The story begins with the physics of the early universe. About 380,000 years after the Big Bang, the scattering of radiation by free electrons generated a small amount of linear polarization in the CMB, a process somewhat analogous to the polarization produced when sunlight scatters in the Earth’s atmosphere. That polarization comes in two distinct varieties. E modes, first detected in 2002, arise from density shifts in the primordial plasma and display symmetric patterns across the sky. B modes, by contrast, have curl-like swirl patterns. Gravitational lensing, the distortion of CMB light by matter lying between us and the early universe, produces B modes that have already been observed, while primordial gravitational waves rippling through spacetime could produce an additional B-mode signal that has so far eluded detection. Finding that primordial signal would transform our understanding of the infant cosmos and could strongly support particular models of cosmic inflation, the theorized exponential expansion that shaped the universe in its first fraction of a second.

Against this backdrop, cosmic birefringence has emerged as one of the most tantalizing possibilities in observational cosmology. Recent analyses have suggested that the polarization of the CMB may have rotated by only a fraction of a degree during its nearly fourteen-billion-year journey. That sounds vanishingly small, but even such a slight rotation would be profound. It could provide evidence for physics beyond the Standard Model of particle physics, and it might offer clues about the nature of dark matter and dark energy, the mysterious components that together account for roughly 95 percent of the universe’s energy density. One possible explanation involves an axion-like field coupled to light, a class of hypothetical particles that would not necessarily constitute dark matter but whose existence would nonetheless revolutionize particle physics. Other theories connect cosmic birefringence to fields associated with dark energy itself, making the measurement a potential window onto some of the deepest mysteries in modern science.

There is, however, a formidable catch, and it lies at the heart of the new research. Even a minuscule error in the orientation of a telescope’s polarization-sensitive detectors can produce almost exactly the same observed effect as a genuine cosmic rotation. From the CMB signal alone, scientists cannot distinguish between a uniform rotation imposed by the cosmos and a common miscalibration of detector orientation, because both produce precisely the same pattern in the data. In other words, the very measurement that could reveal new physics is also the measurement most vulnerable to being faked by instrumental imperfections. As Anto I. Lonappan, a postdoctoral fellow at UC San Diego and lead author of the new study, explains, the stakes of getting this right could hardly be higher. “The signal we are looking for is incredibly small, so we have to be certain that we are seeing the universe and not our instrument,” Lonappan said. “Our method gives us a complementary way to check that distinction. Before interpreting a tiny rotation as new physics, we want to know that the calibration itself can be trusted.”

The UC San Diego team, which also includes Chancellor’s Distinguished Professor of Physics Brian Keating and Associate Professor of Physics Kam Arnold, approached the problem with an elegant strategy built on comparison. Rather than relying on a single map of the sky, the researchers compared maps made from different groups of detectors. The logic is straightforward but powerful: a genuine cosmic rotation would be common to all the maps, because the universe rotates the polarization of every photon in the same way. In the new method, that common rotation cancels out when the maps are compared against one another, leaving behind only the differences in their polarization calibration. The technique is intentionally blind to any rotation shared by all the maps, which means it can determine how well different detector sets are calibrated relative to one another, but it cannot by itself establish the overall polarization angle or the absolute cosmic birefringence signal. That final step still requires an independent absolute calibration reference.

To put their method to the test, the researchers developed a different estimator and applied it to existing observations from the European Space Agency’s Planck satellite, which spent years mapping the CMB across the entire sky. The team applied the technique to eight Planck polarization maps and compared the resulting calibration pattern with that obtained from the established analysis currently used to separate instrumental rotation from cosmic birefringence, an approach known as the Minami-Komatsu analysis. The result was reassuring: the two approaches were found to be consistent, despite relying on different assumptions. As a conditional demonstration, the researchers anchored their differential reconstruction to the common calibration mode inferred by the existing analysis, which reproduced a cosmic-birefringence angle of 0.37 plus or minus 0.12 degrees, consistent with the Minami-Komatsu result. The study, published in the Astrophysical Journal Letters, thus provides an important cross-check on one of cosmology’s most intriguing recent claims.

The significance of this work extends well beyond the specific question of cosmic birefringence. The calibration method developed at UC San Diego could directly support the search for primordial B modes, the curl-like polarization patterns that would constitute evidence for gravitational waves in the early universe. The reason is subtle but critical: relative angle-calibration errors between detector sets can convert E modes into spurious B modes, contaminating exactly the signal that inflation hunters are trying to isolate. By identifying such errors before they can masquerade as a cosmological signal, the new framework acts as a safeguard for the next generation of experiments. As instruments push polarization measurements to increasingly high precision, the margin for instrumental error shrinks dramatically, and independent calibration checks will become an essential part of the analysis pipeline before very small signals are interpreted as evidence for new physics.

That need is about to become acute. Experiments such as those at the Simons Observatory, where Keating serves as principal investigator, are designed to measure CMB polarization with unprecedented sensitivity, and their results will be scrutinized with correspondingly unprecedented rigor. “The detection of primordial B modes would transform our understanding of the early universe, so the measurement must survive rigorous calibration checks,” Keating said. “Anto has developed a useful new framework for testing relative polarization-angle calibration. This is ultimately about knowing when we can trust a measurement.” In a field where entire theories of the universe’s origin can hinge on angles measured to a fraction of a degree, that philosophy, trust but verify, and verify again with an independent method, may prove as important as any detector or telescope.

The broader lesson of the UC San Diego study is a familiar one in the history of science: extraordinary claims demand extraordinary scrutiny. Cosmic birefringence, if confirmed, would rank among the most consequential discoveries in modern physics, opening a new observational window onto dark matter, dark energy, and the fundamental laws that governed the universe’s first instants. But the same fractional-degree rotation that excites theorists can be manufactured by a slightly tilted detector, and the new differential calibration method offers a way to tell the two apart. By demonstrating that an independent estimator, built on different assumptions, agrees with the established Minami-Komatsu analysis when applied to Planck’s eight polarization maps, the researchers have strengthened the foundation on which future claims will rest. Whether the universe truly is twisted remains an open question, but thanks to this work, the answer will rest on firmer ground, and the next generation of CMB experiments will know precisely how much confidence to place in the ancient light they are measuring.

Subject of Research: A new differential polarization calibration method to test cosmic birefringence in the cosmic microwave background

Article Title: Is the universe twisted? A new check on a possible twist in the universe’s oldest light

Article References: Is the universe twisted? A new check on a possible twist in the universe’s oldest light. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: cosmic microwave background, cosmic birefringence, polarization, calibration, Planck satellite, B modes, E modes, dark matter, dark energy, cosmic inflation, Simons Observatory, Standard Model

The signature in question is a subtle shift in what cosmologists call the effective number of relativistic species, denoted N_eff. Any black hole with a mass below roughly 10^15 grams would, by quantum physics, have completely evaporated by today through Hawking radiation, the process by which black holes slowly leak particles and energy. Tiny primordial black holes formed in the early universe would have evaporated almost immediately, injecting entropy and new particles into the primordial plasma of photons, electrons, and neutrinos. This injection of energy subtly raises the radiation content of the universe, an effect that would be recorded today as an excess in N_eff above its standard value of 3.044. Precision measurements of the cosmic microwave background, the relic glow of the Big Bang, can in principle detect such an excess, making evaporating primordial black holes accessible not through telescopes or detectors, but through cosmological bookkeeping.

The difficulty, as the authors emphasize, is that most theoretical studies have modeled primordial black hole populations as monochromatic, meaning every black hole has exactly the same mass. This is a convenient simplification, but it erases the rich variety of mass functions that different formation mechanisms actually predict. A brief ultra-slow-roll phase during inflation, when the universe expanded at a nearly frozen rate, produces a log-normal mass function peaked at a characteristic mass. A scale-invariant spectrum of primordial fluctuations collapsing during a radiation-dominated era produces a power-law distribution. Critical gravitational collapse, in which density perturbations hover just above the threshold for forming a black hole, yields a function with a low-mass power-law tail and an exponential cutoff. And metric preheating, a process in which the oscillations of the inflaton field at the end of inflation resonantly amplify perturbations, produces a numerically determined, sharply peaked distribution.

The new work goes further still by combining all four mechanisms into a single multimodal population, in which several formation channels operate simultaneously at different cosmic epochs and mass scales. Crucially, the authors do not treat the relative weights of the four sub-populations as free parameters to be fitted by hand. Instead, each channel’s weight is derived from the primordial collapse probability, which itself is fixed by the amplitude of the primordial curvature power spectrum at the scale associated with that channel. This ties the resulting mass function directly to inflationary model building: for any specific multi-feature model of the early universe, the population fractions, and therefore the predicted imprint on N_eff, are in principle calculable rather than assumed. The framework was implemented in a new public code called FRISHBEE, an extension of the existing FRISBHEE package, which solves the coupled Friedmann-Boltzmann equations governing the evaporation of the black hole population and the heating of the cosmic plasma.

The numerical results deliver a striking message: the monochromatic approximation systematically underestimates the cosmological imprint of evaporating primordial black holes. Working with initial black hole masses of 10^5, 10^7, and 10^8 grams, all safely within the window where evaporation completes before Big Bang nucleosynthesis and well before neutrino decoupling, the team computed the excess in the effective number of relativistic species for five distributions, three spin configurations, and three weighting schemes. Extended mass functions enhance the signal over the monochromatic benchmark by factors ranging from about 1.03 for the critical collapse case to roughly 1.84 for the log-normal case, with the power-law, metric preheating, and multimodal mixtures falling in between. The hierarchy among the distributions is preserved across the entire mass window, confirming that the shape of the mass function, rather than its characteristic mass alone, is the primary determinant of the evaporation signal.

The physical reason for the enhancement is intuitive. Broad distributions contain a population of lighter black holes that evaporate earlier, injecting their energy into the plasma when the universe was hotter and the number of available particle degrees of freedom was larger. Each unit of deposited energy therefore produces a bigger effect on the radiation content. A monochromatic population, in contrast, dumps all of its energy at one characteristic epoch and misses this compounding advantage. The multimodal mixture, dominated in the mean-mass-weighted scenario by its log-normal component at nearly seventy percent of the total weight, produces an enhancement of about 77 percent over the monochromatic case, and the result proves robust across all three physically motivated weighting scenarios the authors tested, never dropping below roughly 43 percent.

Detectability is where the shape effect becomes potentially decisive. The forthcoming CMB-S4 experiment and the Simons Observatory are expected to measure the excess in the effective number of relativistic species with sensitivities of about 0.06 and 0.05 respectively. For a population of primordial black holes with initial mass 10^7 grams and a scalar dark radiation species emitted by evaporation, the monochromatic prediction of approximately 0.057 falls below the detection threshold and is effectively invisible. But the log-normal, power-law, and multimodal distributions yield values between roughly 0.096 and 0.105, crossing the threshold at the 1.6 to 1.7 sigma level. In other words, the same underlying black hole population can flip from undetectable to marginally observable simply because of the shape of its mass function. For a spin-2, graviton-like dark radiation species, however, the absolute signal drops by more than an order of magnitude, and none of the distributions considered would be detectable at this mass scale.

Spin adds a further twist, and one of the study’s most surprising results. Rotating black holes emit Hawking radiation more efficiently through a process called superradiance, in which co-rotating wave modes are amplified rather than absorbed, extracting both energy and angular momentum from the hole. The amplification grows steeply with the spin of the emitted quantum: negligible for scalars, a few percent for photons, and more than one hundred percent for gravitons, while fermions are protected by Pauli blocking. The authors find that near-extremally spinning black holes, modeled with a Gaussian spin distribution centered at a spin parameter of 0.99, can boost the evaporation signal by factors of six to twelve for spin-2 dark radiation. Yet here the logic reverses: in broad mass distributions, lighter black holes spin down and shed their angular momentum long before they finish evaporating, averaging away the superradiant advantage. For near-extremal spin and spin-2 dark radiation, this effect can outweigh the mass-broadening enhancement entirely, causing the monochromatic approximation to actually overestimate the signal, an inversion the authors quantify in detail.

Taken together, these results elevate the effective number of relativistic species from a mere bound on the existence of primordial black holes to a diagnostic probe of their formation history. A future measurement at the sensitivity of CMB-S4 or the Simons Observatory would discriminate between formation scenarios: a signal near the extended-distribution predictions would disfavor a monochromatic or critical-collapse-dominated population at the 10^7 gram scale, while a non-detection would constrain the broader scenarios. Because the multimodal framework connects the population weights directly to the primordial power spectrum through the collapse probability, precision cosmology could in principle probe the number and relative amplitude of features in the inflaton potential, the physics that governed the universe’s earliest moments. The authors caution that their analysis is confined to the pre-Big Bang nucleosynthesis mass window, and that extended distributions with heavy tails approaching the boundary may require a treatment of competing dilution effects, which they defer to future work. But the central conclusion stands: in the hunt for primordial black holes through their Hawking afterglow, the shape of the population is everything.

Subject of Research: Cosmological imprint of evaporating primordial black holes with multimodal mass and extended spin distributions on the effective number of relativistic species

Article Title: Evaporation of primordial black holes with multimodal mass and extended spin distributions: cosmological imprints on the effective number of relativistic species

Article References: Toghrai, T., Daassou, A., Ouchhaine, Y., Laassiri, H., & Benbrik, R. (2026). Evaporation of primordial black holes with multimodal mass and extended spin distributions: cosmological imprints on the effective number of relativistic species. The European Physical Journal C, 86(9), Article 1087. https://doi.org/10.1140/epjc/s10052-026-16372-x

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16372-x

Keywords: primordial black holes, Hawking radiation, effective number of relativistic species, cosmic microwave background, inflation, mass distribution, black hole spin, superradiance, dark radiation, CMB-S4, Simons Observatory, early universe