The world is discrete

TL;DR

This paper proposes that the scale-free spectrum observed in the cosmic microwave background results from a phase transition in the early universe, suggesting a fundamental small length scale and replacing inflation as the explanation.

Contribution

It introduces a phase transition model to explain the cosmic microwave background spectrum, linking the tilt to an anomalous scaling dimension and implying a fundamental length scale.

Findings

The tilt of 0.04 matches the anomalous scaling dimension.

A phase transition can produce the observed spectrum without inflation.

Indicates existence of a fundamental small length scale in nature.

Abstract

We argue that the scale-free spectrum that is observed in the cosmic microwave background is the result of a phase transition in the early universe. The observed tilt of the spectrum, which has been measured to be 0.04, is shown to be equal to the anomalous scaling dimension of the correlation function. The phase transition replaces inflation as the mechanism that produces this spectrum. The tilt further indicates that there is a fundamental small length scale in nature that we have not yet observed in any other way.