Tiny primordial black holes may leave a many-peaked gravitational-wave signal

Primordial black holes are hypothetical black holes that could have formed in the early universe. In a scenario studied by physicists Debasish Borah and Nayan Das, very light examples evaporate before the start of Big Bang nucleosynthesis, releasing heavy right-handed neutrinos. These particles can decay in ways that create a lepton asymmetry—an imbalance between matter and antimatter in the lepton sector. Early-universe processes can then convert some of that imbalance into the baryon asymmetry: the excess of ordinary matter over antimatter seen today.

The paper asks whether this proposed history could also produce gravitational waves with a recognizable, multi-peaked spectrum. Gravitational waves are ripples in spacetime. Here, the predicted signals are not from colliding black holes, but from several processes in the early universe, including graviton emission during neutrino decay and black-hole evaporation.

Following black holes, neutrinos and gravitons

The authors model black holes with a single initial mass, no spin and no electric charge. They assume these black holes form during a radiation-dominated era and that their initial abundance is high enough for them to dominate the universe’s energy for a time before evaporating. The masses considered are restricted so that evaporation occurs before nucleosynthesis.

To follow the resulting cosmic history, the researchers solve coupled equations tracking the energy densities of black holes, radiation and right-handed neutrinos as the universe expands. They use this evolution to estimate how many neutrinos are produced, how their decays generate a lepton asymmetry, and how different gravitational-wave sources contribute. Their calculations include analytical estimates and numerical solutions, with selected parameter combinations—called benchmark points—used to illustrate possible spectra. They consider both hierarchical neutrino masses and a resonant case, in which two heavy neutrinos have nearly equal masses.

One proposed signal comes directly from neutrino decay: a graviton can be emitted alongside the decay products. The paper also calculates a gravitational-wave background from the hot thermal bath, waves associated with density fluctuations in the black-hole population, and gravitons emitted through Hawking evaporation. The different sources can contribute at different frequencies, producing multiple features in the combined spectrum.

Several peaks, but not an easy detection

The authors find that black-hole evaporation can supply heavy neutrinos without relying on their production from the thermal bath. In their scenario, a period when black holes dominate the universe also helps avoid the strong “washout” that can erase a lepton asymmetry in high-scale thermal leptogenesis. The paper further finds that this period can make the neutrino-decay gravitational-wave contribution more distinct from the background generated by the thermal bath.

The combined spectra in the studied examples have multiple peaks, with frequencies that can extend from the megahertz range to extremely high frequencies. But a multi-peaked prediction is not the same as an observable signal. The authors report that the neutrino-decay contribution remains below the projected sensitivities of the gravitational-wave experiments they consider, even when varying relevant parameters within the successful-leptogenesis scenarios they analyze. In some examples, other predicted sources—particularly gravitons from black-hole evaporation—also make the neutrino-decay component harder to distinguish.

The results depend on the assumed cosmological history and particle-physics parameters. The paper focuses on optimistic benchmark choices and restricts its calculations to cases where the heavy neutrinos remain less important than the total energy density throughout their evolution. The authors note that a period in which the neutrinos themselves dominate would change the history and spectrum, and leave that possibility for future study. Their calculations also assume a simplified, single-mass black-hole population rather than exploring a range of black-hole masses.

The work therefore presents a theoretical possibility, not evidence that primordial black holes existed or that this mechanism explains the observed matter excess. Nor does it establish that the predicted waves can be detected: the paper says the neutrino-decay signal lies beyond the projected reach of the experiments it assesses, while pointing to the need for improved high-frequency detection methods.

This article is based on an arXiv preprint by Borah and Das. A preprint is a research manuscript shared publicly before, or independently of, journal peer review; its claims should be treated as provisional. The paper’s predictions are model-dependent, and the extracted source text may not preserve every detail of its equations and figures.