Double Time is researched at a level 2 Foundry . It increases movement rate for troops travelling more than 500 tiles. As this technology stacks, it is very useful for attacking and defending far away cities. Combined with Rush Attack and Rush Defense, it makes attacking or defending relatively distant players more viable, especially with Cavalry or Knights, the fastest units in the game.
It has a long research time and becomes expensive at higher levels.
See Database entry for details.