The event horizon of a black hole is comparable somewhat to the event horizon of the known universe. The big bang apparently started from a single point which is comparable to a singularity. Imperfections in cosmic background radiation could be comparable to the imperfect distribution of matter entering a black hole. However this is not enough evidence.

http://en.wikipedia.org/wiki/Cosmological_horizon

For this theory to make sense you would need to make the outlandish speculation that time is going backwards in a black hole such that from the perspective of someone inside the black hole it is expanding from a singularity rather than going towards the singularity. There are various problems with this.

1: Light simply doesn't escape the black hole, nothing exceeds the speed of light and starts going backwards in time.

2: Once light or matter reaches the event horizon it is traveling in a straight line towards the singularity, I hear. It would be an eventless universe.

3: Matter entering a black hole never reaches the singularity. In our universe apparently the big bang occurred at a finite point in time about 15 billion years ago.

4: Hawking radiation means black holes eventually evaporate. From our perspective matter entering a black hole would approach but never reach the event horizon before the black hole evaporates.