Cosmological Perturbations in Non-Commutative Inflation

TL;DR

This paper explores a non-commutative space-time inflation model driven by radiation, revealing a nearly scale-invariant fluctuation spectrum with a slight red tilt, differing from standard scalar field inflation.

Contribution

It introduces a novel inflation scenario based on non-commutative geometry with thermal initial conditions, contrasting with traditional quantum vacuum models.

Findings

Spectrum is nearly scale-invariant with a slight red tilt.

Amplitude of fluctuations can be tuned to match observations.

Distinct tilt and amplitude characteristics from standard inflation models.

Abstract

We compute the spectrum of cosmological perturbations in a scenario in which inflation is driven by radiation in a non-commutative space-time. In this scenario, the non-commutativity of space and time leads to a modified dispersion relation for radiation with two branches, which allows for inflation. The initial conditions for the cosmological fluctuations are thermal. This is to be contrasted with the situation in models of inflation in which the accelerated expansion of space is driven by the potential energy of a scalar field, and in which the fluctuations are of quantum vacuum type. We find that, in the limit that the expansion of space is almost exponential, the spectrum of fluctuations is scale-invariant with a slight red tilt. The magnitude of the tilt is different from what is obtained in a usual inflationary model with the same expansion rate during the period of inflation. The amplitude also differs, and can easily be adjusted to agree with observations.