There is no such mod. At least, not as far as I know. Your only options are to either increase the research speed in the game, or write the mod yourself.

Writing the mod isn't hard. It just takes a bit of preparation.

You need the TechTree.xml and the racial-specific tech trees. You can find the former under Galactic Civilizations II\Twilight\Data\English, and the latter in the TechTrees sub-folder of the same location.
Editing the files there, however, is not advised, because, if you make an error, you can screw up the game. For this reason, you should make copies of those files and place them into a mod-folder. You can find a Default one under Galactic Civilizations II\Mods. Make a copy of it, and rename it to something else, like Easier War. Then place a copy of the TechTree.xml into the Data-folder, and copies of the racial-specific tech trees into the TechTrees-folder. Once that is done, you're set.

You can use any text editor to edit XML-files. So open up the TechTree.xml and search for the techs you want to change. Then, edit their costs to want you find appropriate. Once that is done, move on to the racial tech trees. Some of them include weapons and defense technologies that aren't in the TechTree.xml. Most importantly, however, some of them have different costs, which overwrite the values set in the TechTree.xml.

Once your done editing the files, start up the game and go the options. There, activate the "Use Mods" option, and change the Mod Directory to the one you created. Re-start the game, and you're good to go.