The Catastrophe Theory is an opinion held by some Agents of the PPC that HQ is headed for imminent destruction. By looking at the increasing frequency of PPC Emergencies, they have concluded that The End Is Nigh. They even have a graph to demonstrate that fact.
No one is quite sure what to make of this, and after the moratorium on Emergencies, several years have passed without the dreaded Catastrophe occurring. As it stands, the current status and popularity of the Catastrophe Theory within the PPC are unknown, but knowing how askew one's perception of reality can become in HQ, there's probably still someone who is convinced of its validity.
Catastrophe Theory is not particularly related to Cycle Theory, although many of the same people believe in both, and some say that the latter may be a cause of the former.