Possible resolution of a spacetime singularity with field transformations

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.