Non-linear inflationary perturbations

We present a method by which cosmological perturbations can be quantitatively studied in single and multi-field inflationary models beyond linear perturbation theory. A non-linear generalization of the gauge-invariant Sasaki-Mukhanov variables is used in a long-wavelength approximation. These generalized variables remain invariant under time slicing changes on long wavelengths. The equations they obey are relatively simple and can be formulated for a number of time slicing choices. Initial conditions are set after horizon crossing and the subsequent evolution is fully non-linear. We briefly discuss how these methods can be implemented numerically in the study of non-Gaussian signatures from specific inflationary models.Comment: 10 pages, replaced to match JCAP versio

Path Integral for Inflationary Perturbations

The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known gauge-invariant quadratic action for scalar and tensor perturbations, and determine the interactions to arbitrary order. This approach does not require the explicit solution of the energy and momentum constraints, a novel feature which simplifies the determination of the interaction vertices. The constraints and the necessary imposition of gauge conditions is reflected in the appearance of various commuting and anti-commuting auxiliary fields in the action. These auxiliary fields are not propagating physical degrees of freedom but need to be included in internal lines and loops in a diagrammatic expansion. To illustrate the formalism we discuss the tree-level 3-point and 4-point functions of the inflaton perturbations, reproducing the results already obtained by the methods used in the current literature. Loop calculations are left for future work.Comment: (v1) 28 pages, no figures; (v2) 29 pages, minor changes, matches published versio

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

Cosmic Acceleration Driven by Mirage Inhomogeneities

A cosmological model based on an inhomogeneous D3-brane moving in an AdS_5 X S_5 bulk is introduced. Although there is no special points in the bulk, the brane Universe has a center and is isotropic around it. The model has an accelerating expansion and its effective cosmological constant is inversely proportional to the distance from the center, giving a possible geometrical origin for the smallness of a present-day cosmological constant. Besides, if our model is considered as an alternative of early time acceleration, it is shown that the early stage accelerating phase ends in a dust dominated FRW homogeneous Universe. Mirage-driven acceleration thus provides a dark matter component for the brane Universe final state. We finally show that the model fulfills the current constraints on inhomogeneities.Comment: 14 pages, 1 figure, IOP style. v2, changed style, minor corrections, references added, version accepted in Class. Quant. Gra

Multiple field inflation

Inflation offers a simple model for very early evolution of our Universe and the origin of primordial perturbations on large scales. Over the last 25 years we have become familiar with the predictions of single-field models, but inflation with more than one light scalar field can alter preconceptions about the inflationary dynamics and our predictions for the primordial perturbations. I will discuss how future observational data could distinguish between inflation driven by one field, or many fields. As an example, I briefly review the curvaton as an alternative to the inflaton scenario for the origin of structure.Comment: 27 pages, no figures. To appear in proceedings of 22nd IAP Colloquium, Inflation +25, Paris, June 200

Classical approximation to quantum cosmological correlations

We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study $\phi^3$ theory on a de Sitter background for a massless minimally coupled scalar field $\phi$. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale $H$ are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.Comment: 44 pages, 1 figure; v2: corrected errors, added references, conclusions unchanged; v3: added section in which we compare with stochastic approach; this version matches published versio

On the divergences of inflationary superhorizon perturbations

We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that within the stochastic framework they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the $\Delta N$ formalism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for the infrared cutoff would of course be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization group invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.Comment: 12 page

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-Gaussianity in braneworld and tachyon inflation

We calculate the bispectrum of single-field braneworld inflation, triggered by either an ordinary scalar field or a cosmological tachyon, by means of a gradient expansion of large-scale non-linear perturbations coupled to stochastic dynamics. The resulting effect is identical to that for single-field 4D standard inflation, the non-linearity parameter being proportional to the scalar spectral index in the limit of collapsing momentum. If the slow-roll approximation is assumed, braneworld and tachyon non-Gaussianities are subdominant with respect to the post-inflationary contribution. However, bulk physics may considerably strengthen the non-linear signatures. These features do not change significantly when considered in a non-commutative framework.Comment: 17 pages; v2: added references and previously skipped details in the derivation of the result; v3: improved discussio

Nonlinear superhorizon perturbations of non-canonical scalar field

We develop a theory of non-linear cosmological perturbations at superhorizon scales for a scalar field with a Lagrangian of the form $P(X,\phi)$, where $X=-\partial^{\mu}\phi\partial_{\mu}\phi$ and $\phi$ is the scalar field. We employ the ADM formalism and the spatial gradient expansion approach to obtain general solutions valid up to the second order in the gradient expansion. This formulation can be applied to, for example, DBI inflation models to investigate superhorizon evolution of non-Gaussianities. With slight modification, we also obtain general solutions valid up to the same order for a perfect fluid with a general equation of state $P=P(\rho)$.Comment: 14 page