[QUOTE=vicky_molokh;2074982]
Things that worry me:[list]
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[*]The rate of building up colonies. Making multiple self-sustaining colonies (not outposts) with a population ranging from at least a few millions to a billion seems like something that's hard to pull off in 200ish years. It means either focusing more on non-operatic technologies such as creation of rapid-breeding transhumans, or moving lots of people around.
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Well you can't reasonably grow a colony to billions in 200 years ago. And even in space opera, you don't. Star Trek started founding human interstellar colonies abooout...now, and none of them have a population of billions except by virtue of having already been inhabited when humans arrived. Even the really nice planets clock in at no more than under ten million. Which is actually enough. You have a single decent sized city surrounded by some small towns. Science fiction frequently treats planets as single biomes which is of course wrong, but it can look like that when the planet is mostly still uninhabited and you're only visiting the occupied part of it.
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[*]Assuming the colonies will be founded by rather modest populations compared to that of the homeworld, just how fast can they grow, assuming that a new planet both has a biochemically compatible ecosystem (this isn't hard-sci!) and reasonable resource value?
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Assume a perfectly habitable planet (Habitability 6) that does not have any notable resources (RVM 0), that was colonized 200 years. The minimum population (barring catastrophe) using standard assumptions of growth would be 400,000. But the typical population value would 3 million. That fits into the default model of a single modern port city surrounded by a few small somewhat frontiery towns. Give it RVM +1 and roll a 14 and you get as high as 15 million. Having a culture that emphasizes population growth could increase that somewhat maybe as much as three times.
Going further than that, and you can always use the Darkover cheat...which is to say that malfunctions of the early buggy hyperdrives could send colony ships back in time, creating lost colonies that likely regressed in technology at least for a time but have populations that hit the carrying capacity limits of whatever their tech level was by the time they were discovered by the Imperium.