The terrifying scenario could become a reality as the rodents take advantage of larger mammals becoming extinct.
"Animals will evolve, over time, into whatever designs will enable them to survive and to produce offspring," said geologist Dr Jan Zalasiewicz, from the University of Leicester.
"For instance, in the Cretaceous Period, when the dinosaurs lived, there were mammals, but these were very small, rat and mouse-sized, because dinosaurs occupied the larger ecological niches.
"Only once the dinosaurs were out of the way did these tiny mammals evolve into many different forms, including some very large and impressive ones: brontotheriums, horses, mastodons, mammoths, rhinoceri and more.
"Given enough time, rats could probably grow to be at least as large as the capybara, the world's largest rodent, that lives today, that can reach 80 kilos (176 pounds). "If the ecospace was sufficiently empty, then they could get larger still."
The largest extinct rodent known, Josephoartegasia monesi, which lived three million years ago, was larger than a bull and weighed over a ton.
Like its modern-day relative, the sheep-sized capybara, it lived in South America.
A hint of the nightmare to come can be seen on "rat islands" - isolated regions where rats introduced by humans have quickly risen to become the dominant species.
Rat islands act as a "laboratory" for studying the future evolution of the rodents, according to Dr Zalasiewicz.
"Rats are one of the best examples of a species that we have helped spread around the world, and that have successfully adapted to many of the new environments that they found themselves in," he said.
"They are now on many, if not most, islands around the world - and once there, have proved extraordinarily hard to eradicate. They're often there for good, essentially. Once there, they have out-competed many native species and at times have driven them to extinction.”