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The world I'm creating will be referred to as E.

Current E population is growing exponentially, and the population will become completely unsustainable soon.

Global Warming is also increasing exponentially, and every person has been increasing carbon emissions, pollution, etc. over time, just like in real life. Of course, the increasing population makes this worse.

To what degree would birthrates and birth-death ratios have to drop to actually start to decrease the population of E? How would that affect socioeconomics and climate change?

Of course, there's an easy way to drop the population a lot. Namely, killing a lot of people really fast. What kind of event could kill enough people to stabilise/reverse climate change? The event needs to have the sole (or at least sole significant) consequence of massive loss of human life without complete extinction of the human race; no volcanic eruptions causing permanent cloud cover or nuclear winters.

E is not our Earth; it's similar to our Earth, except for what I've laid out. And politically and economically, it could be whatever I say it is.

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    $\begingroup$ The human population is not growing exponentially at all. Population growth is levelling off quickly, and it’s likely to be falling by the second half of this century. $\endgroup$ – Mike Scott Mar 10 at 5:53
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    $\begingroup$ @MikeScott On my Earth, you're wrong. $\endgroup$ – user45266 Mar 10 at 6:01
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    $\begingroup$ "To what degree would birthrates and birth-death ratios have to drop to actually start to decrease the population of the Earth?": Most countries have negative natural population growth already, and human population is not expected to continue growing at all in the second half of the century. Moreover, your political education is out of date; we no longer call it Global Warming: it is Anthropogenic Climate Change nowadays, a nice name which has the advantage that is can be applied irrespective of whether climate does indeed warm up or not. $\endgroup$ – AlexP Mar 10 at 6:04
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    $\begingroup$ @AlexP Again, on my Earth, you're wrong. I've defined that on this planet, natural birthrates are actually increasing for whatever reason. Also, are you being serious about the political education comment? I'm curious. And finally, it's similar to our Earth, except for what I've laid out. And politically and economically, it could be whatever I say it is. $\endgroup$ – user45266 Mar 10 at 6:10
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    $\begingroup$ It seems like you've given yourself free regin to change a few things about how things work on your planet that diverge from those we see on earth. Socioeconomic factors as we understand them lead to lower birthrates as people get wealthier and so on...you've changed how these work on your world. Unless you tell us what you've replaced it with only you can answer your questions about the effect on the economy. $\endgroup$ – Lio Elbammalf Mar 10 at 8:11
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There are a couple of extinction events that might fill the bill.

(1) Global pandemic. The human population becomes infected with novel viruses and/or bacteria with exceptionally high rates of lethality. The diseases will need to have exceptionally rates of infection.

(2) Starvation. Recent studies have indicated massive die-offs of insect populations. If the insects responsible for pollination like bees, butterflies and mosquitoes also die off there will follow massive die-offs of plant species including crop and vegetable species.

With massive crop failures comes massive starvation.

(3) Global warming itself. While there will be minor die-offs of population due to violent weather events. Storms, floods, tornadoes, and typhoons/ hurricanes/ cyclones, these won't be enough by themselves.

So let's global warming really goes for broke and climatic changes includes searingly hot summers and deeply cold winters far beyond the expectations on our world. But these would be plausible in the OP's exponential population expansion world. Heat and cold stress is a massive killer of people. If heat and cold stress was turned up to eleven expect high rates of mortality.

(4) All of the above running in concert.

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    $\begingroup$ "turned up to eleven" degrees per year? $\endgroup$ – John Dvorak Mar 10 at 8:52
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    $\begingroup$ @JohnDvorak: I Believe it’s a reference to Spinal Tap, who were frustrated their amplifiers only went up to ‘10’. The solution, of course, was to make one that could be dialled up to ‘11’. It’s an idiom for going over the top or beyond the expected maximum. $\endgroup$ – Joe Bloggs Mar 10 at 10:13
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    $\begingroup$ @JohnDvorak Joe Bloggs is correct. It's the idiomatic expression for going over the top, really over the top. Think of it as Global Warming in extremis. $\endgroup$ – a4android Mar 11 at 1:24
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I do not believe a mass extinction event could reverse the effects of climate change, killing many humans and destroying machinery would slow it but not reverse it.

Also, natural reversal of climate change might take far too long in your world, long enough that humans may have died out as a species.

However, you did mention the stabalisation of climate change. If you wanted a natural event to wipe out a large portion of the human population, you have several options. Im going to rule out volcanic activity as that would add sulphur and carbon into the atmosphere, adding to climate change. So then the next most plaussible options are earthquakes and tsunamis. If an extremely large earthquake ripped accross a major industrial country, it would destroy machinery and slow down climate change due to factories being destroyed. A similar thing would happen with tsunamis, causing major loss off life and damage to factories.

Although, if your world is sufficently advanced, a major solar flare could be devastating. If your factories, industries and power plants are automated by robots or use highly technical machinery, a solar flare would majorly disrupt and damage electronics, halting all of the world’s automated machinery. This would also reduce the growth of climate change as now no harmful fumes are being pumped into the atmosphere. If your cars and public transport were also automated to some degree, they would also be majorly affected and may cease functioning, further reducing the fumes going into our air. As an aside, this might produce a beautiful aurora borealis across the world.

Many humans would be killed indirectly as a result of the solar flare, planes would fall out of the sky, ships may run aground, trucks and cars may lose control and cause crashes, powerplants and factories may go critical and explode, hospital equipment may cease functioning just to name a handful. I would not be able to give you an estimate of the loss of life but, suffice to say, it would be significant on the global scale.

In terms of the socioeconomics of your world, they may be completely decimated by the flare, preventing all trade and communications. All forms of transportation would no longer work and goods could not be transferred exept by foot or transport that has no electronics.

In conclusion, a solar flare against a sufficiently advanced society, not too far from earth’s own technology, would be devastating for any electronics. Automated factories and powerplants could immediately halt production and irreparable damage may be caused. Cars and trasnportation may also cease functioning and further reduce emmissions into the atmosphere. The effects of the solar flare may revert humans to a pre-industrial state and allow for the stabalisation of climate change.

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The best extinction event to solve Global Warming on an Earth-like planet... is another naturally occurring ice age. Reasoning:

  • Ice Age so far were extinctions events and human population seems to be clearly reduced during them, "surprisingly" civilisations appeared in rare interglacial period;
  • moreover we no longer have to wonder whether reduced population would really reduce their emission accordingly or with changing technological level those issues are barely related (horse power -> coal -> oil -> nuclear).

The issue is governed by Milankovitch cycles which are cyclical fluctuation of Earth orbit shape and axial tilt.

Actually, when think about it, it would actually make a good story. Instead of cliche moral parable, in which human actions lead to some kind of divine punishment / karma, you can offer a much more realistic plot twist - natural environment behaves more in style of cosmic horror story.

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