Possible resolution of a spacetime singularity with field transformations

TL;DR

This paper demonstrates that certain spacetime curvature singularities can be resolved through metric and matter field transformations, allowing classical extension beyond the singularity in specific inflationary models.

Contribution

It introduces a novel method of resolving initial cosmic singularities by applying metric and matter field transformations, extending spacetime beyond the singularity without quantum gravity.

Findings

Transformation to flat geometry removes the curvature singularity.

Matter field singularities can be eliminated through redefinition.

Spacetime can be extended beyond the original singularity.

Abstract

It is widely believed that classical gravity breaks down and quantum gravity is needed to deal with a singularity. We show that there is a class of spacetime curvature singularities which can be resolved with metric and matter field transformations. As an example, we consider an anisotropic power-law inflation model with scalar and gauge fields in which a space-like curvature singularity exists at the beginning of time. First, we provide a transformation of the metric to the flat geometry, i.e. the Minkowski metric. The transformation removes the curvature singularity located at the origin of the time. An essential difference from previous work in the literature is that the origin of time is not sent to past infinity by the transformation but it remains at a finite time in the past. Thus the geometry becomes extendible beyond the singularity. In general, matter fields are still singular in their original form after such a metric transformation. However, we explicitly show that there is a case in which the singular behavior of the matter fields can be completely removed by a re-definition of matter fields. Thus, for the first time, we have resolved a class of initial cosmic singularities and successfully extended the spacetime beyond the singularity in the framework of classical gravity.