Question about research rates

This is probably a simple question, but I'd appreciate it if somebody enlightened me anyway

Does the number of research points for a certain tech change depending on the size of map you play? For example, imagine that on a tiny map you have to create 100 RP for Laser III, does that mean on a gigantic map you have to pay something like 800 RP, or something? This is all assuming you've not adjusted the 'Research Speed option'

The reason I ask is because on the biggest maps you're generating many more RPs than you would on a small map, because of the number of planets colonised. I'm wondering if I need to adjust the 'Research Speed' options on the bigger maps to keep a similar pace of tech advancement.

Thanks is advance!