Cosmology fits to neutrino masses

Cosmology fits to neutrino masses 30th September, 2025 XXI International Workshop on Neutrino Telescopes Padova INFN and Department of Physics and Astronomy Eleonora Di Valentino Royal Society Dorothy Hodgkin Research Fellow School of Mathematics and Statistics University of Sheffield (UK) Neutrinos are the last particles of the Standard Model whose masses are unknown. To constrain their total mass using cosmological data, we rely on the Cosmic Neutrino Background at early times and the growth of structure at late times. Therefore, the main cosmological probes that we can use are the Cosmic Microwave Background and the Large Scale Structure data. With the cosmological data, we can place constraints not only on the total neutrino mass, but also on the neutrino effective number. Why do we care about Σmν from cosmology? Because it is the only way we can currently probe sub-eV masses, and these results already challenge what we expect from oscillation experiments. Neutrino physics and cosmology 2 The Universe originates from a hot Big Bang. The primordial plasma in thermodynamic equilibrium cools with the expansion of the Universe. It goes through the phase of recombination, during which electrons and protons combine to form neutral hydrogen, and decoupling, where the Universe becomes transparent to the motion of photons. The Cosmic Microwave Background (CMB) is the radiation coming from recombination, emitted about 13 billion years ago, just 380,000 years after the Big Bang. Figura: http://wmap.gsfc.nasa.gov CMB constraints 3 Planck collaboration, 2018 The CMB retains the shape of the primordial universe in which photons were in thermodynamic equilibrium, exhibiting a thermal blackbody spectrum that has cooled with the expansion of the universe, reaching a temperature of T=2.725K today. This radiation coming from all directions is almost homogeneous, but also offers an image of the minuscule density differences present at recombination and bears witness to everything that happened to photons as they traveled to us. These effects result in small temperature variations among the photons themselves, on the order of 1/100000, known as anisotropies. 4 Wuensche & Villa, arXiv:1002.4902 Planck 2018, Astron.Astrophys. 641 (2020) A6 5 5 Borstnik et al., hep-ph/0401043 We can extract 4 independent angular spectra from the CMB: •Temperature •Cross Temperature Polarization E •Polarization type E (density fluctuations) •Polarization type B (gravitational waves) Cosmological parameters: (Ωbh2 , Ωmh2 , H0 , ns , τ, As ) Theoretical model We choose a set of cosmological parameters that describes our theoretical model and compute the angular power spectra. Because of the correlations present between the parameters, variation of different quantities can produce similar effects on the CMB. Lemos & Shah, arXiv:2307.13083 6 We compare the angular power spectra we computed with the data and, using a bayesian analysis, we get a combination of cosmological parameter values in agreement with these. Cosmological parameters: (Ωbh2 , Ωmh2 , H0 , ns , τ, As ) Theoretical model Parameter constraints Planck 2018, Astron.Astrophys. 641 (2020) A6 7 Satellite CMB telescopes Ground based CMB telescopes 8 • The cosmological constraints are obtained assuming a cosmological model. • The results are affected by the degeneracy between the parameters that induce similar effects on the observables. CMB constraints 9 SPT-3G D1, arXiv:2506.20707 [astro-ph.CO] The CMB lensing A simulated patch of CMB sky – before dark matter lensing 16 The CMB lensing A simulated patch of CMB sky – after dark matter lensing 17 The total neutrino mass and the CMB However, these effects are strongly degenerate with other cosmological parameters, so how can the CMB set strong constraints on Σmν? This happens because of another secondary source of anisotropies: the CMB lensing. This affects the CMB anisotropy angular spectrum by smearing the high l peaks. Total neutrino mass Planck 2018, Aghanim et al., arXiv:1807.06209 [astro-ph.CO] From CMB we have a very important upper limit on the total neutrino mass. SPT-3G D1, arXiv:2506.20707 [astro-ph.CO] When neutrinos become non-relativistic, will only cluster at scales larger than their free streaming scale, suppressing therefore structure formation at small scales, and affecting the large scale structures. The main LSS observables are the power spectrum of the matter fluctuations in Fourier space Or the two-point correlation function in the configuration space The total neutrino mass and the LSS Whitford et al., arXiv:2112.10302 Chen & Xu, Phys.Lett.B 752 The shape of the matter power spectrum is the key observable for constraining the neutrino masses with cosmological methods. This is defined as the two-point correlation function of the total non-relativistic matter fluctuation in Fourier space: Matter power spectrum Neutrinos with sub-eV masses are hot thermal relics with very large thermal velocity exceeding the escape velocity of the gravitational potentials. Therefore they cluster only at scales larger than their free streaming scale. Massive neutrinos will suppress the structure formation at small scales, affecting the large scale structures (LSS). On larger scales, they cluster in the same way as cold dark matter. Whitford et al., arXiv:2112.10302 Growth rate of structure 22 Matter power spectrum Chabanier et al, arXiv:1905.08103 Abazajian et al., Astropart.Phys. 63 (2015) 66-80 The power spectrum of total matter fluctuations can be obtained using measurements of CMB lensing, galaxy clustering and weak lensing, and the number density of galaxy clusters. 23 Matter power spectrum Green & Meyers, arXiv:2111.01096 The total neutrino mass and the LSS At k > 0.1h/Mpc, we begin to see deviations from the linear evolution, so the perturbation theory breaks down and we need N-body simulations (Elbers et al. MNRAS 2021/2022) or beyond perturbative regime (Effective Field Theory of Large-Scale Structure) to analyse the data. 24 Planck collaboration, arXiv:1807.06210 The total neutrino mass and the LSS CMB lensing can be measured also in a different way, i.e. using the trispectrum (or four-point correlation function) of the CMB maps, resulting in a 40σ measurement of the lensing signal. 25 The total neutrino mass and RSD eBOSS collaboration, Alam et al., Phys.Rev.D 103 (2021) 8, 083533 This RSD effect modifies the galaxy power spectrum and allows for an extraction of the product of the growth rate of structure (f) times the clustering amplitude of the matter power spectrum (σ8), the well-known fσ8 observable. We can see in the figure that massive neutrinos prefer a lower value for the fσ8 data. 32 Before DESI, the most constraining upper bounds was Σmν < 0.087 eV at 95% CL for a combination of all the available data. The total neutrino mass and RSD Di Valentino et al., Phys.Rev.D 104 (2021) 8, 083504 Here we illustrate the theoretical expectations within each mass ordering for the three observables of neutrino masses: beta-decay (mβ), neutrinoless double beta decay mββ and the cosmological measured quantity Σmν. The light green horizontal band represents the most constraining bound before DESI, which is Σmν < 0.087 eV at 95% CL. This very tight limit has crucial implications for direct neutrino mass laboratory searches, suggesting that they are not expected to detect any signal. Constraints on the total neutrino mass Di Valentino et al., Phys.Rev.D 104 (2021) 8, 083504 35 What about external datasets ? The BAO peak of the galaxy correlation function, corresponding to the acoustic scale at decoupling, is one of the prominent observables in present day cosmology, and is very sensitive to massive neutrinos. New DESI BAO measurements Credit: Arnaud de Mattia, CEA Saclay 36 DESI collaboration, Abdul Karim et al., arXiv:2503.14738 New DESI BAO measurements 37 Tightest neutrino mass constraints Wang, Mena, Di Valentino and Gariazzo, Phys.Rev.D 110 (2024) 10, 103536 The tightest bound we find here is Σmν < 0.043 eV at 95% CL after combining Planck CMB with DESI BAO, Type Ia Supernovae, Gamma Ray Bursts, cosmic chronometers, and galaxy clusters, highlighting a clear tension between neutrino oscillation measurements and cosmological constraints. The light green horizontal band represents the most constraining bound after DESI, which is Σmν < 0.072 eV at 95% CL, while the yellow band indicates the tightest bound available in the literature after combining with other cosmological probes, which is Σmν < 0.043 eV at 95% CL, significantly below the minimal value allowed by oscillation data. Constraints on the total neutrino mass 38 Wang, Mena, Di Valentino and Gariazzo, Phys.Rev.D 110 (2024) 10, 103536 Constraints on the total neutrino mass 39 SPT-3G D1, arXiv:2506.20707 [astro-ph.CO] At this point, we should discuss mass ordering. Even though the absolute masses of neutrinos ν are unknown, lower bounds on the total neutrino mass are established through global analyses of oscillation data. These analyses provide the best-fit values for the standard model mass splitting. Neutrino mass ordering By setting the lightest neutrino mass to zero, we can determine the lower bounds on the total neutrino mass for the normal or inverted ordering: Qian and Vogel, arXiv:1505.01891 40 The upper bounds obtained are strongly dependent on the choice of the prior for Σmν used in the cosmological analysis. Neutrino mass ordering DESI collaboration, Elbers et al., arXiv:2503.14744 48 1. A flat ΛCDM model is in agreement with the data In a Bayesian framework, all models can, in principle, agree with the data. What matters is whether they are disfavoured due to a poor fit or because another model is preferred. Therefore, to me, this means that ΛCDM provides a good fit to the data and shows no clear signs of deviation, even when extended. However, currently the cosmological parameters inferred from different probes are not the same. This means ΛCDM appears differently depending on the dataset! 49 But what does it mean that ΛCDM agrees well with each probe? 50 Tensions and Disagreements in ΛCDM CamSpec CamSpec DESI collaboration, Abdul Karim et al., arXiv:2503.14738 The same ΛCDM cannot fit 2 datasets together! 51 Tensions and Disagreements in ΛCDM CamSpec CamSpec The same ΛCDM cannot fit 2 datasets together! SPT-3G D1, arXiv:2506.20707 [astro-ph.CO] 52 CMB tension in ΛCDM ACT collaboration, Louis et al., arXiv:2503.14452 CamSpec CamSpec 53 2. Indication for DDE DESI collaboration, Abdul Karim et al., arXiv:2503.14738 54 DESI collaboration, Elbers et al., arXiv:2503.14744 3. Indication for negative neutrino mass However, introducing more freedom in the DE sector, and in particular considering a dynamical DE as preferred by the BAO DESI data, we can restore larger neutrino masses, more in agreement with laboratory data. Elbers al., arXiv:2407.10965 55 3. Indication for negative neutrino mass Planck 2018, Astron.Astrophys. 641 (2020) A6 The Planck estimate assuming a “vanilla" ΛCDM cosmological model: H0 = 67.36 ± 0.54 km/s/Mpc Riess et al. arXiv:2112.04510 The latest local measurements obtained by the SH0ES collaboration H0 = 73.04 ± 1.04 km/s/Mpc 5σ = one in 3.5 million implausible to reconcile the two by chance 56 4. H0 tension The H0 tension is the most statistically significant, long-lasting and widely persisting disagreement between: The H0 tension is the most statistically significant, long-lasting and widely persisting disagreement between: Planck 2018, Astron.Astrophys. 641 (2020) A6 The Planck estimate assuming a “vanilla" ΛCDM cosmological model: H0 = 67.36 ± 0.54 km/s/Mpc Riess et al. arXiv:2112.04510 The latest local measurements obtained by the SH0ES collaboration H0 = 73.04 ± 1.04 km/s/Mpc 5σ = one in 3.5 million implausible to reconcile the two by chance 57 6.7 sigma 4. H0 tension There is a very strong positive correlation , between Alens and the total neutrino mass. Therefore, to be conservative, we need to take into account this wrong amount of lensing when constraining Σmν. Choudhury and Hannestad, arXiv:1907.12598 [astro-ph.CO] 64 5. AL problem For example, when Alens is free to vary, because of their correlation, the bounds on the total neutrino mass are strongly weakened, up to a factor of ∼3. Capozzi et al., Phys.Rev.D 111 (2025) 9, 093006 65 5. AL problem Neutrino mass profile likelihoods using the full Planck temperature and polarization data in the ΛCDM model, while allowing the unphysical AL parameter to vary, show that the bounds are significantly relaxed. Naredo-Tuero et al., arXiv:2407.13831 66 5. AL problem 6. The optical depth Reionization leaves an imprint on the large-scale CMB E-mode polarization (EE) and causes a suppression of temperature anisotropies at smaller scales (proportional to Ase−2τ). $ Planck measured τ = 0.054 ± 0.008 at 68% CL, $ a significant improvement over the $ WMAP9 value of τ = 0.089 ± 0.014. $ However, the low-ℓ EE signal is extremely weak, in the cosmic variance limited region, $ and close to the detection threshold. $ We tested the EE spectrum: fitting it with a flat line (i.e., no reionization bump) $ yields a p-value of 0.063. $ If we focus only on data points at 2 ≤ l ≤ 15, the case C=0 (no signal) falls within the 1σ range. $ This raises concerns that measurements near the noise level may be significantly affected by statistical fluctuations or foreground uncertainties. 67 Giarè, Di Valentino, Melchiorri, Phys.Rev.D 109 (2024) 10, 103519 In the CMB TT spectrum, massive neutrinos suppress small-scale power, which can be compensated by increasing the optical depth τ. Since TT measures Ase−2τ, raising τ requires raising As, but As also controls structure growth, that is entangled with Σmν effects. This degeneracy means CMB-only data allow biased Σmν values; low-ℓ polarization is essential to pin down τ and break the degeneracy. Jhaveri et al., arXiv:2504.21813 The apparent CMB+BAO preference for negative neutrino masses could be an artifact of the τ–Σmν degeneracy. Allowing either a free lensing amplitude AL or dropping low-ℓ EE τ constraints both restore consistency with minimal neutrino masses. In other words: the “negative neutrino mass” problem disappears if τ is allowed to rise, highlighting that τ systematics strongly impact cosmological neutrino mass bounds. 6. The optical depth Conclusions: Cosmology now probes relics and interactions beyond the reach of laboratory experiments, offering unique access to the total neutrino mass. The tightest cosmological bound on the sum of neutrino masses is Σmν < 0.043 eV (95% CL), and this value is in tension with neutrino oscillation experiments. At the same time, persistent anomalies challenge the ΛCDM framework: • The >6σ H₀ tension • The CMB lensing anomaly (AL > 1) • Low optical depth, possible negative Σmν, and hints of DDE Why does it matter? If tensions reflect new physics, or they’re due to systematics, then the tight neutrino bounds we’ve quoted may be misleading. Either way, we need to understand them. Precision cosmology is only meaningful when the data are internally consistent and trustworthy. Otherwise, we risk confusing artifacts for discoveries, and turning “precision” into a false sense of certainty. We must let the data speak honestly, even if that means questioning our models, methods, or assumptions, before claiming to measure the universe to percent-level accuracy. Thank you! [email protected] https://cosmoversetensions.eu/ 70