Non-Gaussianity of scalar perturbations generated by conformal mechanisms

Abstract

We consider theories which explain the flatness of the power spectrum of scalar perturbations in the Universe by conformal invariance, such as conformal rolling model and Galilean Genesis. We show that to the leading non-linear order, perturbations in all models from this class behave in one and the same way, at least if the energy density of the relevant fields is small compared to the total energy density (spectator approximation). We then turn to the intrinsic non-Gaussianities in these models (as opposed to non-Gaussianities that may be generated during subsequent evolution). The intrinsic bispectrum vanishes, so we perform the complete calculation of the trispectrum and compare it with the trispecta of local forms in various limits. The most peculiar feature of our trispectrum is a (fairly mild) singularity in the limit where two momenta are equal in absolute value and opposite in direction (folded limit). Generically, the intrinsic non-Gaussianity can be of detectable size.

Primordial scalar perturbations via conformal mechanisms: statistical anisotropy

“…Furthermore, one makes use ot the Eqs. (11) and (10) to generate anisotropic maps. We compare values of the quantity C q 2 estimated from these maps with one obtained from the seven-year WMAP data.…”

“…It is assumed that primordial perturbations literally inherit the properties of the phase (up to the possible non-Gaussianities of the local type). Predictions of this particular version of the conformal rolling scenario are the nonGaussianity at the level of the four-point function and the quadrupole statistical anisotropy [9,10]. Conformal rolling scenario with superhorizon modes is natural in the dynamical picture.…”

“…Both they rely on the symmetry breaking pattern: S O(4, 2) → S O(4, 1) created by the background value of the non-zero conformal weight field: radius in case of conformal rolling scenario and Galileon field in case of Galilean Genesis. Moreover, this symmetry breaking pattern fixes the phenomenogical consequences of the Galilean Genesis: these are ones of the conformal rolling scenario with superhorizon perturbations [10].…”

Constraining (pseudo)Conformal Universe and anisotropic inflation with Planck data

“…These field perturbations get reprocessed into adiabatic perturbations at much later epoch. The source of non-trivial phenomenology in this setup is the interaction between zero-weight field perturbations and the Goldstone field associated with the symmetry breaking pattern [8][9][10][11]. In particular, sufficiently long/short wavelength modes of the Goldstone field give rise to SA [8, 10]/non-Gaussianity [9].…”

“…The source of non-trivial phenomenology in this setup is the interaction between zero-weight field perturbations and the Goldstone field associated with the symmetry breaking pattern [8][9][10][11]. In particular, sufficiently long/short wavelength modes of the Goldstone field give rise to SA [8, 10]/non-Gaussianity [9].In the conformal rolling scenario and the Galilean genesis, the symmetry breaking pattern S O(4|2) → S O(4|1) is achieved by introducing the field ρ characterized by the conformal weight Δ = 1. The homogeneous background for the field ρ is fixed by the dilatation invariance, ρ = 1 h(t * − t) .…”