A Concise Introduction to Perturbation Theory in Cosmology

We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected, reference added, version accepted by CQ

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

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-Gaussianity in Curvaton Models with Nearly Quadratic Potential

We consider curvaton models with potentials that depart slightly from the quadratic form. We show that although such a small departure does not modify significantly the Gaussian part of the curvature perturbation, it can have a pronounced effect on the level of non-Gaussianity. We find that unlike in the quadratic case, the limit of small non-Gaussianity, $|f_{NL}|\ll1$, is quite possible even with small curvaton energy density $r\ll1$ . Furthermore, non-Gaussianity does not imply any strict bounds on $r$ but the bounds depend on the assumptions about the higher order terms in the curvaton potential.Comment: 11 pages, 3 figures. Minor changes. Typos corrected and a reference adde

Adiabatic Modes in Cosmology

We show that the field equations for cosmological perturbations in Newtonian gauge always have an adiabatic solution, for which a quantity ${\cal R}$ is non-zero and constant in all eras in the limit of large wavelength, so that it can be used to connect observed cosmological fluctuations in this mode with those at very early times. There is also a second adiabatic mode, for which ${\cal R}$ vanishes for large wavelength, and in general there may be non-adiabatic modes as well. These conclusions apply in all eras and whatever the constituents of the universe, under only a mild technical assumption about the wavelength dependence of the field equations for large wave length. In the absence of anisotropic inertia, the perturbations in the adiabatic modes are given for large wavelength by universal formulas in terms of the Robertson--Walker scale factor. We discuss an apparent discrepancy between these results and what appears to be a conservation law in all modes found for large wavelength in synchronous gauge: it turns out that, although equivalent, synchronous and Newtonian gauges suggest inequivalent assumptions about the behavior of the perturbations for large wavelength.Comment: 24 pages, Latex, no special macro

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

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

Nonlinear curvature perturbations in an exactly soluble model of multi-component slow-roll inflation

Using the nonlinear $\delta N$ formalism, we consider a simple exactly soluble model of multi-component slow-roll inflation in which the nonlinear curvature perturbation can be evaluated analytically.Comment: 4 pages, no figure, typos corrected, references added, final version to be published in CQ

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

Conditions for large non-Gaussianity in two-field slow-roll inflation

We study the level of primordial non-Gaussianity in slow-roll two-field inflation. Using an analytic formula for the nonlinear parameter f_nl in the case of a sum or product separable potential, we find that it is possible to generate significant non-Gaussianity even during slow-roll inflation with Gaussian perturbations at Hubble exit. In this paper we give the general conditions to obtain large non-Gaussianity and calculate the level of fine-tuning required to obtain this. We present explicit models in which the non-Gaussianity at the end of inflation can exceed the current observational bound of |f_nl|<100.Comment: 16 pages, 6 figures, 1 table, v2: typos corrected and references added, matches version accepted by JCA