Physical Foundations of Cosmology

2.3 Conformal diagrams 45

η

π χ

events horizon

π − θ

φ + π

π

image 1

image 2

observer

particle horizon

θ, φ=const

χg

Fig. 2.2.

universe, the particle horizon exists only during the expansion phase, and the event
horizon exists only during the contraction phase.
The pointsχ= 0 ,πare the opposite poles of the three-dimensional sphere
describing the spatial geometry at any given moment of time. Light propagating
with constantθ,φaway from an observer located atχ=0 reaches the opposite
pole atχ=π.Because the coordinate system we are using is singular at the poles,