spatially closed, bouncing universe
Below is a plot of the time evolution of the cosmic scale factor. The filled dot represents where we are on this plot at the present time. This universe never had a big bang, it collapsed from infinity before bouncing at a redshift of .6.
Bouncing universes are essentially infinitely old. We can ask, however, how much time has past since the "bounce". This depends on the value of 
that we measure observationally. ( is believed to be 70
10 km/s/Mpc, but its value is widely debated.)
