[geoschmo]

Technology is a force multiplier. The current state of the military is undergoing a shift towards smaller numbers of more highly trained professional soldiers with a lot more investment in weapons and technology. There is some disagreement about the best way to effect this change, but almost noone disagrees that it's coming. And we are just at the start of this trend now. Forecasted hundreds or thousands of years into the future of your sci-fi universes it's not at all unbelievable that the numbers of military forces needed to conquer or protect populations in the many trillions would seem pathetically small by our current standards. Considering that you can sit in orbit and obliterate a population that won't submit, it doesn't seem like it would take all that many boots on the ground anyway.

Of course conquering and controlling are two different things, but populations can be controlled in other less violent ways for the most part. An empire that's growing will understand this. To the average Joe and Jane in the population it doesn't matter if the seat of the governemnt is on your continent, the other side of the world, or the other side of the galaxy. If they aren't too oppressive you can get along ok.

On the other hand the logistics of supporting a military that is a significant portion of overall population would be simply staggering. And considering that all those support personell and vehicles have to be supported as well and you can see that it's quite possible that a point of diminishing returns could be reached where it's just not practical to get a larger military, even as your empire continues expanding.