Physicists Dismiss Primordial Black Holes as a 'Fine-Tuned' Dark Matter Idea and Treat Particles as the 'Natural' Default. A UC Santa Cruz Theorist Ran 12 Models Through the Same Yardstick and Found the Opposite: One Black Hole Scenario Was Among the Most Natural of All, and a Favorite Higgs-Resonance Particle Model Needed Tuning to a Fraction of a Percent.

For four decades, physicists deciding which dark matter idea deserves their time have leaned on a rule of thumb they call naturalness: a theory is suspect if it only works when its underlying numbers are tuned to many decimal places. By that standard, weakly interacting massive particles have generally been treated as the sensible default and primordial black holes, formed in the first fraction of a second after the Big Bang, as the exotic long shot. A new paper in Physical Review D says the field has been applying that rule by reputation rather than by arithmetic, and that when the arithmetic is done, the reputations do not hold.

Stefano Profumo, a professor of physics at the University of California, Santa Cruz, and deputy director for theory at the Santa Cruz Institute for Particle Physics, took 12 well-studied dark matter scenarios and put each through the same test. The yardstick, known as the Barbieri-Giudice measure, poses one question of any model: if you nudge one of its input parameters by a small amount, how much does the predicted amount of dark matter change? A model whose prediction barely moves is forgiving of its assumptions, and therefore natural. A model whose prediction swings wildly only works because someone has set its dials to exactly the right place.

Profumo ran the test on several flavors of particle dark matter, including the classic WIMP and models in which dark matter annihilates through a resonance tied to the Higgs boson, and on several distinct mechanisms by which the early universe could have produced black holes of the right mass and abundance. "There's a habit of treating primordial black holes as the exotic, fine-tuned alternative, and particle dark matter as the safe, natural default," he said. "When you actually run the numbers side by side, that story doesn't hold up. Some black hole scenarios are about as natural as it gets. Some particle scenarios are wildly fine-tuned. And some of each land right in the middle."

The specifics cut against the conventional wisdom in both directions. Black holes formed from the collapse of networks of "domain walls," sheet-like defects left over from a phase transition in the infant universe, came out among the most natural constructions in the entire study, rivaling the most forgiving particle models. Meanwhile one of the most popular particle scenarios, in which dark matter is produced through a Higgs resonance, ranked among the most fine-tuned of all, requiring one of its parameters to be pinned to within a fraction of a percent of a specific value to give the observed abundance.

The paper does not crown a winner, and Profumo is careful to say that naturalness is a filter for deciding where to look, not a substitute for detection. "Naturalness has real power as a filter for deciding where to look next," he said. "But it can't be a shortcut for dismissing an entire category of ideas, like primordial black holes, just because a few individual models within that category happen to be tuned. The tuning lives in the specific model, not in the kind of dark matter you started with."

The timing is pointed. Decades of direct-detection experiments have steadily shrunk the room for WIMPs without finding one, and last week's LHC search for evaporating microscopic black holes came up empty to 12 TeV. Profumo's contribution is not a new candidate but a common ruler, one that lets a black hole model and a particle model be compared on equal footing rather than by the prestige of the community that proposed them. The result, for anyone keeping score, is that the "safe" bet was never as safe as it looked, and the "exotic" one was never as exotic.