Mindaugas Karciauskas, Konstantinos Dimopoulos, David H. Lyth
We suppose that a vector field perturbation causes part of the primordial curvature perturbation. The non-Gaussianity parameter fNL is then, in general, statistically anisotropic. We calculate its form and magnitude in the curvaton scenario and in the end-of-inflation scenario. We show that this anisotropy could easily be observable.
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We use the delta N -formalism to investigate the non-Gaussianity of the primordial curvature perturbation in the curvaton scenario for the origin of structure. We numerically calculate the full probability distribution function allowing for the non-instantaneous decay of the curvaton and compare this with analytic results derived in the sudden-decay approximation. We also present results for the leading-order contribution to the primordial bispectrum and trispectrum. In the sudden-decay approximation we derive a fully non-linear expression relating the primordial perturbation to the initial cu…
In this paper we explore the connection between anisotropic Gaussian fluctuations and isotropic non-Gaussian fluctuations. We first set up a large angle framework for characterizing non-Gaussian fluctuations: large angle non-Gaussian spectra. We then consider anisotropic Gaussian fluctuations in two different situations. Firstly we look at anisotropic space-times and propose a prescription for superimposed Gaussian fluctuations; we argue against accidental symmetry in the fluctuations and that therefore the fluctuations should be anisotropic. We show how these fluctuations display previously k…
Light scalars may be ubiquitous in nature, and their quantum fluctuations can produce large non-Gaussianity in the cosmic microwave background temperature anisotropy. The non-Gaussianity may be accompanied with a small admixture of isocurvature perturbations, which often have correlations with the curvature perturbations. We present a general method to calculate the non-Gaussianity in the adiabatic and isocurvature perturbations with and without correlations, and see how it works in several explicit examples. We also show that they leave distinct signatures on the bispectrum of the cosmic micr…
We study a scenario that large non-Gaussianity arises from the baryon asymmetry of the Universe. There are baryogenesis scenarios containing a light scalar field, which may result in baryonic isocurvature perturbations with some amount of non-Gaussianity. As an explicit example we consider the Affleck-Dine mechanism and show that a flat direction of the supersymmeteric standard model can generate large non-Gaussianity in the curvature perturbations, satisfying the observational constraints on the baryonic isocurvature perturbations. The sign of a non-linearity parameter, f_{NL}, is negative, i…
Perturbations in a universe with matter and cosmological constant are computed in terms of the primordial scalar perturbation up to second order. The calculation is easy -- a generalization of the spherical dust solution. Our expression might allow accurate measurements of the primordial non-Gaussianity.
We investigate the non-Gaussianity of primordial curvature perturbation in the modulated reheating scenario where the primordial perturbation is generated due to the spacial fluctuation of the inflaton decay rate to radiation. We use the $δN$ formalism to evaluate the trispectrum of curvature perturbation as well as its bispectrum. We give expressions for three non-linear parameters $f_{NL}, τ_{NL}$ and $g_{NL}$ in the modulated reheating scenario. If the intrinsic non-Gaussianity of scalar field fluctuations and third derivative of the decay rate with respect to scalar fields are negligibly s…
In the curvaton model of inflation, where a second scalar field, the "curvaton", is responsible for the observed inhomogeneity, a non-zero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino, cold dark matter and baryon components. We find the current data can only place upper limits on the level of isocurvature perturbations. These can be translated into upper limits on the neutrino degeneracy parameter. In the case that lepton number is created before curvaton decay, we find that the limit on the neutrino degeneracy parameter is comparable w…
We develop a formalism to study non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the CMB temperature fluctuations, which may be confirmed in future experiments, or possibly, even in the currently available observational data. As an explicit example, we consider the QCD axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H_{inf} = O(10^9 - 10^{11})GeV.
We study the effect of primordial isocurvature perturbations on non-Gaussian properties of CMB temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the…
Recently, the primordial non-Gaussianity in the curvaton model has been predicted assuming sudden decay of the curvaton. We extend the calculation to non-instantaneous decay by employing delta N -formalism. The difference between the sudden-decay approximation and our numerical result is larger than 1% only if the non-linearity parameter is small, -1.16 < f_NL < 60. Thus it is safe to use the sudden-decay approximation when deriving constraints for the curvaton model from WMAP3 (f_NL < 114), but with the Planck forecast |f_NL| <5 one should employ the fully numerical result. Often, the curvato…
Preheating can convert superhorizon fluctuations of light scalar fields present at the end of inflation into observable density perturbations. We show in detail how lattice field theory simulations and the separate universes approximation can be used to calculate these perturbations and make predictions for the nonlinearity parameter fNL . We also present a simple approximation scheme that can reproduce these results analytically. Applying these methods to the massless preheating model, we determine the parameter values that are ruled out by too high levels of non-Gaussianity.
If light scalar fields are present at the end of inflation, their non-equilibrium dynamics such as parametric resonance or a phase transition can produce non-Gaussian density perturbations. We show how these perturbations can be calculated using non-linear lattice field theory simulations and the separate universe approximation. In the massless preheating model, we find that some parameter values are excluded while others lead to acceptable but observable levels of non-Gaussianity. This shows that preheating can be an important factor in assessing the viability of inflationary models.
We analyse models of inflation in which isocurvature perturbations present during inflation are converted into the primordial curvature perturbation during instant preheating. This can be due to an asymmetry between the fields present either during inflation or during preheating. We consider all the constraints that the model must satisfy in order to be theoretically valid and to satisfy observations. We show that the constraints are very tight in all of the models proposed and special initial conditions are required for the models to work. In the case where the symmetry is strongly broken dur…
We present a second-order gauge-invariant formalism to study the evolution of curvature perturbations in a Friedmann-Robertson-Walker universe filled by multiple interacting fluids. We apply such a general formalism to describe the evolution of the second-order curvature perturbations in the standard one-single field inflation, in the curvaton and in the inhomogeneous reheating scenarios for the generation of the cosmological perturbations. Moreover, we provide the exact expression for the second-order temperature anisotropies on large scales, including second-order gravitational effects and e…
We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the primordial curvature perturbation. We write down the full non-linear equations that relate the primordial perturbation to the curvaton perturbations on large scales, calculate the power spectrum of the primordial perturbation, and finally go to second order to find the non-linearity parameter, fNL. We find large positive values of fNL if the energy de…
We study non-Gaussianity induced by a pseudo Nambu-Goldstone boson with a cosine-type scalar potential. We focus on how the non-Gaussianity is affected when the pseudo Nambu-Goldstone boson rolls down from near the top of the scalar potential where the deviation from a quadratic potential is large. We find that the resultant non-Gaussianity is similar to that obtained in the quadratic potential, if the pseudo Nambu-Goldstone boson accounts for the curvature perturbation; the non-Gaussianity is enhanced, otherwise.
We investigate the isocurvaton model, in which the isocurvature perturbation plays a role in suppressing the curvature perturbation, and large non-Gaussianity and gravitational waves can be produced with no isocurvature perturbation for dark matter. We show that in the slow roll non-interacting multi-field theory, the isocurvaton mechanism can not be realized. This result can also be generalized to most of the studied models with generalized kinetic terms. We also study the implications for the curvaton model. We show that there is a combined constraint for curvaton on non-Gaussianity, gravita…
We provide the gauge-invariant expression for large-scale cosmic microwave background temperature fluctuations at second-order in perturbation theory. It enables to unambiguously define the nonlinearity parameter f_NL which is used by experimental collaborations to pin down the level of Non-Gaussianity in the temperature fluctuations. Furthermore, it contains a primordial term encoding all the information about the Non-Gaussianity generated at primordial epochs and about the mechanism which gave rise to cosmological perturbations, thus neatly disentangling the primordial contribution to Non-Ga…
A highly non-gaussian cosmological perturbation with a flat spectrum has unusual stochastic properties. We show that they depend on the size of the box within which the perturbation is defined, but that for a typical observer the parameters defining the perturbation `run' to compensate for any change in the box size. Focusing on the primordial curvature perturbation, we show that an un-correlated gaussian-squared component is bounded at around the 10% level by the WMAP bound on the bispectrum, and we show that a competitive bound may follow from the trispectrum when it too is bounded by WMAP. …
This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provi…
Correlated adiabatic and isocurvature perturbation modes are produced during inflation through an oscillation mechanism when extra scalar degrees of freedom other than the inflaton field are present. We show that this correlation generically leads to sizeable non-Gaussian features both in the adiabatic and isocurvature perturbations. The non-Gaussianity is first generated by large non-linearities in some scalar sector and then efficiently transferred to the inflaton sector by the oscillation process. We compute the cosmic microwave background angular bispectrum, providing a characteristic feat…
We compute the fully non-linear Cosmic Microwave Background (CMB) anisotropies on scales larger than the horizon at last-scattering in terms of only the curvature perturbation, providing a generalization of the linear Sachs-Wolfe effect at any order in perturbation theory. We show how to compute the n-point connected correlation functions of the large-scale CMB anisotropies for generic primordial seeds provided by standard slow-roll inflation as well as the curvaton and other scenarios for the generation of cosmological perturbations. As an application of our formalism, we compute the three- a…
We extend the δN formalism so that it gives all of the stochastic properties of the primordial curvature perturbation ζif the initial field perturbations are gaussian. The calculation requires only the knowledge of some family of unperturbed universes. A formula is given for the normalisation \fnl of the bispectrum of ζ, which is the main signal of non-gaussianity. Examples of the use of the formula are given, and its relation to cosmological perturbation theory is explained.
We consider a two-field model for inflation where the second order metric perturbations can be amplified by a parametric resonance during preheating. We demonstrate that there can arise a considerable enhancement of non-Gaussianity sourced by the local terms generated through the coupled perturbations. We argue that the non-Gaussianity parameter could be as large as f_{NL} ~ 50. Our results may provide a useful test of preheating in future CMB experiments.
In this paper we calculate additional contributions to that part of the non-Gaussianity of the curvature perturbation, which come from the three-point correlator of the field perturbations. We estimate this contribution in the following models for its origin: single-component inflation, multi-component chaotic inflation, a two-component "hybrid" inflationary model, and the curvaton scenario. In all of these models, the additional contributions to the primordial non-gaussianity considered here, are too small to be ever detected.
In the present paper, we study the non-Gaussianity of multiple-field inflation model using the method of the field equation. We start from reviewing the background and the perturbation theory of multiple-field inflation, and then derive the Klein-Gorden equation for the perturbations at second order. Afterward, we calculate the tree-level bispectrum of the fields' perturbations and finally give the corresponding parameter $f_{NL}$ for the curvature perturbation $ζ$ in virtue of the $δN$ formalism. We also compare our result with the one already obtained from the Lagrangian formalism, and find …
We study the evolution of cosmological perturbations on large scales, up to second order, for a perfect fluid with generic equation of state. Taking advantage of super-horizon conservation laws, it is possible to follow the evolution of the non-Gaussianity of perturbations through the different stages after inflation. We find that a large non-linearity is generated by the gravitational dynamics from the original inflationary quantum fluctuations. This leads to a significant enhancement of the tiny intrinsic non-Gaussianity produced during inflation in single-field slow-roll models.
The perturbations in the electron number density during recombination contributes to the Cosmic Microwave Background bispectrum through second order terms. Perturbations in the electron density can be a factor of ~5 larger than the baryon density fluctuations on large scales as shown in the calculations by Novosyadlyj. This raises the possibility that the contribution to bispectrum arising from perturbations in the optical depth may be non-negligible. We calculate this bispectrum and find it to peak for squeezed triangles and of peak amplitude of the order of primordial non-Gaussianity of loca…
We present an estimate for the non-linear parameter τ_NL, which measures the non-gaussianity imprinted in the trispectrum of the comoving curvature perturbation, ζ. 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…
We study the one-point probability distribution functions (PDFs) of the peculiar velocity and the density fluctuation in a cosmological fluid. Within the perturbative approach to the structure formation scenario, the effect of ``pressure'' has recently been an area of research interest. The velocity dispersion of the cosmological fluid creates effective ``pressure'' or viscosity terms. From this viewpoint, because the pressure reflects a nonlinear effect of the motion of the fluid, the pressure model would include nonlinear effects. Here we analyze the Lagrangian linear perturbation PDFs for b…
In curvaton-type models, observable non-gaussianity of the curvature perturbation would come from a contribution of the form $(δσ)^2$, where $δσ$ is gaussian. I analyse this situation allowing $δσ$ to be scale-dependent. The actual curvaton model is considered in more detail than before, including its cosmic uncertainty and anthropic status. The status of curvaton-type models after WMAP year three data is considered.
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.
We investigate non-Gaussianity in the modulated reheating scenario where fluctuations of the decay rate of the inflaton generate adiabatic perturbations, paying particular attention to the non-linearity parameters $f_{\rm NL}, τ_{\rm NL}$ and $g_{\rm NL}$ as well as the scalar spectral index and tensor-to-scalar ratio which characterize the nature of the primordial power spectrum. We also take into account the pre-existing adiabatic perturbations produced from the inflaton fluctuations. It has been known that the non-linearity between the curvature perturbations and the fluctuations of the dec…
In this paper we fully calculate the non-Gaussianity of primordial curvature perturbation of island universe by using the second order perturbation equation. We find that for the spectral index $n_s\simeq 0.96$, which is favored by current observations, the non-Gaussianity level $f_{NL}$ seen in island will generally lie between 30 $\sim$ 60, which may be tested by the coming observations. In the landscape, the island universe is one of anthropically acceptable cosmological histories. Thus the results obtained in some sense means the coming observations, especially the measurement of non-Gauss…
In this paper we derive a generic expression, which is valid for scales larger than Hubble radius and contains only the local terms, for the second order curvature perturbations for more than one field, provided the expansion is sourced by the energy density of a single field. As an application, motivated by our previous paper [1], we apply our formalism to two fields during preheating, where the inflaton oscillations are sourced by $λϕ^4$ potential which is governing the expansion of the Universe. A second field $σ$, coupled to the inflaton through $g^2ϕ^2σ^2$, is excited from the vacuum fluc…
Employing the perturbative treatment of gravitational clustering, we discuss possible effects of primordial non-Gaussianity on the matter power spectrum. As gravitational clustering develops, the coupling between different Fourier modes of density perturbations becomes important and the primordial non-Gaussianity which intrinsically possesses a non-trivial mode-correlation can affect the late-time evolution of the power spectrum. We quantitatively estimate the non-Gaussian effect on power spectrum from the perturbation theory. The potential impact on the cosmological parameter estimation using…
The generation of non-gaussianity is studied in a three fluid curvaton model. By utilizing second order perturbation theory we derive general formulae for the large scale temperature fluctuation and non-gaussianity parameter, $f_{NL}$, that includes the possibility of a non-adiabatic final state. In the adiabatic limit we recover previously known results. The results are applied to a three fluid curvaton model where the curvaton decays into radiation and matter. We find that the amount of non-gaussianity decreases as the final state of the system becomes more adiabatic and that the generated n…
Several conserved and/or gauge invariant quantities described as the second-order curvature perturbation have been given in the literature. We revisit various scenarios for the generation of second-order non-gaussianity in the primordial curvature perturbation ζ, employing for the first time a unified notation and focusing on the normalisation f_{NL} of the bispectrum. When the classical curvature perturbation first appears a few Hubble times after horizon exit, |f_{NL}| is much less than 1 and is, therefore, negligible. Thereafter ζ(and hence f_{NL}) is conserved as long as the pressure is a …
Recently we studied inflation models in which the inflaton potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, $f_{NL}$, can be as large as 10^2.
We study the non-gaussianity from the bispectrum in multi-field inflation models with a general kinetic term. The models include the multi-field K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special cases. We find that, in general, the sound speeds for the adiabatic and entropy perturbations are different and they can be smaller than 1. Then the non-gaussianity can be enhanced. The multi-field DBI-inflation is shown to be a special case where both sound speeds are the same due to a special form of the kinetic term. We derive the exact second and third order actions inclu…
We discuss how primordial (e.g. inflationary) non-Gaussianity in the cosmological perturbations is left imprinted in the Large-Scale Structure of the universe. Our findings show that the information on the primordial non-Gaussianity set on super-Hubble scales flows into Post-Newtonian terms, leaving an observable imprint in the Large-Scale Structure. Future high-precision measurements of the statistics of the dark matter density and peculiar velocity fields will allow to pin down the primordial non-Gaussianity, thus representing a tool complementary to studies of the Cosmic Microwave Backgroun…
The scalar mode density perturbations in a the warm inflationary scenario are analysed with a view to predicting the amount of non-gaussianity produced by this scenario. The analysis assumes that the inflaton evolution is strongly damped by the radiation, with damping terms that are temperature independent. Entropy fluctuations during warm inflation play a crucial role in generating non-gaussianity and result in a distinctive signal which should be observable by the Planck satellite.
The most detailed constraints on the accelerating expansion of the universe and details of nature of dark energy are derived from the high redshift supernova data, assuming that the errors in the measurements are Gaussian in nature. There is a possibility that there are direction dependent systematics in the data, either due to uncorrected, known physical processes or because there are tiny departures from the cosmological principle, making the universe slightly anisotropic. To investigate this possibility we introduce a statistic based on the extreme value theory and apply it to the gold data…
In the framework of inflationary models with non-vacuum initial states for cosmological perturbations, we study non-Gaussian signatures on the cosmic microwave background radiation produced by a broken-scale-invariant model which incorporates a feature at a privileged scale in the primordial power spectrum.
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us towards a physical theory for the origin of st…
We give a concise formula for the non-Gaussianity of the primordial curvature perturbation generated on super-horizon scales in multi-scalar inflation model without assuming slow-roll conditions. This is an extension of our previous work. Using this formula, we study the generation of non-Gaussianity for the double inflation models in which the slow-roll conditions are temporarily violated after horizon exit, and we show that the non-linear parameter $f_{NL}$ for such models is suppressed by the slow-roll parameters evaluated at the time of horizon exit.
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 pot…
In this paper, Gaussianity of eigenmodes and non-Gaussianity in the Cosmic Microwave Background (CMB) temperature fluctuations in two smallest compact hyperbolic (CH) models are investigated. First, it is numerically found that the expansion coefficients of low-lying eigenmodes on the two CH manifolds behave as if they are Gaussian random numbers at almost all the places. Next, non-Gaussianity of the temperature fluctuations in the (l,m) space in these models is studied. Assuming that the initial fluctuations are Gaussian, the real expansion coefficients b_{l m} of the temperature fluctuations…
Seery and Lidsey have calculated the three-point correlator of the light scalar fields, a few Hubble times after horizon exit during inflation. Lyth and Rodriguez have calculated the contribution of this correlator to the three-point correlator of the primordial curvature perturbation. We calculate an upper bound on that contribution, showing that it is too small ever to be observable.
We study the power of several scalar quantities constructed on the sphere (presented in Monteserin et al. 2005) to detect non-Gaussianity on the temperature distribution of the cosmic microwave background (CMB). The test has been performed using non-Gaussian CMB simulations with injected skewness or kurtosis generated through the Edgeworth expansion. We have also taken into account in the analysis the effect of anisotropic noise and the presence of a Galactic mask. We find that the best scalars to detect an excess of skewness in the simulations are the derivative of the gradient, the fractiona…
We investigate non-Gaussianity in general multiple-field inflation using the formalism we developed in earlier papers. We use a perturbative expansion of the non-linear equations to calculate the three-point correlator of the curvature perturbation analytically. We derive a general expression that involves only a time integral over background and linear perturbation quantities. We work out this expression explicitly for the two-field slow-roll case, and find that non-Gaussianity can be orders of magnitude larger than in the single-field case. In particular, the bispectrum divided by the square…
We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the primordial curvature perturbation. We write down the full non-linear equations that relate the primordial perturbation to the curvaton perturbations on large scales, and solve them in a sudden-decay approximation. We calculate the power spectrum of the primordial perturbation, and finally go to second order to find the non-linearity parameter, fNL. No…
We analyze the cosmic non-gaussianity produced in inflation models with multiple uncoupled fields with monomial potentials, such as Nflation. Using the horizon-crossing approximation to compute the non-gaussianity, we show that when each field has the same form of potential, the prediction is independent the number of fields, their initial conditions, and the spectrum of masses/couplings. It depends only on the number of e-foldings after the horizon crossing of observable perturbations. We also provide a further generalization to the case where the fields can have monomial potentials with diff…
We analyze the non-Gaussianity for primordial curvature perturbations generated in multi-scalar slow-roll inflation model including the model with non-separable potential by making use of $δN$ formalism. Many authors have investigated the possibility of large non-Gaussianity for the models with separable potential, and they have found that the non-linear parameter, $f_{NL}$, is suppressed by the slow-roll parameters. We show that for the non-separable models $f_{NL}$ is given by the product of a factor which is suppressed by the slow-roll parameters and a possible enhancement factor which is g…
After simplifying and improving the non-Gaussian formalism we developed in previous work, we derive a quantitative expression for the three-point correlator (bispectrum) of the curvature perturbation in general multiple-field inflation models. Our result describes the evolution of non-Gaussianity on superhorizon scales caused by the nonlinear influence of isocurvature perturbations on the adiabatic perturbation during inflation. We then study a simple quadratic two-field potential and find that when slow roll breaks down and the field trajectory changes direction in field space, the non-Gaussi…
We investigate the relative sensitivities of several tests for deviations from Gaussianity in the primordial distribution of density perturbations. We consider models for non-Gaussianity that mimic that which comes from inflation as well as that which comes from topological defects. The tests we consider involve the cosmic microwave background (CMB), large-scale structure (LSS), high-redshift galaxies, and the abundances and properties of clusters. We find that the CMB is superior at finding non-Gaussianity in the primordial gravitational potential (as inflation would produce), while observati…
Gaussianity of the cosmological perturbations in the universe is one of the key predictions of standard inflation, but it is violated by other models of structure formation such as topological defects. We present the first test of the Gaussianity of the cosmic microwave background (CMB) on sub-degree angular scales, where deviations from Gaussianity are most likely to occur. We apply the methods of moments, cumulants, the Kolmogorov test, the $χ^2$ test, and Minkowski functionals in eigen, real, Wiener-filtered and signal-whitened spaces, to the MAXIMA-1 CMB anisotropy data. We conclude that t…
We investigate consistency relations for non-Gaussianity. We provide a model-independent dynamical proof for the consistency relation of 3-point correlation functions from the Hamiltonian and field redefinition. This relation can be applied to single field inflation, multi-field inflation and the curvaton scenario. This relation can also be generalized to $n$-point correlation functions up to arbitrary order in perturbation theory and with arbitrary number of loops.
We compute the fourth order action in perturbation theory for scalar and second order tensor perturbations for a minimally coupled single field inflationary model, where the inflaton's lagrangian is a general function of the field's value and its kinetic energy. We obtain the fourth order action in two gauges, the comoving gauge and the uniform curvature gauge. Using the comoving gauge action we calculate the trispectrum at leading order in slow-roll, finding agreement with a previously known result in the literature. We point out that in general to obtain the correct leading order trispectrum…
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, th…
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