These are more pessimistic predictions, of course, but the more optimistic ones are based on the observable trend that higher standards of living correlate with lower birth rates.
Some back of the napkin math:
- India population = 1,324,171,354 [0]
- India growth rate = 1.19% [0]
- India CO2 metric tons per capita = 1.58 [1]
Assuming each additional person has the same per capita carbon footprint:
1,324,171,354 * 1.0119 * 1.58 = 2,117,087,809 additional tons CO2/year
Compare to the United States:
- US population = 328,863,150 [2]
- US growth rate = 0.62% [2]
- US CO2 metric tons per capita = 15.53 [1]
328,863,150 * 1.0062 * 15.53 = 5,138,909,636 additional tons CO2/year
So even though the US has 1/4 the population and a lower growth rate, the growth of carbon footprint is 2.5 times higher. These numbers are obviously very inexact, but the point is that if you believe that the current rate of CO2 output is unsustainable (and this is hard to dispute), then even if the world population levels off, this is likely due to increased prosperity. And increased prosperity means more consumption per capita and more consumption means more carbon footprint (and other environmental damage).
[0] https://en.wikipedia.org/wiki/Demographics_of_India
[1] https://www.ucsusa.org/global-warming/science-and-impacts/sc...
[2] https://en.wikipedia.org/wiki/Demography_of_the_United_State...
E.g. providing energy to villages that currently don't have any so they can turn on the light at night (education) and pump clean water (health), actually helps achieve this.
(If the scale disappears on mobile, it's 1960 - 2015)