Evolution of Gravitational Perturbations in Non-Commutative Inflation

TL;DR

This paper investigates how linear cosmological perturbations evolve during non-commutative inflation, highlighting conditions for constant curvature perturbations and the potential for parametric amplification due to oscillating matter fields.

Contribution

It analyzes the evolution of perturbations in non-commutative inflation, revealing conditions for their constancy and demonstrating parametric amplification caused by oscillating matter fields.

Findings

Curvature perturbations remain constant on super-Hubble scales with a single non-commutative radiation fluid.

Oscillating matter fields can lead to parametric amplification of curvature perturbations.

Numerical solutions confirm resonance driven by entropy mode oscillations.

Abstract

We consider the non-commutative inflation model of [3] in which it is the unconventional dispersion relation for regular radiation which drives the accelerated expansion of space. In this model, we study the evolution of linear cosmological perturbations through the transition between the phase of accelerated expansion and the regular radiation-dominated phase of Standard Cosmology, the transition which is analogous to the reheating period in scalar field-driven models of inflation. If matter consists of only a single non-commutative radiation fluid, then the curvature perturbations are constant on super-Hubble scales. On the other hand, if we include additional matter fields which oscillate during the transition period, e.g. scalar moduli fields, then there can be parametric amplification of the amplitude of the curvature perturbations. We demonstrate this explicitly by numerically solving the full system of perturbation equations in the case where matter consists of both the non-commutative radiation field and a light scalar field which undergoes oscillations. Our model is an example where the parametric resonance of the curvature fluctuations is driven by the oscillations not of the inflaton field, but of the entropy mode