@Tomice
Taking your your neighbors cities comes at a cost (you have to build a larger army to attack than you need to defend, and the city you end up with is either a puppet or annex).
And getting more cities is not necessarily always better.
The pros and cons with expanding for science for instance. Expanding causes your population to grow faster, which will increase your base science, up until you reach the happiness cap.
Staying small causes your population to grow more slowly, but it will keep growing in cities that are already developed with libraries and universities, and you will be getting more use out of National College.
Happiness is really a great mechanic, as expanding to quickly grow your population comes at a cost (less total population in the long run, and less efficient use of that population).
Anyway, you said that you would like all victory types to be possible with empires large and small. Since that's exactly what I'm trying to do with culture, my mod is apparently fulfilling the purpose you are describing. This mod is not intended to modify science and diplo victories, so I don't really need feedback on those just yet.
@BjoernLars
The current rate is pretty similar to what you describe, but I don't really want the increase in cost to become so dramatic beyond a certain point (or typical civs will just plan ahead for exactly 18 policies and work to get those). The rate increase more gradually than an exponential, but it starts out slower and ends up faster, as I mentioned.
@QES, jwallstone
I've been saying from the beginning that large empires will not be better at a culture victory than small ones. They will be about equal. Combined with the fact that small empires actually can do fine in science and diplo (seriously, I've won many games on Immortal with 5 or less cities for most of the game), and there's not really a problem.
I just don't like the thought process that leads a player to decide "I want to settle another city but I don't want it to make winning harder, so I'll just stick with these." If a player wants to expand, they should be able to. If they want to stay small, that should be fine too. The current culture system outright discourages expansion. I want it to be somewhat neutral.
Anyway, if you like how the culture costs are calculated now, then you don't really need a mod for it.