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

A conservative finite volume method for the population balance equation with aggregation, fragmentation, nucleation and growth

In the present paper, we present a method for solving the population balance equation (PBE) with the complete range of kinetic processes included: namely aggregation, fragmentation, nucleation and growth. The method is based on the finite volume scheme and features guaranteed conservation of the first moment by construction, accurate prediction of the size distribution, applicability to an arbitrary non-uniform grid, robustness and computational efficiency which is instrumental for coupling with computational fluid dynamics (CFD). The treatment of aggregation is based on the previous work by Liu and Rigopoulos (2019). An analysis of the aggregation terms in the PBE is made, and the source of conservation error in finite element/volume methods is elucidated. It is subsequently shown how this error is overcome in the present method via a coordinate transformation applied to the aggregation birth double integral resulting from the application of the finite volume method. The contributions to the birth term are delineated and their corresponding death fluxes identified. An aggregation map is then constructed for mapping birth and death fluxes, thus allowing the finite volume method to operate in terms of fluxes and achieve conservation of mass. The method is then extended to fragmentation, for which a map is also constructed to represent the birth and death fluxes. In the implementation, the aggregation and fragmentation maps are pre-tabulated to allow fast computation. It is also shown how the method can be coupled with a total variation diminishing (TVD) scheme for the treatment of growth with minimal numerical diffusion. The method is validated with a number of test cases including analytical solutions and numerical solutions of the discrete PBE for aggregation (theoretical and free molecule/Brownian kernels), fragmentation, aggregation-fragmentation and aggregation-growth. In all cases, the method produces very accurate results, while also being computationally efficient due to the pre-tabulation of the maps and the simplicity of the algorithm carried out per time step

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

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

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

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

A non-linear approximation for perturbations in \Lambda CDM

We describe inhomogeneities in a {\Lambda}CDM universe with a gradient series expansion and show that it describes the gravitational evolution far into the non-linear regime and beyond the capacity of standard perturbation theory at any order. We compare the gradient expansion with exact inhomogeneous {\Lambda}LTB solutions (Lema\^itre-Tolman-Bondi metric with the inclusion of a cosmological constant) describing growing structure in a {\Lambda}CDM universe and find that the expansion approximates the exact solution well, following the collapse of an over-density all the way into a singularity.Comment: 11 pages, 3 figures, matches published versio

Gauge-invariant perturbations at second order in two-field inflation

We study the second-order gauge-invariant adiabatic and isocurvature perturbations in terms of the scalar fields present during inflation, along with the related fully non-linear space gradient of these quantities. We discuss the relation with other perturbation quantities defined in the literature. We also construct the exact cubic action of the second-order perturbations (beyond any slow-roll or super-horizon approximations and including tensor perturbations), both in the uniform energy density gauge and the flat gauge in order to settle various gauge-related issues. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale.Comment: 28 pages, no figures. v2: Added a summary subsection 4.3 with further discussion of the results. Generalized all super-horizon results of section 4 and appendix A to exact ones. Other minor textual changes and references added. Conclusions unchanged. Matches published versio