newtonian cosmologies
total energy > 0
(equivalent to k in Zeilik 25-1)
total energy = 0
total energy < 0
galaxies can recede to infinite distance;
universe expands forever
galaxies can recede to infinite distance,
but just barely;
universe expands forever
galaxies
cannot
recede to infinite distance; instead the universe reaches some maximum size, and then contracts
open
open (but also called "flat")
closed
r <
r
crit
r
=
r
crit
= 3H
2
/(8
p
G)
r
>
r
crit
1/H > t > 2/3 1/H
age = t = 2/3 1/H
t < 2/3 1/H
hyperbolic geometry
euclidean (plane) geometry
spherical geometry