Known universe

According to Borusa, a President of Gallifrey would wield more power than anyone in the known universe upon their being introduced to the Matrix. (TV: The Invasion of Time)

The First Doctor referred to his TARDIS as "the most powerful space-time machine in the known universe". (TV: Twice Upon a Time) The Fifth Doctor observed that Terminus was at the exact centre of the known universe. (TV: Terminus) The Eleventh Doctor promoted the Church of the Papal Mainframe as the security hub of the known universe. (TV: The Time of the Doctor)

The Twelfth Doctor claimed that his TARDIS should have been able to detect anything in the known universe. This led him to determine that the Boneless were from another universe. (TV: Flatline) Quantifer was located on the edge of the known universe. (TV: Resolution) A version of the Ninth Doctor calculated that he had saved every planet in the known universe a minimum number of 27 times. (TV: The Curse of Fatal Death)

The Fourth Doctor claimed that the Louvre was the only gallery in the known universe with a picture like the Mona Lisa. (TV: City of Death)

History
A Red Dalek that led the Thaleks declared, upon remembering of the true nature of the Daleks, they would spread "the doctrine" of extermination "across the known universe" once they managed to reunite "with [their] brothers on Skaro". However, upon saying the word "exterminate," the Thalek city was set to self-destruct, destroying the Red Dalek and its subordinates. (AUDIO: Brotherhood of the Daleks)

The known universe was a front of the Last Great Time War between the Daleks and Time Lords. The campaign waged by the Doctor of War was said to be the bloodiest campaign waged in its history, as well as being the bloodiest crusade in the history of the unknown universe and partly known universe. (PROSE: The Day of the Doctor)