The bispectrum of the metric perturbation is thus composed of (i) a local contribution due to the second-order gauge-transformation, and (ii) the instrinsic bispectrum of the field perturbations on spatially flat hypersurfaces. We generalise previous results to allow for scale-dependence of the scalar field power spectra and correlations that can develop between fields on super-Hubble scales.Comment: 11 pages, RevTex; minor changes to text; conclusions unchanged; version to appear in JCA

Diagrammatic approach to non-Gaussianity from inflation

We present Feynman type diagrams for calculating the n-point function of the primordial curvature perturbation in terms of scalar field perturbations during inflation. The diagrams can be used to evaluate the corresponding terms in the n-point function at tree level or any required loop level. Rules are presented for drawing the diagrams and writing down the corresponding terms in real space and Fourier space. We show that vertices can be renormalised to automatically account for diagrams with dressed vertices. We apply these rules to calculate the primordial power spectrum up to two loops, the bispectrum including loop corrections, and the trispectrum.Comment: 17 pages, 13 figures. v2: Comments and references added, v3: Introduction expanded, subsection on evaluating loop diagrams added, minor errors corrected, references adde

Non-gaussianity from the inflationary trispectrum

We present an estimate for the non-linear parameter \tau_NL, which measures the non-gaussianity imprinted in the trispectrum of the comoving curvature perturbation, \zeta. 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 Nflation-type scenarios, where the potential is a sum of monomials, the non-gaussianity measured by \tau_NL is independent of the couplings and initial conditions.Comment: 15 pages, uses iopart.sty. Replaced with version accepted by JCAP; journal reference adde

Fields Annihilation and Particles Creation in DBI inflation

We consider a model of DBI inflation where two stacks of mobile branes are moving ultra relativistically in a warped throat. The stack closer to the tip of the throat is annihilated with the background anti-branes while inflation proceeds by the second stack. The effects of branes annihilation and particles creation during DBI inflation on the curvature perturbations power spectrum and the scalar spectral index are studied. We show that for super-horizon scales, modes which are outside the sound horizon at the time of branes collision, the spectral index has a shift to blue spectrum compared to the standard DBI inflation. For small scales the power spectrum approaches to its background DBI inflation value with the decaying superimposed oscillatory modulations.Comment: First revision: minor changes, the background spectral index is corrected, new references are added. Second revision: minor changes, new references are added, accepted for publication in JCA

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 which governs inflation is formulated.Comment: 28 pages, uses feynmp.sty and ioplatex journal style. v2: supersedes version published in JCAP. Some corrections and refinements to the discussion and conclusions. v3: Corrects misidentification of quantum correction with an IR effect. Improvements to the discussio