Horizon-preserving dualities and perturbations in non-canonical scalar field cosmologies

TL;DR

This paper extends the concept of cosmological dualities to non-canonical scalar fields with variable sound speed, identifying three classes of models and analyzing their perturbation spectra.

Contribution

It introduces a family of three dualities preserving the acoustic horizon in non-canonical scalar field cosmologies and explores their implications.

Findings

Identifies three classes of dual models: DBI inflation, cyclic contraction, and stalled cosmology.

Finds cyclic contraction and stalled cosmology predict blue spectra inconsistent with observations.

Constructs dual slow-roll analogs and solves for curvature perturbations in all models.

Abstract

We generalize the cosmological duality between inflation and cyclic contraction under the interchange $a \leftrightarrow H$ to the case of non-canonical scalar field theories with varying speed of sound. The single duality in the canonical case generalizes to a family of three dualities constructed to leave the cosmological acoustic horizon invariant. We find three classes of models: (I) DBI inflation, (II) the non-canonical generalization of cyclic contraction, and (III) a new cosmological solution with rapidly decreasing speed of sound and relatively slowly growing scale factor, which we dub {\it stalled} cosmology. We construct dual analogs to the inflationary slow roll approximation, and solve for the curvature perturbation in all three cases. Both cyclic contraction and stalled cosmology predict a strongly blue spectrum for the curvature perturbations inconsistent with observations.