What does it take to have $N_{ m eff} < 3$ at CMB times?

The vast majority of extensions of the Standard Model affecting the number of effective relativistic neutrino species ($N_{\rm eff}$) do so additively, namely, they enhance this quantity with some light state contributing to dark radiation. In this work, we consider precisely the opposite case: new physics scenarios that can lead to $N_{\rm eff} < 3$ that are consistent with all known cosmological, astrophysical, and laboratory data. We are motivated by three main reasons: 1) a recent measurement from ACT and SPT in combination with Planck that leads to $N_{\rm eff} = 2.81\pm0.12$, 2) by a new and powerful measurement of the primordial helium abundance, which anchors $N_{\rm eff}$ to be very close to the Standard Model value one second after the Big Bang, 3) by the deployment of the Simons Observatory which will provide precise tests of the radiation content in the Universe and which may detect with a high significance cosmologies with $N_{\rm eff}<3$. We survey the main theoretical possibilities and find that only a few simple scenarios can consistently give $N_{\rm eff}=2.81\pm0.12$. One class consists of thermal electrophilic relics with masses $m\sim 8!-!13,{\rm MeV}$. Another consists of out-of-equilibrium particles decaying to $e^+e^-$ or $γγ$, with a rather particular lifetime $0.05,{\rm s}\lesssim τ\lesssim 3,{\rm min}$, mass $250,{\rm MeV}\lesssim m \lesssim 600,{\rm MeV}$, and abundance $ρ/ρ_γ\sim 0.1$ at decay. Thermal electrophilic particles are especially interesting because they can account for the dark matter in the Universe and can be tested in experiments such as SENSEI, DAMIC-M, and Oscura. We conclude that if the Simons Observatory confirms that $N_{\rm eff} \simeq 2.8$, it will point to very specific extensions of the Standard Model.

💡 Research Summary

The paper addresses the intriguing possibility that the effective number of relativistic neutrino species, N_eff, could be significantly below the Standard Model (SM) prediction of ≈ 3.044. This interest is motivated by three recent developments: (i) a combined analysis of ACT, SPT and Planck data that yields N_eff = 2.81 ± 0.12, a ~2σ downward shift; (ii) a new, high‑precision measurement of the primordial helium abundance (Y_P = 0.2458 ± 0.0013) which translates into an early‑Universe expansion rate corresponding to N_ν = 2.93 ± 0.08, again close to but slightly below the SM value; and (iii) the upcoming Simons Observatory (SO), which aims for σ(N_eff) ≈ 0.045 and could confirm or refute a sub‑SM N_eff with high significance.

The authors first lay out the formal definition of N_eff and explain why any deviation from the SM value must arise from either (a) a reduction of the neutrino energy density ρ_ν, (b) an increase of the photon/electron/positron energy density ρ_γ, or (c) a combination of both. They systematically evaluate each route against existing laboratory, astrophysical, and cosmological constraints.

Reducing ρ_ν alone would require neutrinos to decouple earlier than in the SM, which in turn demands non‑standard neutrino‑charged‑lepton interactions that are tightly bounded, or a very low reheating temperature (T_R ≈ MeV) that would leave insufficient time for neutrinos to thermalize. Such low‑reheating scenarios, however, typically over‑heat the photon bath before Big‑Bang Nucleosynthesis (BBN), leading to helium and deuterium abundances in strong tension with observations. Consequently, the authors deem pure ρ_ν reduction implausible.

Increasing ρ_γ is more viable, but the timing of the energy injection is crucial. Neutrinos stay in thermal contact with the electromagnetic plasma down to T ≈ 2 MeV (t ≈ 0.1 s). Energy injected earlier than this is shared with neutrinos, raising N_eff instead of lowering it. Moreover, BBN tightly constrains any change in the baryon‑to‑photon ratio between nucleosynthesis (t ≈ 3 min) and recombination (t ≈ 380 kyr). An injection that would shift N_eff by ΔN_eff ≈ ‑0.2 must therefore occur in the narrow window 0.05 s ≲ t ≲ 100 s. Within this window, three concrete mechanisms are explored.

1. Thermal electrophilic relics (mass ≈ 8–13 MeV).
   A new particle that couples preferentially to electrons (and positrons) remains in thermal equilibrium with the electromagnetic plasma. It decouples after neutrinos have frozen out, and its subsequent annihilation or decay deposits entropy solely into photons and e⁺e⁻ pairs. This raises the photon temperature relative to the neutrino temperature, reducing N_eff to ≈ 2.8. Because the particle mass is close to the electron mass, the effect is sizable yet compatible with BBN: the extra entropy is injected after the neutron‑proton freeze‑out but before deuterium formation, preserving the observed helium and deuterium yields. The same particle can serve as dark matter; its electron‑scattering cross‑section falls within the reach of upcoming low‑threshold direct‑detection experiments such as SENSEI, DAMIC‑M, and Oscura.

2. Out‑of‑equilibrium decays to e⁺e⁻ or γγ (mass ≈ 250–600 MeV, lifetime ≈ 0.05 s–3 min).
   A heavier, metastable species (e.g., an axion‑like particle or a dark photon) is produced in the early Universe but decays well after neutrino decoupling. Its decay injects energetic electrons/positrons or photons, heating the electromagnetic plasma without re‑thermalizing the neutrinos. The authors map the viable region in the (m, τ) plane that yields ΔN_eff ≈ ‑0.2 while respecting BBN constraints (no over‑production of ⁴He), supernova cooling limits, and CMB spectral‑distortion bounds. The required abundance at decay is modest (ρ_X/ρ_γ ≈ 0.1), ensuring that the decay does not dominate the energy budget.

3. Combined ν‑γ manipulation (more elaborate models).
   The paper briefly mentions scenarios where a sterile neutrino or other dark sector state first extracts energy from the neutrino bath and later decays preferentially into photons. While theoretically possible, such constructions demand finely tuned temperature‑dependent mixings and are left for future work.

The authors perform detailed Boltzmann‑code calculations (modifying CLASS) to track the evolution of T_γ/T_ν and the resulting N_eff for each model. They confront the predictions with current data: the helium measurement forces N_eff ≈ 2.93 at t ≈ 1 s, while the ACT+SPT+Planck result prefers N_eff ≈ 2.81 at recombination. Both thermal electrophilic relics and the specified decaying particles can interpolate between these two epochs, delivering a consistent picture.

Finally, the paper emphasizes the experimental outlook. The Simons Observatory’s projected sensitivity (σ ≈ 0.045) would be sufficient to confirm a N_eff ≈ 2.8 at >5σ, effectively ruling out the SM value if the low‑N_eff scenario is realized. Moreover, the electrophilic relics can be probed directly in laboratory searches for sub‑GeV dark matter, while the decaying particle scenario could leave imprints in future CMB spectral‑distortion missions (e.g., PIXIE) or in precise measurements of the cosmic neutrino background.

In summary, the work identifies two minimal and experimentally testable extensions of the Standard Model—thermal electrophilic particles of ~10 MeV mass and out‑of‑equilibrium decays of ~300 MeV particles with lifetimes of seconds to minutes—that can naturally produce N_eff ≈ 2.8 while satisfying all current cosmological, astrophysical, and laboratory constraints. Confirmation of such a low N_eff by the Simons Observatory would point decisively toward these specific new‑physics avenues.