Poincare–Einstein approach to Penrose’s conformal cyclic cosmology * *Dedicated to C Robin Graham for the occasion of his 65th birthday.

Abstract

We consider two consecutive eons in Penrose’s conformal cyclic cosmology and study how the matter content of the past eon determines the matter content of the present eon by means of the reciprocity hypothesis of Roger Penrose. We assume that the only matter content in the final stages of the past eon is a spherical wave described by Einstein’s equations with a pure radiation energy momentum tensor and with a cosmological constant. Using the Poincare-Einstein type of expansion to determine the metric in the past eon, applying the reciprocity hypothesis to get the metric in the present eon, and using the Einstein equations in the present eon to interpret its matter content, we show that the single spherical wave from the previous eon in the new eon splits into three portions of radiation: the two spherical waves, one which is a damped continuation from the previous eon, the other is focusing in the new eon as it encountered a mirror at the Big Bang surface, and in addition a lump of scattered radiation described by the statistical physics.