Abstract:
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 during inflation the non-Gaussianity parameter f_NL is generally large and negative.

Abstract:
We study the non-Gaussianity generated during multiple-field inflation. We provide an exact expression for the bispectrum parameter f_NL which is valid beyond the slow-roll regime, valid for certain classes of inflationary models. We then study a new, exact multi-field inflationary model considering a case where the bispectrum grows to observable values at the end of inflation. We show that in this case the trispectrum is also large and may even provide the dominant signal of non-Gaussianity.

Abstract:
Primordial black holes (PBHs) can form in the early Universe from the collapse of rare, large density fluctuations. They have never been observed, but this fact is enough to constrain the amplitude of fluctuations on very small scales which cannot be otherwise probed. Because PBHs form only in very rare large fluctuations, the number of PBHs formed is extremely sensitive to changes in the shape of the tail of the fluctuation distribution - which depends on the amount of non-Gaussianity present. We first study how local non-Gaussianity of arbitrary size up to fifth order affects the abundance and constraints from PBHs, finding that they depend strongly on even small amounts of non-Gaussianity and the upper bound on the allowed amplitude of the power spectrum can vary by several orders of magnitude. The sign of the non-linearity parameters (f_{NL}, g_{NL}, etc) are particularly important. We also study the abundance and constraints from PBHs in the curvaton scenario, in which case the complete non-linear probability distribution is known, and find that truncating to any given order (i.e. to order f_{NL} or g_{NL}, etc) does not give accurate results.

Abstract:
We review models which generate a large non-Gaussianity of the local form. We first briefly consider three models which generate the non-Gaussianity either at or after the end of inflation; the curvaton scenario, modulated (p)reheating, and an inhomogeneous end of inflation. We then focus on ways of generating the non-Gaussianity during inflation. We derive general conditions which a product or sum separable potential must satisfy in order to generate a large local bispectrum during slow-roll inflation. As an application, we consider two-field hybrid inflation. We then derive a formalism not based on slow roll which can be applied to models in which the slow-roll parameters become large before inflation ends. An exactly soluble two-field model is given in which this happens. Finally, we also consider further non-Gaussian observables, a scale dependence of and the trispectrum. 1. Introduction There are many models of the universe which can predict a large non-Gaussianity. However the predicted amplitude and the shape of the non-Gaussianity are different among different classes of models. One category is those which generate the non-Gaussianity due to nontrivial classical dynamics on superhorizon scales. These models predict the shape of the bispectrum to be of the so-called “local type”, which can be expressed as an expansion of the Bardeen potential [1] where is the curvature perturbation on a Newtonian slice and is its linear and Gaussian part. denotes the ensemble average in a statistically homogeneous distribution. The current limit on the local type of the nonlinearity parameter from seven years of WMAP data [2] is at the 95% confidence level. Constraints are expected to improve rapidly and significantly, first with Planck data and later using large scale structure data, see the recent reviews [3–5]. The Bardeen potential is related to the primordial curvature perturbation of on large scales and in the matter dominated era by . The curvature perturbation at horizon exit is determined by the classical perturbations of the scalar fields, . The subsequent evolution of can be conveniently described by the formalism [6–11]. The curvature perturbation is given by up to quadratic terms [11] where is the e-folding number evaluated in an unperturbed Universe, from the epoch of horizon exit to later epoch of uniform energy density hypersurface (for an extension to include gradient terms, see [12]). The power spectrum and the bispectrum are defined by From this, we can define the observable quantities, the spectral index, the tensor-to-scalar ratio, and the

Abstract:
We reinspect the calculation for the mass fraction of primordial black holes (PBHs) which are formed from primordial perturbations, finding that performing the calculation using the comoving curvature perturbation $\mathcal{R}_{c}$ in the standard way vastly overestimates the number of PBHs, by many orders of magnitude. This is because PBHs form shortly after horizon entry, meaning modes significantly larger than the PBH are unobservable and should not affect whether a PBH forms or not - this important effect is not taken into account by smoothing the distribution in the standard fashion. We discuss alternative methods and argue that the density contrast, $\Delta$, should be used instead as super-horizon modes are damped by a factor $k^{2}$. We make a comparison between using a Press-Schechter approach and peaks theory, finding that the two are in close agreement in the region of interest. We also investigate the effect of varying the spectral index, and the running of the spectral index, on the abundance of primordial black holes.

Abstract:
We investigate the scale-dependence of f_NL in the self-interacting curvaton model. We show that the scale-dependence, encoded in the spectral index n_{f_NL}, can be observable by future cosmic microwave background observations, such as CMBpol, in a significant part of the parameter space of the model. We point out that together with information about the trispectrum g_NL, the self-interacting curvaton model parameters could be completely fixed by observations. We also discuss the scale-dependence of g_NL and its implications for the curvaton model, arguing that it could provide a complementary probe in cases where the theoretical value of n_{f_NL} is below observational sensitivity.

Abstract:
Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |f_NL|>> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |fNL^{obs.}|<10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations.

Abstract:
We compute the scale dependence of fNL for models of multi-field inflation, allowing for an arbitrary field space metric. We show that, in addition to multi-field effects and self interactions, the curved field space metric provides another source of scale dependence, which arises from the field-space Riemann curvature tensor and its derivatives. The scale dependence may be detectable within the near future if the amplitude of fNL is not too far from the current observational bounds.

Abstract:
We consider possible scale-dependence of the non-linearity parameter f_NL in local and quasi-local models of non-Gaussian primordial density perturbations. In the simplest model where the primordial perturbations are a quadratic local function of a single Gaussian field then f_NL is scale-independent by construction. However scale-dependence can arise due to either a local function of more than one Gaussian field, or due to non-linear evolution of modes after horizon-exit during inflation. We show that the scale dependence of f_NL is typically first order in slow-roll. For some models this may be observable with experiments such as Planck provided that f_NL is close to the current observational bounds.

Abstract:
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.