Primordial black holes from a type-IIB/F theory inflaton potential

In the earliest moments of our universe, a fraction of a second after the beginning, space itself underwent a period of unimaginable expansion known as cosmic inflation. This rapid stretching smoothed out the cosmos and planted the seeds for everything we see today, from galaxies to stars. However, the theory of inflation also suggests that under specific, rare conditions, the universe could have produced tiny, dense clumps of matter that collapsed immediately into black holes. These are called primordial black holes. Unlike the black holes formed by dying stars, these would have been born from the raw energy of the early universe. For decades, scientists have wondered if these objects exist and whether they could make up the invisible "dark matter" that holds galaxies together. The challenge has been finding a physical mechanism that creates enough of these black holes without breaking the rules of our current understanding of physics.

A team of researchers from the University of Burdwan in India has taken a fresh look at this problem by using a specific framework from string theory, a leading candidate for a theory of everything. They focused on a mathematical landscape called the "inflaton potential," which describes the energy field responsible for driving the universe's initial expansion. In their model, they started with a version of this field that successfully explains the smooth, large-scale structure of the universe we observe today. To this established model, they introduced a very small, localized disturbance. Imagine the smooth slope of a hill suddenly having a tiny, gentle bump on it. In the language of the researchers, this bump was created by slightly deforming one of the fundamental geometric shapes that define the hidden dimensions of string theory. This small change was not just a random tweak; it was designed to test how the universe behaves when the smooth expansion of inflation hits a temporary, localized slowdown.

When the field driving inflation rolls over this bump, it does not speed up or stop completely; instead, it slows down significantly more than usual. The researchers call this an "ultra-slow-roll" phase. During this brief pause, the quantum fluctuations in the universe, which are usually tiny and harmless, get amplified dramatically. Think of it as a momentary pause in a rushing river that allows a small ripple to grow into a massive wave. In their simulations, this amplification caused the density of matter in certain regions to spike to a level far higher than the average. When the universe continued to expand and these dense regions eventually re-entered the observable horizon, the gravity within them became so strong that they collapsed instantly into black holes.

The study calculated the properties of these hypothetical black holes with great precision. They found that the process would produce black holes with a mass roughly equivalent to that of Earth or Jupiter, a size far smaller than the black holes formed by stars. These objects would be incredibly light in astronomical terms, yet massive enough to survive to the present day. The researchers determined that these black holes would take an almost incomprehensible amount of time to evaporate, far longer than the current age of the universe. This means that if they were created in the numbers suggested by their model, they would still be around today, potentially contributing to the dark matter that permeates the cosmos.

However, the existence of these objects is not without constraints. The team checked their results against real-world observations, specifically looking at data from microlensing surveys. These surveys search for the temporary brightening of distant stars caused by the gravity of passing objects. The researchers found that for their model to be consistent with what we see in the sky, the density of the primordial fluctuations must stay below a specific threshold. If the fluctuations were any stronger, the resulting abundance of black holes would be too high, contradicting the lack of observed microlensing events. Their calculations suggest that while these black holes could exist, they would make up only a small fraction of the total dark matter, roughly 0.12 percent, rather than being the sole explanation for it.

Beyond the black holes themselves, the study points to a potential way to test these ideas in the future. The violent process of creating these black holes would also generate ripples in spacetime known as gravitational waves. The researchers noted that the specific frequency of these waves falls within the sensitivity range of the Square Kilometer Array, a massive radio telescope project currently under development. This suggests that future observations could either detect these waves, providing strong evidence for the existence of these primordial black holes, or rule out this specific mechanism entirely. The work offers a concrete path forward, moving the search for these elusive objects from pure theory into the realm of observable science.