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Instead of an expanding balloon, just use a flat piece of paper as your model of space-time (after dimensional reduction): Due to conformal flatness of the FLRW metric, it's possible to represent the Hubble flow as vertical lines, the spatial surfaces at constant cosmological time as horizontal lines and light rays as straight lines angled at 45°. The geodesics for massive particles not following the Hubble flow however would be more complicated, but are of no particular interest. The big bang happens at the lower edge of the paper, the upper edge represents t=inf. The observable universe is bounded by two light rays that meet at infinity. In our toy model with 1 spatial dimension, if an observer follows the Hubble flow along a vertical line, the number of observable galaxies will be proportional to the width of the intersection of the cone formed by light rays and the horizontal line representing space at the time when galaxies first formed. As ASCII, it looks like this: conformal time
^
| "us"
t=inf +------------x------------+
| /|\ |
| / | \ <------------ cosmic event horizon
| / | \ | (bounds observable universe)
| / | \ |
t=now +-------/----x----\-------+
| / /|\ \ |
| / / | \ <------------ light emitted by farthest
| / / | \ \ | visible galaxy as it formed
| / / | \ \ |
+--x----x----|----x----x--+ <---- time of galaxy formation
| /: : | : :\ |
|/ : : | : : \|
t=0 +--:----:----+----:----:--+---> comoving distance
: : : :
: |<------->| <--- currently visible galaxies
: :
|<----------------->| <--- asymptotically visible galaxies
Galaxies that are visible right now will continue to be visible forever in theory, but may become undetectable in practice due to increasing redshift. They will also not be seen to cross any 'edge of the universe', but instead appear to become fainter, redder and frozen in time.As time goes by, we will continue to observe new galaxies being formed, which increases the total number of theoretically visible galaxies. In practice, redshift may again prevent us from doing so in practice. |