The Conformal Singularity as a Cosmological Mirror: Classical Theory

Abstract

In Robertson-Walker coordinates the cosmological scale factor asymptotes to an exponential as the evolution becomes dominated by dark energy. The singularity, which in the Robertson-Walker system is characterized by the red-shift of all radiation to nothing, is at infinity therefore. Since the Robertson-Walker time is the proper time of a co-moving observer the Robertson-Walker chart is geodesicallycomplete in the future time direction complete that is from the perspective of matter geodesics. Yet when the metric is expressed in conformal coordinates electromagnetic radiation can be made to appear to be completely insensitive to the scale factor including the singularity, which presents no barrier to its passage therefore. The conformal chart extends beyond the singularity and under reasonable assumptions the conformal Friedmann equation predicts a development of the scale factor that is anti-symmetric about the time of the singularity.