Neutrinos and the Hubble Tension: A Clue or a Red Herring?

The Hubble constant $H_0$ measures the present-day rate of expansion of the universe — the proportionality factor between a galaxy’s recession velocity and its distance. It is one of the most fundamental numbers in cosmology. It is also, at the moment, one of the most contested.

Two independent families of measurement — one anchored in the physics of the early universe, the other in the local distance ladder — give values of $H_0$ that disagree by approximately 5 standard deviations. This discrepancy, known as the Hubble tension, is either the most important unsolved problem in cosmology or an unusually persistent concatenation of systematic errors. Distinguishing between these possibilities requires understanding what assumptions each measurement rests on — and neutrino physics enters on both sides.

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The Two Measurements

The CMB inference. The Planck satellite measured the temperature and polarisation anisotropies of the cosmic microwave background with extraordinary precision. Within the standard flat $\Lambda$CDM cosmological model — six free parameters, a cosmological constant, and cold dark matter — the Planck data yield:

$H_0=67.36\pm 0.54\text{km/s/Mpc}\text{(Planck 2018)}$

This is not a direct measurement of the present expansion rate. It is an inference: given a model, the CMB peak positions, heights, and spacing constrain the angular diameter distance to the last scattering surface at $z\approx 1100$, the baryon density, and the matter density. $H_0$ is then derived from the remaining freedom in the model. The result is sensitive to the assumed cosmological model and to every species that contributes energy density during or before recombination.

The distance ladder. The local measurement proceeds in rungs. Cepheid variable stars, calibrated geometrically via parallax and eclipsing binaries in the Milky Way, provide distances to nearby galaxies. Those galaxies host Type Ia supernovae, which serve as standardizable candles at cosmological distances. The recession velocities of the host galaxies, divided by the Cepheid-calibrated distances, give $H_0$ directly, without reference to any cosmological model:

$H_0=73.04\pm 1.04\text{km/s/Mpc}\text{(SH0ES 2022, Riess et al.)}$

Independent local measurements using gravitational lensing time delays (H0LiCOW/TDCOSMO), the tip of the red giant branch (TRGB/CCHP), surface brightness fluctuations, and Mira variable stars give results scattered between approximately 69 and 74 km/s/Mpc, with most sitting above the Planck inference.

The discrepancy between the Planck and SH0ES anchors is $\Delta H_0\approx 5.7\text{km/s/Mpc}$, a $\sim 5\sigma$ tension assuming Gaussian errors. No identified systematic error in either measurement accounts for it.

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Where Neutrinos Enter

Neutrinos affect cosmological observables through several channels, each sensitive to a different aspect of their properties.

The Effective Number of Relativistic Species, $N_{\text{eff}}$

The Standard Model predicts $N_{\text{eff}}=3.044$ — three neutrino flavors, each contributing slightly less than one full relativistic species because neutrino decoupling is not perfectly instantaneous, allowing a small energy transfer from electron-positron annihilation into the neutrino sector. The precise value of 3.044 is a Standard Model prediction that can be verified by CMB observations.

The total radiation energy density in the early universe is parameterized as:

${\rho }_{\text{rad}}={\rho }_{\gamma }\left[1+\frac{7}{8}{\left(\frac{4}{11}\right)}^{4/3}{N}_{\text{eff}}\right]$

where ${\rho }_{\gamma }$ is the photon energy density. An excess $\Delta N_{\text{eff}}>0$ — from additional relativistic species such as a light sterile neutrino, a dark photon, or the relativistic decay products of a light particle — increases ${\rho }_{\text{rad}}$. This speeds up the expansion rate at fixed redshift and shifts the sound horizon at recombination:

$r_s\propto \frac{1}{\sqrt{{\rho }_{\text{tot}}(z_{\ast })}}\propto \frac{1}{\sqrt{H(z_{\ast }{)}^2}}$

A smaller sound horizon corresponds to higher CMB peak multipoles and, for fixed angular peak positions, to a larger $H_0$. A simple estimate gives:

$\Delta H_0\approx 1\text{km/s/Mpc per}\Delta N_{\text{eff}}\approx 0.2$

Closing the full 5.7 km/s/Mpc gap with $N_{\text{eff}}$ alone would require $\Delta N_{\text{eff}}\approx 1$ — equivalent to adding one additional light neutrino species. This is already excluded by Planck at high confidence: the CMB data constrain $N_{\text{eff}}=2.99\pm 0.17$ (Planck 2018 TT+TE+EE+lowE+lensing+BAO), and $\Delta N_{\text{eff}}=1$ is ruled out at $\sim 6\sigma$.

Smaller additions — $\Delta N_{\text{eff}}\sim 0.3$ — are still allowed within current error bars and would shift $H_0$ upward by roughly 1.5 km/s/Mpc, reducing but not eliminating the tension.

The Sum of Neutrino Masses, $\Sigma m_{\nu }$

Massive neutrinos affect the expansion history in a different way from $N_{\text{eff}}$. At early times, neutrinos with masses below the thermal energy at a given epoch ($m\lesssim 3kT(z)$) behave as radiation. As the universe cools below the neutrino mass, they transition to non-relativistic matter. This transition reduces the growth of large-scale structure on scales smaller than the free-streaming length:

${\lambda }_{\text{fs}}\approx 340\text{Mpc}\cdot \frac{1\text{eV}}{m_{\nu }}$

The matter power spectrum is suppressed on scales below ${\lambda }_{\text{fs}}$ by approximately $8\%$ per unit of $\Sigma m_{\nu }$ in eV. Baryon acoustic oscillation (BAO) surveys measuring the large-scale structure of the galaxy distribution are therefore sensitive to $\Sigma m_{\nu }$ through this suppression and through the shift in the matter-radiation equality redshift.

The interplay between $\Sigma m_{\nu }$ and $H_0$ in cosmological data is a degeneracy rather than a simple correlation. Increasing $\Sigma m_{\nu }$ requires decreasing the matter density ${\Omega }_m$ to maintain the BAO scale; this in turn allows a larger $H_0$ when fit to CMB data. The degeneracy is partially broken by CMB lensing and galaxy weak lensing, but residual correlation remains.

A counterintuitive consequence: Planck’s $H_0$ tension with the local measurements tightens the cosmological bound on $\Sigma m_{\nu }$. If $H_0$ were allowed to be larger (as the local measurements suggest), the preferred $\Sigma m_{\nu }$ would also shift, relaxing the neutrino mass bound. Conversely, fixing $H_0$ to the Planck-preferred value and constraining $\Sigma m_{\nu }$ from structure growth gives the tightest cosmological neutrino mass bounds — $\Sigma m_{\nu }<0.12\text{eV}$ at 95% CL (Planck 2018 + BAO) — but this bound weakens significantly if the Hubble tension is resolved by new early-universe physics that modifies the assumed cosmology.

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Proposed Solutions Involving Neutrino-Like Physics

Several proposed resolutions to the Hubble tension invoke physics in or near the neutrino sector.

Early Dark Energy

Early dark energy (EDE) models add a component of energy density that is significant around the epoch of matter-radiation equality ($z\sim 3000$) and dilutes away quickly afterward, mimicking an increase in $N_{\text{eff}}$ without requiring additional particle species. Many EDE models invoke a light axion-like field. The extra energy density reduces the sound horizon and raises the CMB-preferred $H_0$, at the cost of increasing ${\sigma }_8$ (the amplitude of matter fluctuations) in tension with weak lensing surveys.

EDE does not directly involve neutrinos, but it is degenerate with $\Sigma m_{\nu }$ in cosmological fits. If early dark energy is present, the inferred $\Sigma m_{\nu }$ from Planck data shifts — in some analyses toward values large enough to be in mild tension with oscillation lower bounds.

Interacting Neutrinos

In the Standard Model, neutrinos decouple from the photon-baryon plasma at $T\approx 2$ MeV, well before recombination. If neutrinos interact with a new light mediator — a light scalar or vector boson — they could remain partially coupled to the plasma to lower temperatures, modifying the damping tail of the CMB and the phase of BAO oscillations in ways that shift the inferred $H_0$.

Models of self-interacting neutrinos (SI$\nu$) have been studied as a possible resolution to the Hubble tension. In the strongly interacting regime, neutrinos that scatter on each other via a new interaction delay free-streaming; this modifies the CMB acoustic peaks at high multipoles and can shift $H_0$ upward. However, analyses using full Planck data find that this scenario is constrained by the CMB polarisation, and the strongly interacting mode is disfavored at $\sim 3$–$4\sigma$ when polarisation data are included.

Additional Light Sterile Neutrinos

A sterile neutrino with mass below $\sim 1$ eV that is thermalized in the early universe contributes $\Delta N_{\text{eff}}=1$ and is excluded by CMB data as discussed above. A sterile neutrino thermalized only partially — through a small mixing angle — contributes $\Delta N_{\text{eff}}<1$ and is constrained depending on its mixing and mass.

The constraints from BBN (Big Bang nucleosynthesis), which is sensitive to $N_{\text{eff}}$ at $T\sim 1$ MeV, and from CMB acoustic physics together limit the parameter space of light sterile neutrinos that could meaningfully shift $H_0$.

$N_{\text{eff}}$ from Dark Sector Thermalization

If a dark sector — a set of particles that interact with each other but not with Standard Model fields — thermalizes via its own interactions and contributes to the radiation energy density, it appears in cosmological data as an additional contribution to $N_{\text{eff}}$. The current constraint $N_{\text{eff}}=2.99\pm 0.17$ allows a dark sector contribution of up to $\Delta N_{\text{eff}}\approx 0.3$ at $1\sigma$. Future CMB experiments (CMB-S4, Simons Observatory) will constrain $N_{\text{eff}}$ to $\pm 0.05$, which will either detect or definitively exclude small contributions at the level of a partial thermalized species.

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The Constraint Side: Hubble Tension Bounds on Neutrino Mass

The Hubble tension creates an important meta-issue for the cosmological bound on $\Sigma m_{\nu }$. The bound of $\Sigma m_{\nu }<0.12\text{eV}$ from Planck 2018 is derived assuming the standard $\Lambda$CDM model with the Planck-preferred $H_0$. If the true $H_0$ is 73 km/s/Mpc and the discrepancy reflects new physics at early times, the inferred cosmological bound shifts.

Analyses that marginalize over the Hubble tension by including a free early dark energy component or by allowing $N_{\text{eff}}$ to vary find that the $\Sigma m_{\nu }$ bound relaxes to $\sim 0.3$–$0.5\text{eV}$ — a factor of three to four weaker than the standard result. This matters because it widens the gap between the cosmological bound and the direct laboratory bound from KATRIN ($m_{\nu }<0.45\text{eV}$), potentially even allowing the two to overlap.

In other words: if the Hubble tension is resolved by new early-universe physics, the cosmological neutrino mass bound weakens substantially, and the region of mass space accessible to KATRIN, Project 8, and HOLMES becomes cosmologically viable rather than excluded.

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The Outlook: CMB-S4 and DESI

Two programs will decisively sharpen this picture over the next decade.

CMB-S4 will measure $N_{\text{eff}}$ to a precision of $\sigma (N_{\text{eff}})\approx 0.025$ — sufficient to detect even a partial thermalization of a new light species, and to test the Standard Model prediction of 3.044 at the level of the electroweak correction. It will also measure $\Sigma m_{\nu }$ from CMB lensing with a sensitivity approaching the minimum mass implied by normal ordering ($\Sigma m_{\nu }\sim 0.06\text{eV}$), independent of the Hubble tension.

DESI (Dark Energy Spectroscopic Instrument) is already measuring the BAO scale across cosmic history with unprecedented precision. Its neutrino mass sensitivity comes from combining the redshift-dependent BAO scale with CMB data to separate the effects of $\Sigma m_{\nu }$, $H_0$, and ${\Omega }_m$. Preliminary DESI results have already provided competitive $\Sigma m_{\nu }$ bounds and will over the next few years break the degeneracy between the Hubble tension and neutrino mass more cleanly than any previous survey.

If CMB-S4 measures $N_{\text{eff}}>3.1$ at high significance, it will require new physics in the radiation content of the early universe — possibly but not necessarily involving neutrino-like particles. If it confirms $N_{\text{eff}}=3.044$ with small error bars and the local $H_0$ measurements remain at 73 km/s/Mpc, the Hubble tension will have survived every test and will point to a systematic error somewhere that no one has yet identified.

Either outcome will constrain neutrino physics. The tension may be a clue to new light species. Or it may be a reminder that even the most carefully constructed cosmological analyses rest on model assumptions that the universe is not obliged to satisfy.

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Related reading: the effective number of neutrino species from cosmology article covers $N_{\text{eff}}$ in detail. The cosmological neutrino mass bounds article discusses how structure formation constrains $\Sigma m_{\nu }$. The cosmic neutrino background article covers the relic neutrino sea that underpins the $N_{\text{eff}}$ concept.