Large Blue Spectral Index From a Conformal Limit of a Rotating Complex Scalar

TL;DR

This paper demonstrates how a conformal limit of a rotating complex scalar with a quartic potential can produce a large blue spectral index for axionic isocurvature perturbations, offering a novel mechanism different from traditional models.

Contribution

It introduces a new approach to generate a large blue spectral index using a conformal limit of a rotating complex scalar with a quartic potential, distinct from existing models.

Findings

Achieves a spectral index of 3 in a conformal limit.

Identifies a new scenario involving a superfluid or slowed radial field.

Discusses parameter space compatible with axion dark matter.

Abstract

One well known method of generating a large blue spectral index for axionic isocurvature perturbations is through a flat direction not having a quartic potential term for the radial partner of the axion field. In this work, we show how one can obtain a large blue spectral index even with a quartic potential term associated with the Peccei-Quinn symmetry breaking radial partner. We use the fact that a large radial direction with a quartic term can naturally induce a conformal limit which generates an isocurvature spectral index of 3. We point out that this conformal representation is intrinsically different from both the ordinary equilibrium axion scenario or massless fields in Minkowski spacetime. Another way to view this limit is as a scenario where the angular momentum of the initial conditions slows down the radial field or as a superfluid limit. Quantization of the non-static system in which derivative of the radial field and the derivative of the angular field do not commute is treated with great care to compute the vacuum state. The parametric region consistent with axion dark matter and isocurvature cosmology is discussed.