Agricultural Technology
This is my first post on the new website, and a very smart one it is too (website that is).
Population increase: first, the establishment of the Roman Empire did actually lead to a population increase anyway.
This is everywhere attested to by archeologists and scholars.
However if you want to take it to the next level there are a couple of possibilities.
One is that malaria remains in Africa and does not infect the Mediterranean world.
Another is that some Roman doctor discovers the connection between filfth and disease and gets people to accept the need to change their ways.
Heightened standards of cleanliness particularly as regards water supply and sewerage have actually made more of a difference to human life than anti-biotics.
The Romans are of course famous for this sort of thing, but it never extended to the villages and farms where 80% of the population lived.
Another thing that would have caused a population increase would have been the introduction of more productive agriculture such as happened in the sadly misnamed Dark Ages with the 3 field system and the mould-board plough.
The latter meant that the heavy soils of Northern Europe could be cultivated efficently, which the Romans never achieved.
The second meant that two thirds instead of half one's fields could be productive at any one time.
This sounds like small potatoes now but at the time it was a veritable revolution: it was the first major improvement in agriculture since it had been invented thousands of years before.
It gave Europe the economic strength not merely to survive the Dark Ages but ultimately to do wierd things like establish a new civilisation, settle America and conquer the world.
The widespread adoption of water-mills, another Dark Age innovation, would have been a great boost too.