knocking at our doors?
birthrates started decreasing decades ago. they will increase after some time, in a kind of oscillation. endless population increase of course isnt possible.

It's the Malthus effect.  Population in Europe boomed due to cheap energy (clean coal) and the railroad and automobile revolution in 1890s.  There was another boom in the late 1940s due to the Highway Revolution and increasing automobile ownership.

Despite those technologies – we now live in a post-industrial economy where the former manufacturing jobs (many of which were located in small towns in the rurals) no longer exist – therefore everyone is now migrating into the (very expensive) cities in order to create a livelihood for themselves and their families.  There's literally no opportunity to have large families in the cities therefore this is the reason why the fertility rate is below replacement in many countries.

Really if we want more children and for more people to be born then we need to bypass the Malthus Effect.  We need flying cars or it needs to be socially acceptable for every office job to be telecommuted – so people once again have an incentive to leave the cities and live in the countryside (where real estate and cost of living is lower and more tolerating towards large families)