Federation universe

The "Federation" universe was a parallel universe where Earth was part of the United Federation of Planets meta-government from the 23rd and 24th centuries onward.

This universe was joined together with the Doctor's universe by a faction of Cybermen so that they could form an alliance with the Borg, a similar cybernetic race native to this universe. The only known people who were aware of the two universes having been merged were the Eleventh Doctor and Guinan.

While the planet Earth and humans existed in both universes, some of the species native to the Federation universe were not known to exist in the Doctor's universe, including the Borg, the Klingons, the Vulcans and the Deltans. Aside from the Federation itself, major powers included the Klingon Empire and the Borg Collective.

Following the Doctor and the crew of the USS Enterprise defeating the intruding Cybermen, the Doctor speculated that all the influences of N-Space had been removed from this reality before he, Amy and Rory returned to N-Space. (COMIC: Assimilation²)

Alternate timeline
In a potential history shown by the Eleventh Doctor to Jean-Luc Picard, the Cybermen, having integrated both the Doctor's N-Space and Picard's parallel universe, successfully conquered the Borg Collective and began a campaign to convert the galaxy.

Throughout the 25th century, the Cybermen converted the Klingons by 2418, the Raxacoricofallapatorians by 2448, the Vulcans by 2468, and the Judoon by 2493. By 2533, the Cybermen had conquered Earth and vanquished San Francisco's Starfleet Academy, the last holdout of free humanity. (COMIC: Assimilation²)

Behind the scenes
This universe is the setting of the Star Trek franchise and appears in relation to Doctor Who only in the Assimilation² crossover comic.