I wish I could find the source, but when I've looked into this in the past I was reasonably convinced that the population would go up a bit, but not catastrophi

I wish I could find the source, but when I've looked into this in the past I was reasonably convinced that the population would go up a bit, but not catastrophically, with the basic idea being that people die all the time for lots of reasons, only one of which is "aging" (aging is multiple things, blah blah). So people's lifespans would be much longer on average, but not infinitely long. Something more like 300 or 400 years, with a pretty big standard deviation.