⚛️ phenomenology

Less isn't more: Cosmological bounds on the neutrino masses are robust to changes in the neutrino abundance

This paper demonstrates that cosmological upper limits on the sum of neutrino masses remain robust against variations in neutrino abundance caused by post-decoupling photon injection or dark radiation, with such modifications shifting the 95% credible bounds by at most 0.004 eV and potentially worsening the tension between cosmological constraints and measured mass splittings.

Original authors: Sebastian J. Figueroa, Alexander C. Sobotka, Adrienne L. Erickcek

Published 2026-09-15

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CC BY 4.0

Original authors: Sebastian J. Figueroa, Alexander C. Sobotka, Adrienne L. Erickcek

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is filled with a ghostly sea of particles called neutrinos. These tiny, nearly massless particles were created in the first second after the Big Bang and have been streaming through space ever since, passing through stars, planets, and even our own bodies without leaving a trace. While we cannot see them directly, their presence is felt in the way the universe expands and how galaxies clump together. For decades, physicists have known that at least two types of these particles must have a tiny amount of mass, a fact confirmed by experiments that watch them change their identity as they travel. However, these experiments cannot tell us exactly how heavy they are, only that they are not weightless. To find the answer, cosmologists look at the oldest light in the sky, the cosmic microwave background, which acts as a snapshot of the infant universe. By studying how this light has been stretched and distorted over billions of years, scientists can calculate the total weight of all the neutrinos in the cosmos.

Recently, a tension has emerged between what we know from particle physics and what we see in the cosmos. The minimum weight required by particle experiments is slightly higher than the maximum weight allowed by the most precise cosmic measurements. This discrepancy has led some researchers to wonder if our understanding of the universe's history is incomplete. Perhaps the number of neutrinos we assume exists is wrong, or maybe they interact with invisible forces we haven't discovered yet. If the universe contained fewer neutrinos than we think, the rules of the cosmic game would change, potentially allowing for heavier neutrinos and resolving the conflict. A team of researchers set out to test this specific idea: could a change in the thermal history of the universe, specifically a reduction in the number of neutrinos, loosen the strict limits on their mass?

The researchers investigated a scenario where a mysterious, heavy particle decays into light and invisible radiation after the neutrinos have already separated from the rest of the universe. Imagine the early universe as a hot, dense soup where all particles are mixed together. As it cools, the neutrinos break away and begin their lonely journey. If a heavy particle were to decay later, dumping extra energy into the light particles (photons) but not into the neutrinos, it would effectively heat up the light while leaving the neutrinos cold. This would make the neutrinos appear less abundant relative to the light, a situation that might allow the universe to accommodate heavier neutrinos without contradicting the observations. The team built a detailed computer model of this process, simulating how such a decay would alter the expansion of the universe and the patterns seen in the cosmic microwave background. They combined their simulations with the most powerful astronomical data available, including maps of the early universe from the Planck satellite, measurements of how gravity bends that light, and surveys of galaxy distributions from the Dark Energy Spectroscopic Instrument.

The results were surprising and robust. The team found that reducing the number of neutrinos does not loosen the constraints on their mass; in fact, it often tightens them. When the neutrino population is smaller, the universe's expansion history changes in a way that makes the presence of heavy neutrinos even more problematic for the data, exacerbating the tension with the measured mass splittings. The researchers discovered that the only way to make the data fit a heavier neutrino mass is to add a significant amount of invisible radiation to the mix, which compensates for the missing neutrinos. Even in this best-case scenario, the limit on the total mass of the three neutrino types only relaxes by a tiny fraction, moving from a maximum of about 0.0691 electron volts to 0.0710 electron volts. This difference is so small that it does not resolve the tension with particle physics experiments. Furthermore, when the researchers tested a more general approach—simply changing the temperature of the neutrino background without assuming a specific decay mechanism—they found the same result. The limits on neutrino mass remained stubbornly tight, shifting by less than 0.004 electron volts in most cases.

The study concludes that the strict upper limits on neutrino mass derived from cosmology are not an artifact of assuming a standard number of neutrinos. The constraints are robust against changes in the neutrino abundance. If the universe had fewer neutrinos than we think, the cosmological data would actually demand that they be even lighter, not heavier. This finding suggests that the tension between cosmological limits and particle physics measurements is not easily solved by tweaking the number of neutrinos. Instead, the discrepancy points toward something more fundamental, perhaps a need to revise our understanding of how the universe expanded or how matter clumped together, rather than a simple error in counting the ghostly particles that permeate the cosmos. The cosmic ledger remains balanced, and the mystery of the neutrino's true weight persists.

Technical Summary: "Less isn't more: Cosmological bounds on the neutrino masses are robust to changes in the neutrino abundance"

Problem Statement
Recent cosmological observations, particularly from the Dark Energy Spectroscopic Instrument (DESI) combined with Planck CMB data, have yielded stringent upper limits on the sum of neutrino masses ( $\sum m_\nu$ ). For the degenerate ordering (DO), these limits ( $\sum m_\nu < 0.0642$ eV in the specific DESI DR2 analysis) are approaching or conflicting with the minimum values inferred from neutrino oscillation experiments ( $\sum m_\nu \gtrsim 0.058$ eV for normal ordering). This tension has prompted investigations into whether modified thermal histories could relax these bounds. Specifically, it has been hypothesized that if the relic neutrino abundance were lower than the standard $\Lambda$ CDM prediction—perhaps due to entropy injection after neutrino decoupling—the inferred upper limit on neutrino masses might be loosened. This paper investigates whether reducing the neutrino-to-photon ratio actually relaxes cosmological constraints on $\sum m_\nu$ or if other physical effects counteract this expectation.

Methodology
The authors employ two distinct frameworks to test the robustness of neutrino-mass constraints against changes in neutrino abundance:

Physical Decay Model ( $Y$ -decay): They model a subdominant hidden-sector particle ( $Y$ ) that decays into photons and dark radiation (DR) between Big Bang Nucleosynthesis (BBN) and recombination. This decay injects entropy into the photon bath, lowering the neutrino-to-photon ratio ( $n_\nu/n_\gamma$ ) and thus the effective number of relativistic species ( $N_{\text{eff}}$ ), unless compensated by DR injection. The model is implemented in a modified version of the Boltzmann solver CLASS, which includes perturbation equations for the decaying $Y$ particles and their decay products.
Model-Agnostic Analysis: To isolate the impact of neutrino abundance without assuming a specific decay mechanism, they treat the cosmic neutrino background (C $\nu$ B) temperature ( $T_\nu$ ) as a free parameter, allowing the neutrino-to-photon ratio to vary directly.

Both frameworks are analyzed using Markov Chain Monte Carlo (MCMC) methods with MontePython. The datasets utilized include:

Primary CMB anisotropies from Planck (PR3/PR4).
CMB lensing reconstructions from Planck and the Atacama Cosmology Telescope (ACT).
Baryon Acoustic Oscillation (BAO) data from DESI (DR2).
Constraints on spectral distortions ( $\mu$ and $y$ ) from COBE/FIRAS.
Primordial deuterium abundance (D/H) measurements.

The analysis covers three neutrino mass orderings: Degenerate (DO), Normal (NO), and Inverted (IO), using both fixed mass splittings and marginalized sampling of the lightest neutrino mass ( $m_0$ ) and splittings.

Key Contributions and Results

Robustness of Bounds: Contrary to the intuition that reducing neutrino abundance would loosen mass constraints, the authors find that cosmological bounds on $\sum m_\nu$ are robust to changes in thermal history. In fact, scenarios that reduce neutrino abundance exclusively (via photon injection) often tighten the bounds.
Degenerate Ordering (DO) Results:
- Standard Thermal History: $\sum m_\nu < 0.0691$ eV (95% CrI).
- Exclusive Photon Injection ( $Y \to \gamma$ ): The bound tightens to $\sum m_\nu < 0.0652$ eV. This occurs because reducing $N_{\text{eff}}$ increases the sound horizon angle ( $\theta_s$ ), requiring a lower Hubble constant ( $h$ ) to compensate. A lower $h$ increases the matter density parameter ( $\Omega_m$ ), which is strongly disfavored by DESI BAO data.
- Photon + Dark Radiation Injection: The bound relaxes slightly to $\sum m_\nu < 0.0710$ eV. The injection of DR increases $N_{\text{eff}}$ , which favors a higher $h$ and allows for larger neutrino masses, but the effect is marginal.
- Model-Agnostic $T_\nu$ Variation: Varying $T_\nu$ directly yields $\sum m_\nu < 0.0724$ eV, confirming that constraints on the specific $Y$ -decay scenario are not driving the stringency of the limits.
Normal and Inverted Orderings: The same qualitative patterns hold for NO and IO. The shift in the bound on $\sum m_\nu$ due to decay scenarios is at most 0.004 eV relative to the standard thermal history. Marginalizing over mass splitting uncertainties yields slightly tighter constraints than fixed splittings due to prior volume effects, but the relaxation from decay scenarios remains minimal (maximum relaxation of 0.0032 eV for the lightest mass).
Correlations: The analysis identifies a positive correlation between neutrino abundance and neutrino mass. A larger abundance increases the pre-recombination radiation density, mitigating the suppression of structure growth by massive neutrinos. Conversely, reducing the abundance exacerbates the tension between the CMB acoustic scale and the matter power spectrum, leading to tighter mass limits.

Significance and Claims
The paper concludes that the stringency of current cosmological neutrino-mass bounds is not an artifact of assuming a standard thermal history. The authors explicitly state that "less isn't more": reducing the neutrino abundance does not resolve the tension between cosmological upper limits and oscillation-derived lower limits. Instead, reducing the neutrino abundance tightens the bounds on $\sum m_\nu$ because the accompanying decrease in $N_{\text{eff}}$ exacerbates the impact of massive neutrinos on the CMB and structure formation.

The authors claim that their results indicate that "reducing the pre-recombination radiation density will only worsen the emerging tension between cosmological bounds on the neutrino masses and the measured mass splittings." They further assert that the preference for negative effective neutrino masses seen in some DESI analyses is likely a diagnostic of dataset systematics or missing physics (such as modified structure growth or dynamical dark energy) rather than a signal of non-standard neutrino abundance. The study demonstrates that even with significant modifications to the thermal history, cosmological data continues to impose tight constraints on neutrino masses that are difficult to reconcile with the minimum values required by oscillation experiments.

Technical Summary: "Less isn't more: Cosmological bounds on the neutrino masses are robust to changes in the neutrino abundance"

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