There are two different effects at play here. On the one hand, there will be a dark age because all the stars will burn out. This has nothing to do with the cos

There are two different effects at play here. On the one hand, there will be a dark age because all the stars will burn out. This has nothing to do with the cosmological event horizon. The cosmological event horizon is caused by the accelerating expansion of the universe. Space is expanding uniformly, so the more space there is between us and some object, the faster it is moving away from us. Objects that are farther than the Hubble Distance from us are receding faster than the speed of light, and so their light will never reach us. Over time, everything that isn't gravitationally bound to us will recede into the distance, redshift and disappear, leaving only our galaxy within the observable universe.