If you can’t spare an hour, please watch Rosling’s TED talk: https://www.ted.com/talks/hans_rosling_shows_the_best_stats_...
Since permanent growth comes from fertility and as "Don't Panic" shows we're getting to a sustainable average of 2 child per woman, augmenting our lifespan will only increase our maximum population, not our population growth.
However I think YC research would be better spent trying to find better ways to fight climate change, world stability and/or lift billions out of poverty. This way if we ever augment lifespans in a significant way it will be available to more people and in a healthier world. Also lifting billions out of great poverty will have the added benefit of allowing more minds to work on issues like increasing life expectancy.