The UN assumption that population will peak absolutley by 2050. Then with the fertility rates at negative today, they assume it will correct itself immediately to replacement rates?

I disagree with that assumption.

I see a repeat of the Roman empire's 200 year decline of absolute population. Contraception and overpopulation concepts are hard wired into many people's brains. Many will voluntarily eliminate their bloodlines. When the contraceptive peoples are all but wiped out, the pronatal people will be left to replenish the earth.