The paper, titled “A Smooth Exit from Eternal Inflation?,” was authored by Hawking and Thomas Hertog, a theoretical physicist from the Institute for Theoretical Physics at the University of Leuven in Belgium. It’s currently being reviewed by an undisclosed science journal, but for now it’s sitting at the arXiv in its preprint form. The paper was first submitted to the preprint server on July 24, 2017, but it underwent a revision on March 4, 2018.

Understandably, the paper is getting a lot of attention, particularly because Hawking was working on it just days before his death. The Sunday Times said the new paper could be Hawking’s most important scientific legacy, while fellow researchers told The Telegraph that if the new evidence had been discovered before Hawking died, “it may have secured the Nobel Prize which had eluded him for so long.”

High praise. So what’s all the fuss about?

Some physicists believe the Universe will expand forever, a theory known as eternal inflation. This process involves an intermingling of quantum mechanics and Einstein’s equations of general relativity, leading to speculation that some patches of the cosmos produce an infinite number of universes, i.e. multiverses, in an endless, self-perpetuating process. In 1980, this led cosmologists Alan Guth and Andrei Linde to speculate that “in the multiverse that results from eternal inflation, anything that can happen will happen an infinite number of times.”

“Inflation is a stage of exponentially fast expansion of the universe, which makes the universe very large and uniform. Long time ago, it was realized that in some parts of the universe inflation may continue forever,” Linde told Gizmodo. “As a result of this process, which I called eternal inflation, the universe may split into many exponentially large parts with different properties; the universe becomes a multiverse.”

This theory gave rise to the Anthropic Principle—the idea that observers (e.g. you and me) will only find themselves in a universe that’s compatible for life. Other types of universes may exist, but we’ll never be able to observe them, according to this view of the cosmos.

Avi Loeb, chair of the Harvard Astronomy Department, says the new paper by Hawking and Hertog uses math to get around this mathematical and philosophical bottleneck and make actual predictions about the type of universes that are allowed to exist in the multiverse.

“This requires making use of the quantum language to describe everything, including all possible types of universes that are born in the multiverse,” Loeb told Gizmodo. “They conjecture—but not prove—that only a limited set of possible universes are allowed. Anthropic reasoning should apply only to a restricted subset of all possibilities.”

For example, some universes may feature different constants than what we’re used to, or more dimensions. Some of these universes may “work,” but most of them likely won’t. Hawking and Loeb are trying to peel back through the conjectured mathematical infinity, and show which kinds of universes can pop into existence and which may be able to harbor observers. The scientists say it may eventually be possible to see signs of the multiverse in the background radiation of the universe, but that has yet to be proven. If someone down the line can expand on this work, and show us what we should be looking for, then it can be said that Hawking and Loeb were truly onto something. But for now, that’s a big if.

And indeed, Loeb says this is a “very interesting” idea that will likely stimulate further discussion among scientists who study the embryonic stage of the universe, and for scientists who like ideas that can be ruled out or confirmed by observations or experiments. “The traditional formulation of the multiverse theory could not be falsified if ‘anything that can happen will happen an infinite number of times’,” said Loeb. “I like the Hawking and Hertog concept much more. But more work is needed to flesh it out in more detail.”

Frank Wilczek, a theoretical physicist at MIT and Nobel laureate, was less charitable about the new work.

“It’s heavy on speculative assumptions, and I don’t see any concrete predictions,” Wilczek told Gizmodo. “Very hard to understand, though, at least for me, and I may be missing something.”

Linde says that the processes behind eternal inflation are quite complicated, requiring the investigation of quantum fluctuations on incredibly large scale. But it’s this problem that Hawking and Hertog investigated in the new paper.