FRW Universe Models in Conformally Flat Spacetime Coordinates

TL;DR

This paper explores how different conformally flat coordinate systems affect the interpretation of universe models, revealing phenomena like continual creation in certain cosmological scenarios and providing methods for Penrose diagram construction.

Contribution

It derives a general formula for transformations to conformally flat coordinates and interprets their physical meaning across various universe models.

Findings

Continual creation appears in conformal time in negatively curved Friedmann-Robertson-Walker models.

Conformal coordinates reveal quantum fluctuation origins of inflationary eras.

Provides a method for constructing Penrose diagrams in different universe models.

Abstract

The 3-space of a universe model is defined at a certain simultaneity. Hence space depends on which time is used. We find a general formula generating all known transformations to conformally flat spacetime coordinates, and work out the physical interpretation of conformal coordinate systems in different universe models. We show that continual creation appears when conformal time is used in Friedmann-Robertson-Walker models with negative spatial curvature, and in universe models where the inflationary era started as a quantum fluctuation at t > 0, for example at the Planck time. A general procedure is given for finding coordinates to be used in Penrose diagrams.