Attractor Solutions in Tachyacoustic Cosmology

TL;DR

This paper investigates the stability of tachyacoustic cosmological models, showing that certain non-canonical Lagrangian solutions act as dynamical attractors, offering a potential alternative to inflation.

Contribution

It provides the first phase-space analysis of tachyacoustic models with specific Lagrangians, demonstrating their dynamical stability as attractors.

Findings

Power-law solutions are dynamical attractors in both models.

Tachyacoustic models can generate scale-invariant spectra.

Models remain stable during decelerating expansion.

Abstract

We study the dynamical stability of "tachyacoustic" cosmological models, in which primordial perturbations are generated by a shrinking sound horizon during a period of decelerating expansion. Such models represent a potential alternative to inflationary cosmology, but the phase-space behavior of tachyacoustic solutions has not previously been investigated. We numerically evaluate the dynamics of two non-canonical Lagrangians, a cuscuton-like Lagrangian and a Dirac-Born-Infeld Lagrangian, which generate a scale-invariant spectrum of perturbations. We show that the power-law background solutions in both cases are dynamical attractors.