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

TL;DR

This paper investigates how conformal scalar fields can generate primordial density perturbations with specific statistical anisotropy, analyzing infrared effects and their impact on observable anisotropic signatures in the early universe.

Contribution

It demonstrates that infrared effects are negligible at linear order in the quartic coupling and evaluates the resulting statistical anisotropy, including its quadratic order enhancements.

Findings

Infrared effects are absorbed at linear order, avoiding potential divergences.

Statistical anisotropy has a momentum-dependent larger term and a momentum-independent smaller term.

Quadratic order effects cause a mild logarithmic enhancement of anisotropy.

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.