A large fraction of the information collected by cosmological surveys is simply discarded to avoid length scales which are difficult to model theoretically. We introduce a new technique which enables the extraction of useful information from the bispectrum of galaxies well beyond the conventional limits of perturbation theory. Our results strongly suggest that this method increases the range of...

Speckle interferometry is a common method used to obtain astronomical images using ground-based telescopes to image through a turbulent atmosphere-telescope system. However, when imaging more complicated astronomical objects such as satellites, speckle interferometry methods necessitate the separate recovery of the object’s Fourier phase to obtain more detailed images. Bispectral methods are on...

We consider the problem of system reconstruction from higher-order spectra (HOS) slices. We establish that the impulse response of a complex system can be reconstructed up to a scalar and a circular shift based on any pair of HOS slices, as long as the distance between the two slices satisses a certain condition. One slice is suucient for the reconstruction in the case of a real system. We prop...

Trapped inflation is a mechanism in which particle production from the moving inflaton is the main source of friction in the inflaton equation of motion. The produced fields source inflaton perturbations, which dominate over the vacuum ones. We review the computation of the perturbations performed in the original work and in a successive analysis that makes use of the effective field theory (EF...

We propose an asymptotically unbiased and consistent estimate of the bispectrum of a stationary continuous-time process X = {X(t)}t∈R. The estimate is constructed from observations obtained by a random sampling of the time by {X(τk)}k∈Z, where {τk}k∈Z is a sequence of real random variables, generated from a Poisson counting process. Moreover, we establish the asymptotic normality of the constru...

In the standard picture of cosmological structure formation, initially random-phase fluctuations are amplified by non-linear gravitational instability to produce a final distribution of mass which is highly non-Gaussian and has highly-coupled Fourier phases. We use the Zel’dovich approximation in one dimension to elucidate the onset of non-linearity including mode spawning, merging and coupling...

Non-Gaussianity in the inflationary perturbations can couple observable scales to modes of much longer wavelength (even superhorizon), leaving as a signature a large-angle modulation of the observed cosmic microwave background power spectrum. This provides an alternative origin for a power asymmetry that is otherwise often ascribed to a breaking of statistical isotropy. The non-Gaussian modulat...

Bouchet et al. (1992) showed that in an open or closed Universe with only pressureless matter, gravitational instability from Gaussian initial conditions induces a normalized skewness, S3 ≡ 〈δ 〉 〈δ〉 −2 , that has only a very weak dependence on the nonrelativistic-matter density. Here we generalize this result to a plethora of models with various contributions to the total energy density, includ...

We use the δN-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 lead...

We consider the problem of system reconstruction from higher order spectra (HOS) slices. We establish that the impulse response of a complex system can be reconstructed up to a scalar and a shift based on any pair of HOS slices, as long as the distance between the two slices satisfies a certain condition. One slice is sufficient for the reconstruction in the case of a real system. We propose a ...