Well I don't think demographic transition is completely influenced by the richness of the country, Israel is an example so I think that if you keep 2-2.5 rates you can maybe have a billion people in Europe(think about Imperial Russia without wwars and cwars).
Well maybe a couple billions more but not 7.5 more.
Technically the Indian subcontinent and China do have more than 3 billion people. I think people mean with India in this case the subcontinent.
A lot of Israel's growth is driven by fundamentalist nutjobs. I've seen that as an explanation for why the US has such a high fertility rate as well. I'm not sure how much they correlate. I think that such an environment might still hinder technology thanks to the lack of women in science (even as contributing members to male-led scientific teams), thus ignoring half the human race's potential. Although admittedly not as much as keeping everyone poor might.
Imperial Russia was bound to end in either disaster or intense reform which either way would have slowed the population growth as it did OTL. In any case, development would have naturally slowed population growth thanks to demographic transition.
Most experts in this field are saying that somewhere around 11 bn is the best we can conceivably achieve. That takes into account technologies that don't really exist yet, including growing plants in solution rather than dirt. With that, 11bn is guessed for sometime in the mid 22nd century.
So can science be accelerated by a century and a half? I'm doubtful about this. If we pushed the POD back to a time before there was rapid science advancement (so pre 1300), and said "in this ATL there is now rapid science advancement rather than everyone being more devoted to God than logic" (referring to stuff like murdering cats and using leaches to get rid of 'bad blood') then maybe.
Post 1500 you had pretty good technological advancement as it was. I don't think this can be pushed quite as far as we would like.
- BNC
The 10 billion estimate is based on stagnating fertility rates (including in undeveloped nations) and possible ecological damage (thanks to global warming and other such issues). It's more than doable based on the number of food, and even logistically, it's more than doable, assuming everyone wants to live like a developing world peasant ruled by an elite class. For the OP's sake, this would incidentally stagnate technology.
Besides, more desalination, plus seawater greenhouses mean we can be growing all sorts of vegetables in the Sahara, Australian Outback, etc. With skill marketing/research/agronomy, we can domesticate tons of unusual plants to use as vegetables and sell them to the public (an American bushfood market comparable to the Australian bushfood market might as well be the tip of the iceberg!). This means we can be growing more staple crops using land we currently use to grow vegetables.
Really, everything is based on getting the food (and water) to people instead of any agricultural limitations. So many famines in the past 200 years (and probably beyond) could have been solved with getting the food to the people, since the food was there, just for reasons it couldn't reach who it needed to. For instance, in the 1930s people starved in the US and beyond (the Soviet Union most infamously) while grain was rotting in silos throughout the Great Plains unable to be sold/brought to market for various reasons. The myth of "peak food" needs to die (we live in a world where obesity is now a disease of poverty in many places, that should say it all). There's many reasons why we can't/shouldn't exceed that many people. But we
can. And the other essential need, peak water, is solvable through desalination. To construct the desalination, you will need more power...which incidentally we've been able to do since the mid-20th century with more nuclear engineering (not even getting into solar energy and such). All humans need is food (with enough nutrients to not fatally malnourish you) and water. It doesn't matter how bad your life is, until something kills you, you'll persist. That's an utterly horrible way to live, but food and water is all people need in the end.
Yeah but having to make such a massive distribution network it will be more vulnerable.
These things seem to be subject to some sort of a law similar to the square-cube law: The larger and more complex a society is, the higher the chance it will get absolutely destroyed. With about 15 billion people you're guaranteed to get some sort of happening to send everyone back to the stone age.
But i realize OP said human population without stating which planet, it could be more plausible to somehow boost human technology and annex various planets (i used annex extremely deliberately)
No, if everything broke down, you see billions (let's say 14-14.5 billion) starve/kill each other for food, but not Stone Age. I don't even think humanity is capable of sending everyone to the Stone Age, only a supervolcano/asteroid/comet is by virtue of there being only a few thousand people left alive. You'd leave a few hundred million to a billion left alive, and that's comfortably capable of rebuilding society.
Most ideally, more land in space is the way to do this thing. Maybe we build space colonies ("free" land), then with artificial wombs and incentives for "childbearing" (if you want a kid, you get benefits), we're able to raise fertility back to replacement levels minimum. And we do all this in the mid-20th century at latest. So 10 billion on Earth, 4-5 billion in space. With a 1500 POD, that isn't too impossible. But as for Earth, that's more difficult.