Non-Commutative Inflation

TL;DR

This paper proposes a model where space-time quantization causes inflation driven by radiation pressure, eliminating the need for an inflaton field and naturally transitioning to a standard Big Bang universe.

Contribution

It introduces a non-commutative space-time framework that induces inflation through modified dispersion relations without an inflaton, providing a new mechanism for early universe expansion.

Findings

Inflation arises from negative radiation pressure due to maximal momentum dispersion relations.

The model naturally exits inflation as the universe cools below the Planck temperature.

Predicted curvature fluctuations can match observational data.

Abstract

We show how a radiation dominated universe subject to space-time quantization may give rise to inflation as the radiation temperature exceeds the Planck temperature. We consider dispersion relations with a maximal momentum (i.e. a mimimum Compton wavelength, or quantum of space), noting that some of these lead to a trans-Planckian branch where energy increases with decreasing momenta. This feature translates into negative radiation pressure and, in well-defined circumstances, into an inflationary equation of state. We thus realize the inflationary scenario without the aid of an inflaton field. As the radiation cools down below the Planck temperature, inflation gracefully exits into a standard Big Bang universe, dispensing with a period of reheating. Thermal fluctuations in the radiation bath will in this case generate curvature fluctuations on cosmological scales whose amplitude and spectrum can be tuned to agree with observations.