The Divergent Universe was a pocket universe that had no concept of time. It was home to the Divergence and other species. Rassilon kept it, among other pocket universes, inside his dungeon on Gallifrey. He considered it the most "significant" of the universes he held. (AUDIO: Zagreus)
Rassilon found the Divergence inhabiting our universe, and deduced they would eventually surpass the Time Lords in power. To prevent this, he used his new control over Time and Space to seal them away in their own reality. To keep them imprisoned to the End of Time, Rassilon installed a mobius loop which took all life out of that universe once every twenty to thirty millennia before regurgitating the universe in its original form. A side effect of this was the lack of Time as a linear concept within the universe — cause and effect ultimately had no meaning because no matter what happened things would always return to how they had started.
Rassilon used the force of anti-time to craft a weapon capable of forever destroying the Divergence. He infected the Eighth Doctor with it, creating the Zagreus persona. However Rassilon's attempts to direct Zagreus failed and Zagreus hurled Rassilon into the Divergent Universe to directly confront his enemies. (AUDIO: Zagreus)
Soon after, the Doctor exiled himself to the same universe to control his Zagreus persona. Rassilon extracted Zagreus from the Doctor, and then used both personas to break the cycle of destruction and recreation. (AUDIO: The Next Life)
Time in this universe flowed in a similar way to how it flowed in N-Space, from one moment to the next, but travel back and forth across the time stream was not possible, as the looping nature of time in this reality meant that there were no definitive temporal coordinates as every moment had happened before. The inhabitants also had no understanding of the concept of time. (AUDIO: The Creed of the Kromon)
One special planet, Bortresoye, was crafted by the Divergence as a "crucible world" for evolutionary experiments. Portions of many worlds were placed on it, accessed via interzone portals. This world followed similar cycles as that of its universe, but at a vastly accelerated rate. (AUDIO: The Last)
At the end of each cycle in the universe, a small blue planet would make its way through the nine galaxies, exterminating all life as it passed, per Rassilon's design. The Church of the Foundation worked in concert with it, preaching the doctrine "All things must die." The universe could only end and reset once all life was extinguished. (AUDIO: The Next Life)
Behind the scenes
The story arc
The term Divergent Universe also describes the story arc for the Eighth Doctor in audio.
Broadly speaking its narrative begins in Storm Warning, the first Eighth Doctor audio story. This sets up the Doctor's transgression of the Laws of Time, which unleashes the anti-time he absorbs in Neverland.
The Time of the Daleks is also a narrative precursor; it establishes that the Daleks get caught inside the time vortex — an important point of both Neverland, which acts as the prologue for the arc, and Terror Firma, which acts as an epilogue.
A strict definition of the arc, however, has it begin with the closing moments of Zagreus, as the Doctor and Charley exile themselves to the Divergent Universe, and continues through to the closing scene of The Next Life, when they return to the main universe.
Unmade third season
The Eighth Doctor's time in the "divergent universe" was originally planned to go on longer than the eight audio stories produced. However, due to the series returning to television in 2005, it was decided to end the arc early as so not to alienate any new listeners that Big Finish Productions might acquire as a result of the TV revival (the Eighth Doctor's audios also were made increasingly similar in style to the revived series).
Several of the Eighth Doctor audio plays released after The Next Life, the last story set in the "divergent universe", were rewritten to take their new setting into account. However, some of these stories still feature remnants of ideas that seem more suited to the "divergent universe" arc, for example, the experiments and sealed off worlds as featured in Scaredy Cat.
In an interview with fanzine The Finished Product, producer Gary Russell revealed that a third season of stories set within the divergent universe was planned and would likely have comprised of:
A fourth and final season in the divergent universe was also planned that would have concluded with The Next Life.