Two early-universe changes improve a fit to cosmic expansion data—but not across every test

The universe’s expansion rate presents cosmologists with a stubborn disagreement. Measurements based on nearby stars and supernovae give a different answer from the value inferred from the cosmic microwave background—the ancient light left from the early universe—under the standard cosmological model. This mismatch is known as the Hubble tension.

A preprint posted on November 10 asks whether two proposed changes to early-universe physics might help more together than either does alone. Magnus Uggerhøj and colleagues at Aarhus University find a substantial improvement for one particular combination of data. They do not find the same advantage across all their tests.

Two changes, connected through gravity

The standard model, called Lambda cold dark matter or ΛCDM, includes dark energy and cold dark matter. The researchers extended it with two hypothetical ingredients.

First, they allowed neutrinos—light particles that normally travel almost freely through the universe—to scatter off one another through a new interaction. Delaying their free movement changes the pattern of temperature and polarisation fluctuations in the cosmic microwave background.

Second, they included a dark sector derived from a model called hot new early dark energy. In this scenario, an early phase transition converts stored vacuum energy into dark radiation: hypothetical particles that behave as radiation but are distinct from ordinary light. A fraction of dark matter initially interacts with that radiation, then stops as the dark sector cools. This mechanism is called dark radiation matter decoupling, or DRMD.

Extra radiation changes the early expansion rate and shortens the distance that sound waves could travel before the ancient light was released. That distance acts as a ruler in cosmological inference. Dark matter’s temporary interaction with dark radiation also changes how density fluctuations grow. The neutrinos and dark sector do not interact directly in the model; their effects meet through gravity.

Making a difficult calculation practical

The combined model has 12 cosmological parameters, alongside additional parameters describing observational uncertainties. Some combinations of parameter values produce similar predictions, while the neutrino interaction has separate regions of good fit. Exploring this landscape with direct calculations alone would be prohibitively expensive, the authors report.

They used CLiENT, a neural-network emulator that learns how well different parameter choices match the data. For each data combination, training required roughly 300,000 evaluations of the original likelihood—the calculation of how compatible the observations are with a model.

The team then explored parameter distributions and searched for best fits. Importantly, all reported chi-squared fit scores were calculated with the original likelihood, not simply read from the neural network.

The strongest result needs the local calibration

The researchers tested two main combinations of observations, each with and without the SH0ES calibration of supernova brightness. One used Planck cosmic microwave background measurements, DESI galaxy-distance measurements and Pantheon+ supernovae. The other assigned the microwave background’s finer angular detail to the Atacama Cosmology Telescope and South Pole Telescope.

With those finer-scale measurements and SH0ES, the combined model reduced chi-squared by 27.6 relative to the study’s ΛCDM baseline. Lower scores indicate better fits. DRMD alone reduced it by 9.9, and neutrino self-interactions alone by 4.0: the combination improved the fit by more than their separate improvements added together.

That advantage survived the Akaike information criterion, which penalises additional adjustable parameters. Relative to DRMD alone, the combined model improved this criterion by 15.7 points.

For that data combination, the inferred Hubble constant was 70.94 ± 0.60 kilometres per second per megaparsec, with the quoted uncertainty representing a 68% interval. This is a model-dependent inference, not a new direct measurement of expansion.

The qualification matters: much of the improvement came from accommodating the SH0ES calibration. Some microwave background measurements pushed back against the changes needed to do so. In the other three analyses, the extra complexity was not significantly preferred over the individual extensions after the parameter penalty.

Better fits are not particle discoveries

The finer-scale microwave background data also largely removed a strongly interacting neutrino solution allowed by the Planck-based analysis. The combined model instead favoured an intermediate interaction strength.

Other conclusions depended on statistical treatment. Best-fit searches favoured a small interacting dark matter fraction, whereas distributions averaged over the explored parameter space gave only upper limits. The authors therefore caution against treating a better-fitting configuration as a detection.

There is also a physical modelling limitation. Standard calculations of nonlinear structure growth have not been calibrated for some of the dark-sector patterns studied here. The team excluded a troublesome region with very little dark radiation, but some remaining results still touch uncertain territory.

The preprint’s strongest lesson is methodological: combinations of proposed mechanisms can contain useful fits that separate tests miss. It does not establish that these particles or interactions exist, or that the Hubble tension has been resolved.