The dinosaurs became extinct 65.5 million years ago, clearing the way for the age of mammals.  But for the first 10 or 12 million years after the dinosaurs were gone, mammals did precious little with the opportunity.  Most of them remained small and non-diverse.  Moreover, the same marsupials and multituberculates which had lived under the feet of the dinosaurs before the extinction came back to rule the planet after the dinosaurs were gone.  Mammals did not change that much after the dinosaurs were gone.  Wolves and wildcats were still a long time in the future.  Instead, the biggest carnivores of those times were silly looking ostrich-type flightless birds that looked more like Sesame Street's Big Bird than any real carnivore.  In essence, the birds were awkwardly evolving back toward being dinosaurs to fill the niche left empty by the dinosaurs.  But for the 10 million years or so during which flightless birds were evolving back toward dinosaurs, they never got much beyond the appearance of a gorilla-sized turkey. 

     One would think that if ever in the history of the planet there was an opportunity for a lineage to undergo a massive degree of adaption and speciation, it would have been the opportunity afforded the mammals and birds immediately after the dinosaurs went extinct, because the competition was eliminated.  But such was not the case.

     The major breakthrough for mammals did not come with the death of the dinosaurs.  Rather, it came about 10 million years later.  About 55 million years ago, "there was an explosion in mammalian variety."  The distinct lineages of monkey-like primates, elephants, rodents, full-fledged bats, whales, horses, and the primitive ancestors of cattle and pigs all made their debut at that time.[1]

     Why did all these important lineages suddenly evolve their unique traits 55 million years ago?  According to molecular data, which estimates divergence times based on calibration to the amount of divergence in the fossil record, they should have diverged much earlier, toward the middle of the time of the dinosaurs.  Yet the fossil record marks their sudden origins about 10 million years after the dinosaurs became extinct.  This discrepancy between molecular data and the fossil record could be explained if there was a 100-fold increase in DNA mutations that lasted over a period of 500,000 years.[2]  What could cause such a drastic increase in mutations?  Whatever the cause, one fact is undeniable – the diversification of the mammals in the early Eocene is separated in time from the extinction of the dinosaurs by a substantial space of at least 10 million years, and therefore the greatest diversification of the mammals was not a direct result of the dinosaurs becoming extinct.  Rather, there was another unseen force at play which seems to have dramatically increased mutation rates for a relatively short period of time, about 55 million years ago. 

     The heart of the question is, what accelerates the mutation rate?