Cosmic neutrinos

Neutrinos are among the most abundant particles in the universe, second only to photons. Every cubic centimetre of space contains approximately 336 relic neutrinos left over from the earliest moments of the Big Bang, forming a pervasive cosmic neutrino background (CNB or CνB) analogous to the cosmic microwave background (CMB) of photons but far more difficult to detect. The existence of this relic neutrino population is a firm prediction of Big Bang cosmology, and although the CNB has never been directly observed, its influence on primordial nucleosynthesis, on the anisotropy pattern of the CMB, and on the growth of large-scale cosmic structure provides robust indirect confirmation of its presence.^{1, 3} Beyond the relic background, neutrinos are produced copiously in stellar nuclear reactions, supernova explosions, and high-energy astrophysical phenomena, making them messengers that carry information from environments opaque to light and providing a unique window onto some of the most extreme processes in the cosmos.^{6, 15}

The neutrino

The neutrino was first postulated by Wolfgang Pauli in 1930 to explain the continuous energy spectrum of electrons emitted in nuclear beta decay, which would violate energy conservation if the electron were the only particle emitted. Enrico Fermi incorporated Pauli's hypothetical particle into a successful theory of beta decay in 1934 and gave it its name. The neutrino was finally detected experimentally in 1956 by Clyde Cowan and Frederick Reines, who observed the inverse beta-decay reaction of antineutrinos from a nuclear reactor interacting with protons in a tank of cadmium-doped water.¹⁰

There are three known flavours of neutrino, each associated with a charged lepton: the electron neutrino (ν_e), the muon neutrino (ν_μ), and the tau neutrino (ν_τ). Each has a corresponding antineutrino. Neutrinos interact with other matter only through the weak nuclear force and gravity, making them extraordinarily difficult to detect. A neutrino produced in the Sun's core can pass through the entire Earth with a probability of interaction of roughly one in ten billion.⁷

The discovery of neutrino oscillations, the quantum-mechanical phenomenon in which neutrinos change flavour as they propagate, demonstrated that neutrinos have non-zero masses, contrary to the original Standard Model assumption. The Super-Kamiokande experiment in 1998 provided the first definitive evidence for atmospheric neutrino oscillations, and subsequent experiments with solar, reactor, and accelerator neutrinos have confirmed oscillations among all three flavours.⁵ Oscillation experiments measure the differences between the squared masses of the three neutrino mass eigenstates but cannot determine the absolute mass scale, which remains one of the outstanding problems in particle physics.⁷

The cosmic neutrino background

In the first second after the Big Bang, the universe was a dense, hot plasma in which neutrinos were kept in thermal equilibrium with electrons, positrons, and photons through rapid weak-interaction processes. As the universe expanded and cooled, the rate of these weak interactions fell below the Hubble expansion rate at a temperature of approximately 1 MeV (roughly 10¹⁰ kelvin), corresponding to an age of about one second. At this point, neutrinos decoupled from the plasma and began streaming freely through the universe, their energy distribution frozen at the thermal spectrum corresponding to the decoupling temperature.^{1, 14}

Shortly after neutrino decoupling, at a temperature of about 0.5 MeV, electron-positron annihilation heated the photon plasma but not the already-decoupled neutrinos, creating a temperature difference between the photon background and the neutrino background that persists to the present day. The relationship between the two temperatures is T_ν = (4/11)^1/3 T_γ. Given the current CMB temperature of 2.725 kelvin, the predicted temperature of the cosmic neutrino background is approximately 1.95 kelvin, corresponding to a mean neutrino energy of about 5 × 10⁻⁴ eV per neutrino.^{1, 14}

The predicted number density of relic neutrinos is approximately 112 per cubic centimetre per flavour, or 336 per cubic centimetre for all three flavours combined (plus their antiparticles). This makes the CNB one of the most abundant known components of the universe by particle number, yet its direct detection remains beyond current experimental capabilities because the interaction cross-section of sub-meV neutrinos is vanishingly small.^{1, 16}

Indirect evidence for the CNB

Although no experiment has directly detected the cosmic neutrino background, its existence is confirmed by multiple independent lines of indirect evidence that are sensitive to the number and properties of light relic particles in the early universe.

Big Bang nucleosynthesis. The primordial abundances of light elements, particularly helium-4 and deuterium, depend sensitively on the expansion rate of the universe during the epoch of primordial nucleosynthesis (roughly 1 to 200 seconds after the Big Bang). Each additional species of light neutrino increases the energy density and hence the expansion rate, which in turn increases the neutron-to-proton ratio at the time of nucleosynthesis and raises the predicted helium-4 abundance. The observed primordial helium abundance of approximately 24.5 percent by mass is consistent with the standard model prediction for three neutrino species and excludes, at high confidence, the possibility that fewer than two or more than four light neutrino species were present.⁴

Cosmic microwave background. The number of relativistic species present before and during photon decoupling affects the CMB power spectrum in several ways: it changes the damping tail of the anisotropy spectrum at high multipoles, shifts the positions and heights of the acoustic peaks, and alters the epoch of matter-radiation equality. The Planck satellite's measurement of the CMB anisotropies yields an effective number of neutrino species N_eff = 2.99 ± 0.17, in excellent agreement with the Standard Model prediction of N_eff = 3.044 (the small excess above 3 arises from residual neutrino heating during electron-positron annihilation).^{3, 14}

These two independent measurements, one probing the universe at an age of seconds and the other at an age of 380,000 years, converge on the same conclusion: three species of light neutrinos existed in the early universe with the thermal properties predicted by standard cosmology.^{1, 3}

Neutrino mass and cosmological constraints

The discovery of neutrino oscillations established that neutrinos have mass, but oscillation experiments measure only the differences between squared masses, not the absolute masses themselves. The two measured squared-mass differences are Δm²₂₁ ≈ 7.5 × 10⁻⁵ eV² (solar) and |Δm²₃₁| ≈ 2.5 × 10⁻³ eV² (atmospheric), which imply that the sum of the three neutrino masses Σm_ν must be at least approximately 0.06 eV in the normal hierarchy or approximately 0.1 eV in the inverted hierarchy.⁷

Cosmological observations provide the most stringent upper bounds on the sum of neutrino masses, because even tiny neutrino masses have measurable effects on the growth of cosmic structure. Massive neutrinos stream freely out of gravitational potential wells on scales smaller than their free-streaming length, suppressing the growth of matter density perturbations on those scales. This suppression is proportional to the fraction of the total matter density contributed by neutrinos, which depends on Σm_ν. The effect is detectable in the matter power spectrum measured by galaxy surveys and in the CMB lensing signal.^{2, 8}

The Planck 2018 analysis, combining CMB temperature and polarisation data with CMB lensing, yields an upper bound of Σm_ν < 0.12 eV at 95 percent confidence, among the tightest constraints available.³ When combined with baryon acoustic oscillation measurements from galaxy surveys, this bound tightens further. These cosmological limits are considerably more restrictive than the best direct laboratory measurement from the KATRIN experiment, which established an upper limit on the electron antineutrino mass of 0.8 eV (at 90 percent confidence) from the endpoint of the tritium beta-decay spectrum.¹¹

Constraints on the sum of neutrino masses^{3, 7, 11}

Astrophysical neutrinos

In addition to the relic background, neutrinos are produced by numerous astrophysical sources throughout the observable universe. The Sun produces approximately 2 × 10³⁸ electron neutrinos per second through the nuclear fusion reactions in its core, and roughly 65 billion solar neutrinos pass through every square centimetre of the Earth's surface every second. The detection of solar neutrinos, beginning with Raymond Davis's pioneering chlorine experiment in the 1960s, provided the first observational confirmation that the Sun is powered by nuclear fusion and, through the "solar neutrino problem" (a measured deficit relative to theoretical predictions), eventually led to the discovery of neutrino oscillations.⁶

Core-collapse supernovae are the most prolific astrophysical neutrino sources. When a massive star exhausts its nuclear fuel and its iron core collapses to form a neutron star or black hole, approximately 99 percent of the roughly 3 × 10⁵³ ergs of gravitational binding energy released is carried away by neutrinos of all flavours, emitted in a burst lasting approximately 10 seconds. The detection of 24 neutrinos from Supernova 1987A in the Large Magellanic Cloud by the Kamiokande-II and IMB detectors on 23 February 1987 provided the first direct observation of neutrinos from a supernova, confirming the basic theory of core collapse and establishing neutrino astronomy as an observational discipline.⁹

The cumulative neutrino emission from all past core-collapse supernovae throughout cosmic history forms a diffuse supernova neutrino background (DSNB), a faint, isotropic flux of electron antineutrinos with energies of roughly 10 to 30 MeV. The DSNB has not yet been definitively detected, but the Super-Kamiokande experiment, upgraded with gadolinium loading to improve neutron tagging, is approaching the sensitivity needed for a first detection.¹³

At the highest energies, the IceCube Neutrino Observatory at the South Pole, which instruments a cubic kilometre of Antarctic ice with optical sensors, has detected high-energy astrophysical neutrinos with energies ranging from tens of TeV to several PeV. These neutrinos are believed to originate from the most energetic environments in the universe, including active galactic nuclei, gamma-ray bursts, and starburst galaxies. In 2018, IceCube identified the blazar TXS 0506+056 as a likely source of a 290 TeV neutrino, marking the beginning of high-energy neutrino source identification.¹⁵

Prospects for direct CNB detection

Directly detecting the cosmic neutrino background is one of the grand challenges of experimental physics. The energy of relic neutrinos, approximately 0.0005 eV, is billions of times lower than the energies of neutrinos from nuclear reactors or the Sun, and the interaction cross-section at these energies is correspondingly minuscule. No existing technology is remotely sensitive enough to detect individual relic neutrino interactions.^{1, 16}

The most promising proposed approach is the PTOLEMY experiment, which would attempt to detect relic neutrinos through their capture on tritium nuclei: ν_e + ³H → ³He + e⁻. In this reaction, the emitted electron carries slightly more energy than the endpoint energy of ordinary tritium beta decay, producing a tiny spectral feature at 2m_ν above the endpoint. Detecting this feature would require an energy resolution of order 0.1 eV, a target mass of approximately 100 grams of tritium, and the ability to distinguish the signal from the overwhelming background of ordinary beta-decay electrons. These requirements are extraordinarily challenging with current technology, but the experiment represents the most concrete path toward a direct CNB detection.¹⁶

Cosmological significance

Neutrinos play a role in cosmology that is disproportionate to their tiny masses. They contributed significantly to the radiation energy density of the early universe, affecting the expansion rate during primordial nucleosynthesis and during the epoch when the CMB anisotropies were imprinted. Their transition from relativistic to non-relativistic behaviour as the universe cooled altered the growth of cosmic structure, leaving detectable signatures in the distribution of galaxies and in the CMB lensing signal. And their mass, even at the sub-eV level, affects the late-time expansion history and the total matter budget of the universe.^{1, 2, 8}

The interplay between neutrino physics and cosmology flows in both directions. Cosmological observations constrain neutrino properties more tightly than any laboratory experiment for the absolute mass scale, the number of species, and possible interactions with dark sectors. Conversely, the measured properties of neutrinos constrain cosmological models, ruling out or supporting particular scenarios for dark matter, dark energy, and the thermal history of the early universe. The cosmic neutrino background, though invisible to current detectors, exerts a gravitational influence on every structure in the universe, from the largest galaxy clusters down to the distribution of matter in the cosmic web, a silent but consequential presence woven into the fabric of the cosmos.^{2, 12}