From Cosmic Bounces to Primordial Black Holes: The Role of Primordial Magnetic Fields

The universe is filled with invisible threads of magnetic force. We see their effects in the swirling galaxies and the space between them, but their origin remains one of cosmology's most persistent mysteries. Standard physics suggests that the rapid expansion of the early universe should have stretched and diluted any magnetic fields until they vanished, leaving a silent, unmagnetized cosmos. To explain why magnetic fields exist today, scientists have proposed that something must have broken this silence in the first moments after the Big Bang, amplifying tiny quantum fluctuations into the vast fields we observe. One compelling idea involves a period where the universe was not expanding, but contracting, before bouncing back into the expansion we see today. In this scenario, a special connection between the fabric of space and electromagnetic fields could have acted as a cosmic amplifier, turning a whisper of magnetism into a roar.

A recent study by researchers at the Indian Institute of Technology (Indian School of Mines) investigates what happens when these amplified magnetic fields are present in such a bouncing universe. The team focused on a specific moment: the transition from a contracting phase to the hot, expanding era filled with radiation. They found that the magnetic fields generated during the contraction did not just fade away; instead, their internal pressure created ripples in the density of the universe. These ripples were strong enough to cause pockets of matter to collapse under their own gravity, forming tiny black holes. By carefully tracking how these magnetic fields evolved and how they influenced the surrounding matter, the researchers calculated exactly how many of these black holes would form and how heavy they would be.

The researchers built a detailed model of a universe that contracts smoothly, avoiding a violent crash, and then bounces back into expansion. During the contraction phase, they introduced a mechanism where the strength of the electromagnetic field changes over time, breaking the usual rules that would otherwise prevent magnetic fields from growing. This allowed quantum fluctuations to be stretched and amplified, creating a strong magnetic field that filled the cosmos. As the universe bounced and entered the radiation-dominated era, this magnetic field exerted a unique kind of stress. Unlike the smooth pressure of a gas, magnetic fields push and pull in specific directions, creating unevenness in the distribution of matter. The researchers calculated that this unevenness was sufficient to trigger the collapse of dense regions into primordial black holes.

To determine the fate of these black holes, the team performed complex calculations that traced the magnetic fields from their creation through the bounce and into the expanding universe. They paid close attention to the smallest scales of these fields, as the physics of the collapse depends heavily on the most energetic, high-frequency parts of the magnetic spectrum. Their results showed that the process creates a population of black holes that are significantly lighter than our sun. For their standard set of parameters, the most common mass for these black holes is in a range far smaller than the stars we see today, yet large enough to be detected by future astronomical surveys.

The study also quantified how common these black holes would be. The researchers found that while they are produced in large numbers, they do not make up all the dark matter in the universe. In their primary scenario, these black holes account for only about one hundred-thousandth of the total dark matter density. This means they form a subdominant population, a hidden layer of the cosmos that exists alongside other forms of dark matter. This result is crucial because it keeps the model safe from a major cosmological problem: if too many black holes formed, they would have caused the universe to collapse back on itself long ago. The researchers confirmed that their model stays well within the safety limits, producing enough black holes to be interesting but not enough to overclose the universe.

The team also explored how changing the conditions of the early universe would alter the outcome. They discovered that the mass and abundance of the black holes are extremely sensitive to the duration of the contraction phase and the energy scale at which the bounce occurs. By adjusting these variables, they found that it is possible to shift the mass of the black holes to even smaller scales, potentially reaching the mass of an asteroid. In these specific, finely tuned scenarios, the black holes could become much more abundant, potentially making up the entirety of the dark matter. However, the researchers emphasized that this requires the universe to have contracted for a longer time and reached a higher energy state than in their primary example.

A key finding of the paper is the strict boundary it sets on the physics of the early universe. The researchers showed that if the energy scale of the bounce were any higher, or if the contraction were slightly faster, the number of black holes would explode, violating the known limits of the universe's density. This creates a clear physical boundary: the energy scale at the end of contraction cannot exceed a specific limit, and the rate of contraction cannot be too steep. These limits are not just mathematical constraints; they are physical requirements that ensure the magnetic fields do not become so strong that they destroy the background universe before the bounce can happen.

The study also clarified how the method of calculation affects the predicted results. The researchers compared two different ways of estimating the black hole population. One method assumes all collapsing regions form black holes of a single, fixed mass, while the other accounts for the fact that regions just barely heavy enough to collapse will form much lighter black holes. They found that the more detailed method, which accounts for this variation, produces a wider range of black hole masses, with a significant number of very light objects. This detailed view is essential for comparing their predictions with real-world observations, such as the way stars are magnified when light passes near a compact object.

Ultimately, this work connects the invisible magnetic fields of the early universe to the tangible existence of black holes. It demonstrates that a non-singular bounce, where the universe contracts and then expands without a singularity, can naturally generate the conditions for black hole formation through magnetic fields alone. The findings suggest that if our universe underwent such a bounce, it would be populated by a vast number of tiny, sub-solar black holes. While they are too rare to be the sole source of dark matter in the most likely scenarios, their presence offers a testable prediction. Future observations looking for the gravitational signatures of these small, dark objects could either confirm this picture of our cosmic origins or rule it out, providing a new window into the very first moments of time.