The Trans-Planckian problem in Tachyacoustic Cosmology

TL;DR

This paper examines Tachyacoustic cosmology models that generate scale-invariant perturbations through superluminal sound speeds, revealing fundamental bounds and limitations related to the trans-Planckian problem and horizon size.

Contribution

It derives bounds on acoustic horizon size in Tachyacoustic models and demonstrates their inability to resolve the horizon problem without trans-Planckian issues.

Findings

Existing models cannot solve the horizon problem without trans-Planckian violations.

Derived bounds constrain the duration of tachyacoustic evolution.

Physical scales at perturbation freeze-out are necessarily trans-Planckian.

Abstract

We study Tachyacoustic models of cosmology, for which a scale-invariant perturbation spectrum is generated via superluminal sound speed instead of accelerated expansion, as in the case of inflation. We derive two bounds on the size of acoustic horizon which constrain the duration of tachyacoustic evolution, and therefore generation of primordial perturbations. We show that existing models cannot solve the horizon problem without violating the condition that all physical scales -- such as the Hubble parameter, the pressure, and the length scale at which quantum modes freeze out and become classical -- be sub-Planckian.