![[Graphics:DzDangleSummarygr32.gif]](DzDangleSummarygr32.gif)
-only Universe-only UniverseIn this case ![[Graphics:DzDangleSummarygr33.gif]](DzDangleSummarygr33.gif)
so
![[Graphics:DzDangleSummarygr34.gif]](DzDangleSummarygr34.gif)
which is real if ![[Graphics:DzDangleSummarygr35.gif]](DzDangleSummarygr35.gif)
. If ![[Graphics:DzDangleSummarygr36.gif]](DzDangleSummarygr36.gif)
then the universe is contracting at early times, reaches a minimum size, and starts to re-expand again. The redshift at turnaround, ![[Graphics:DzDangleSummarygr37.gif]](DzDangleSummarygr37.gif)
, is the maximum value of the redshift, larger values are not physically meaningful.