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Massive sterile neutrinos in the early universe: From thermal decoupling to cosmological constraints
High Energy Physics - Phenomenology · Submitted 23 Apr 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We also identify the parameter space allowed by current Planck satellite data and forecast the parameter space probed by future Stage-4 ground-based CMB observations, expected to match or surpass BBN sensitivity.
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The abstract, sentence by sentence
We consider relatively heavy neutrinos $\nu_H$, mostly contributing to a sterile state $\nu_s$, with mass in the range 10 MeV $\lesssim m_s \lesssim m_{\pi} \sim 135$ MeV, which are thermally produced in the early universe in collisional processes involving active neutrinos, and freezing out after the QCD phase transition. If these neutrinos decay after the active neutrino decoupling, they generate extra neutrino radiation, but also contribute to entropy production. Thus, they alter the value of the effective number of neutrino species $N_{\rm eff}$ as for instance measured by the cosmic microwave background (CMB), as well as affect primordial nucleosynthesis (BBN), notably ${}^4$He production. We provide a detailed account of the solution of the relevant Boltzmann equations. We also identify the parameter space allowed by current Planck satellite data and forecast the parameter space probed by future Stage-4 ground-based CMB observations, expected to match or surpass BBN sensitivity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider relatively heavy neutrinos $\nu_H$, mostly contributing to a sterile state $\nu_s$, with mass in the range 10 MeV $\lesssim m_s \lesssim m_{\pi} \sim 135$ MeV, which are thermally produced in the early universe in collisional processes involving active neutrinos, and freezing out after the QCD phase transition. | contribution 0.76 | 0.29 | 0.06 | asserted 0.96 |
| s1 | If these neutrinos decay after the active neutrino decoupling, they generate extra neutrino radiation, but also contribute to entropy production. | background 0.42 | 0.15 | 0.07 | asserted 0.56 |
| s2 | Thus, they alter the value of the effective number of neutrino species $N_{\rm eff}$ as for instance measured by the cosmic microwave background (CMB), as well as affect primordial nucleosynthesis (BBN), notably ${}^4$He production. | interpretation 0.62 | 0.18 | 0.17 | asserted 0.94 |
| s3 | We provide a detailed account of the solution of the relevant Boltzmann equations. | method 0.73 | 0.93 | 0.04 | asserted 0.97 |
| s4 | We also identify the parameter space allowed by current Planck satellite data and forecast the parameter space probed by future Stage-4 ground-based CMB observations, expected to match or surpass BBN sensitivity. | contribution 0.66 | 0.88 | 0.37 | asserted 0.57 |
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The paper
Original abstract
We consider relatively heavy neutrinos $\nu_H$, mostly contributing to a sterile state $\nu_s$, with mass in the range 10 MeV $\lesssim m_s \lesssim m_{\pi} \sim 135$ MeV, which are thermally produced in the early universe in collisional processes involving active neutrinos, and freezing out after the QCD phase transition. If these neutrinos decay after the active neutrino decoupling, they generate extra neutrino radiation, but also contribute to entropy production. Thus, they alter the value of the effective number of neutrino species $N_{\rm eff}$ as for instance measured by the cosmic microwave background (CMB), as well as affect primordial nucleosynthesis (BBN), notably ${}^4$He production. We provide a detailed account of the solution of the relevant Boltzmann equations. We also identify the parameter space allowed by current Planck satellite data and forecast the parameter space probed by future Stage-4 ground-based CMB observations, expected to match or surpass BBN sensitivity.
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References
How the literature uses it
23 arXiv papers cite this in 33 sentences
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We provide a detailed account of the solution of the relevant Boltzmann equations and we identify the parameter space constrained by current Planck satellite data and forecast the parameter space probed by future Stage-4 ground-based CMB (CMB-S4) observations.
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These results, however, contradicted Ref. [ref] (see also [ref] ), which studied the same setup with HNLs with masses below the pion mass and found that $N_eff$ may only increase.
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In this figure we include other relevant constraints from the other supernova arguments (green shaded region enclosed by dotted line) [ref] , BBN & CMB assuming the standard cosmology (light-gray shaded region) [ref] and experiments (dark-gray shaded region) [ref] .
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For comparison we show that these small mixing parameters can be probed only with cosmological arguments, evaluating the impact of $ν_s$ decays on Big-Bang Nucleosynthesis (BBN) and on the effective number of neutrino species $N_eff$ [ref] (blue area).
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In particular, any modifications of the standard evolution in the period when neutrinos decouple from the thermal bath at temperatures $T ≲5 MeV$ can alter primordial neutrino properties [ref] , which then may affect key cosmological observables, including primordial nuclear abundances [ref] , Cosmic Microwave Background (CMB) [ref] , and constraints on neutrino masses [ref] .
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These can be broadly classified into non-standard neutrino interactions [ref] , where neutrinos interact with new light mediators, altering their decoupling and thermal history; scenarios involving a neutrino-antineutrino asymmetry [ref] , leading to differences in the number densities of neutrinos and antineutrinos; and models introducing decaying new physics particles, often referred to as long-lived particles (LLPs) [ref] .
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* $𝐦^𝐞𝐟𝐟_ν,𝐬𝐭𝐞𝐫𝐢𝐥𝐞$ is the effective mass of sterile neutrinos [ref] .
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In particular, contrarily to the results of [ref] , we always obtain $ΔN_eff>0$ for the parameter space of interest.
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In conclusion, to the best of our knowledge, we attribute our departure from the results in [ref] on the CMB constraints at large masses to some unidentified systematics, probably the same effects responsible for the “universal” $ΔN_eff<0$ outcome described in [ref] which appears unphysical, for the reasons detailed above.
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A precise standard model calculation, $Y_p, SM^prec$, for the best-fit cosmological parameter $Ω_bh^2=0.02225$ [ref] with a number of subtle effects included (see [ref] for details), is available from [ref] .
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Our BBN constraints are largely consistent with recent calculations presented in [ref] , while our CMB constraints are consistent with theirs at low masses, while more stringent than theirs at high masses.
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We repeated the derivation of [ref] under these approximation, finding: [equation] and [equation] in agreement with their results quoted as
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[This is explicitly shown in their Eq. (D.1), where their factor two larger value in $|M|^2$ is compensated by the further $1/g$ in their integral prefactor, $g=2$ being the spin multiplicity.] In relation instead to the Ref. [ref] , we find systematically lower matrix elements compared to their Tables 1, 2, by a factor 2.
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