Cosmological density perturbations from conformal scalar field: infrared properties and statistical anisotropy

TL;DR

This work analyzes cosmological perturbations generated by a complex conformal scalar rolling down a negative quartic potential. The authors show that infrared effects from radial (modulus) perturbations are benign at linear order in the self-coupling $h$ after a field redefinition, and they compute the resulting statistical anisotropy in the adiabatic perturbations. At leading order in $h$, anisotropy contains a decaying, $k$-dependent term, while at order $h^2$ deep infrared modes induce a logarithmically enhanced, $k$-independent component; together these predict a distinctive anisotropic pattern in the primordial power spectrum ${\cal P}_\zeta({\bf k})$. The analysis uses a gradient expansion to separate local time shifts and boosts, considers phase perturbations conversion to adiabatic modes via curvaton-like or modulated-decay mechanisms, and highlights potential observational signatures and non-Gaussianities, with applicability to any horizon-proproblem cosmology.

Abstract

We consider a scenario in which primordial scalar perturbations are generated when complex conformal scalar field rolls down its negative quartic potential. Initially, these are the perturbations of the phase of this field; they are converted into the adiabatic perturbations at a later stage. A potentially dangerous feature of this scenario is the existence of perturbations in the radial field direction, which have red power spectrum. We show, however, that to the linear order in the small parameter - the quartic self-coupling - the infrared effects are completely harmless, as they can be absorbed into field redefinition. We then evaluate the statistical anisotropy inherent in the model due to the existence of the long-ranged radial perturbations. To the linear order in the quartic self-coupling the statistical anisotropy is free of the infrared effects. The latter show up at the quadratic order in the self-coupling and result in the mild (logarithmic) enhancement of the corresponding contribution to the statistical anisotropy. The resulting statistical anisotropy is a combination of a larger term which, however, decays as momentum increases, and a smaller term which is independent of momentum.

Figures (2)

• Figure 1: The scalar potential. Bullets show the evolution of the scalar field. Arrows at the end point at the bottom of the potential indicate that there are perturbations of the phase.
• Figure 2: The scalar potential in the pseudo-Nambu-Goldstone scenario.