Harrison--Zeldovich spectrum from conformal invariance

TL;DR

This paper demonstrates that conformal invariance in multi-component scalar field theories with specific symmetries and potential conditions naturally produces a flat spectrum of perturbations, offering a new mechanism for generating cosmological fluctuations.

Contribution

It introduces a novel mechanism linking conformal invariance and negative quartic potentials to the generation of flat spectrum perturbations in scalar fields.

Findings

Flat spectrum of perturbations arises from conformal invariance.

A new conversion mechanism to adiabatic perturbations is proposed.

The theory requires specific symmetry and potential conditions.

Abstract

We show that flat spectrum of small perturbations of field(s) is generated in a simple way in a theory of multi-component scalar field provided this theory is conformally invariant, it has some global symmetry and the quartic potential is negative. We suggest a mechanism of converting these field perturbations into adiabatic scalar perturbations with flat spectrum.