REVIEW
The oscillation effects on thermalization of the neutrinos in the universe with low reheating temperature
Astrophysics · Submitted 19 May 2005 · 56 references
Pith's verdict: The sign reversal of the Yp–TR relation is a real and useful result, but the quoted 2 MeV bound is softer than the paper's framing implies.
T0 · AI review
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Referee report
The paper
The paper claims
Neutrino flavor mixing reverses the predicted trend of primordial helium-4 with the reheating temperature, tightening the lower bound on reheating to about 2 MeV.
The reading
What carries the argument
The load-bearing object is the $2 times 2$ neutrino density matrix $rho_p$ in flavor space, expanded in Pauli matrices as $rho_p = sum_i P_i(p), sigma_i/2$, whose diagonal entries are the $nu_e$ and $nu'_mu$ occupation numbers and whose off-diagonal entries carry the flavor coherence. Its evolution is governed by $H a, d rho_p/d a = -i[Omega(p), rho_p] + I_{rm coll}(p)$, where $Omega$ contains the vacuum oscillation term built from the solar mass splitting and mixing angle plus a refractive term from $W$-exchange with the electron-positron plasma, and $I_{rm coll}$ encodes $nu + e^pm leftrightarrow nu + e^pm$ and $nu + barnu leftrightarrow e^- + e^+$ with the spin-dependent $G_L$, $G_R$ couplings. Setting the reactor angle to zero lets the three-flavor problem collapse to this two-flavor system plus a decoupled $nu'_tau$ that is tracked with the no-mixing collision term. The resulting spectra are then passed to a BBN code with modified $n leftrightarrow p$ rates and a modified photon-temperature evolution equation.
Extended reading notes
Core claim
The paper's central claim is that neutrino oscillations change the sign of the reheating-temperature dependence of primordial helium-4. In the no-oscillation case, lowering the reheating temperature $T_R$ reduces the total neutrino energy density, slows the expansion, delays neutron-proton freeze-out, and lowers the helium mass fraction $Y_p$ — the picture assumed in earlier work. With oscillations switched on, the large solar mixing angle equalizes the electron and muon neutrino distributions, so electron neutrinos are converted away and their occupation number drops further than in the no-mixing case. Since only $f_{nu_e}$ controls the charged-current rate for $n leftrightarrow p$, the weak rates fall, freeze-out happens earlier, and $Y_p$ rises as $T_R$ decreases. The authors report that $Y_p$ does not decrease at all as $T_R$ is lowered when oscillations are included, even though the effective neutrino number $N_nu$ does decrease over the same range. They also find that the total neutrino production is more efficient with mixing, so $N_nu$ sits above the no-oscillation value by up to about 0.2 for $T_R$ between 2 and 5 MeV. Combining deuterium and helium-4 abundance data in a $chi^2$ analysis over the $eta$–$T_R$ plane, they quote a 95% confidence lower bound of about 1 MeV without oscillations, tightened to about 2 MeV with oscillations (equivalently $N_nu$ greater than about 1.2).
Load-bearing premise
The argument assumes the reactor mixing angle is zero, which reduces the three-neutrino problem to a two-flavor density matrix and lets the third state decouple; the authors assert that a nonzero value would only deplete electron neutrinos further and raise helium-4 more, but no three-flavor calculation is shown here.
Editorial extensions
If this is right
- A measurement of $N_nu$ below 3 combined with a helium-4 abundance above the standard prediction would point specifically to MeV-scale reheating, since the two observables move in opposite directions there.
- Cosmological limits on $N_nu$ alone cannot be used to bound the reheating temperature reliably, because the helium-4 response to $T_R$ has the opposite sign once mixing is included.
- The deuterium and lithium-7 predictions are nearly unaffected by oscillations, so only helium-4 and $N_nu$ carry the discriminating power in this scenario.
- Future CMB determinations of both $Y_p$ and $N_nu$ could identify a single consistent reheating temperature if the scenario is realized.
Reading between the lines
- Because the effect runs through the electron-neutrino occupation number rather than the total energy density, any process that further depletes $nu_e$ — self-interactions such as $nu_e barnu_e leftrightarrow nu_mu barnu_mu$, or a nonzero reactor angle — should push helium-4 up further, so the reported 2 MeV bound is plausibly conservative rather than aggressive.
- The same logic applies to any late-time entropy injection that leaves neutrinos under-thermalized, so the qualitative reversal is not specific to inflaton decay and could be searched for in moduli or Q-ball dominated cosmologies.
- The near-independence of deuterium on the mixing angle suggests that the long-standing tension between the baryon density preferred by deuterium and by helium-4 cannot be relieved by lowering the reheating temperature, contrary to what was sometimes assumed.
Original abstract
We study how the oscillations of the neutrinos affect their thermalization process during the reheating period with temperature O(1) MeV in the early universe. We follow the evolution of the neutrino density matrices and investigate how the predictions of big bang nucleosynthesis vary with the reheating temperature. For the reheating temperature of several MeV, we find that including the oscillations makes different predictions, especially for $^4$He abundance. Also, the effects on the lower bound of the reheating temperature from cosmological observations are discussed.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We study how the oscillations of the neutrinos affect their thermalization process during the reheating period with temperature O(1) MeV in the early universe. We follow the evolution of the neutrino density matrices and investigate how the predictions of big bang nucleosynthesis vary with the reheating temperature. For the reheating temperature of several MeV, we find that including the oscillations makes different predictions, especially for $^4$He abundance. Also, the effects on the lower bound of the reheating temperature from cosmological observations are discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study how the oscillations of the neutrinos affect their thermalization process during the reheating period with temperature O(1) MeV in the early universe. | contribution 0.99 | 0.82 | 0.06 | asserted 0.53 |
| s1 | We follow the evolution of the neutrino density matrices and investigate how the predictions of big bang nucleosynthesis vary with the reheating temperature. | method 0.86 | 0.92 | 0.05 | asserted 0.85 |
| s2 | For the reheating temperature of several MeV, we find that including the oscillations makes different predictions, especially for $^4$He abundance. | result 1.00 | 0.95 | 0.57 | asserted 1.00 |
| s3 | Also, the effects on the lower bound of the reheating temperature from cosmological observations are discussed. | contribution 0.50 | 0.52 | 0.09 | unclear 0.60 |
What was examined, and what was not
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Figures
Showing 5 of the paper's 8 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:astro-ph/0505395 by the authors.
References
How the literature uses it
89 arXiv papers cite this in 111 sentences
Papers citing it · 95 sentences without a confident label
Uses its method or tool 1 paper
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In the text, we define [equation] According to Ref [ref] , the $eν$ collision terms are written in the form of [equation] where $G_F$ is the Fermi constant.
Cosmological Constraint on Dark Photon from $N_{\rm eff}$ · Neutrino-Electron Collision Terms · 0.93
Uses its data or values 10 papers
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This temperature may have been as low as $∼$4 MeV [ref] once all cosmological data are taken into account, while BBN-only data impose a lower bound of $∼$2 MeV on $T_RH$ [ref] if active neutrino oscillations are taken into account (up from $∼$0.7 MeV [ref] if they are not).
MeV sterile neutrinos in low reheating temperature cosmological scenarios · Introduction · 0.93
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The current upper bound provided by the joint analysis of BICEP2/Keck Array and Planck data is $r<0.12$ [ref] , whereas no strict lower bound exists other than the requirement for realising successful BBN at $T∼1$ MeV [ref] .
A novel way to determine the scale of inflation · Introduction · 0.97
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Indeed, the thermalization process of two- and three-flavor neutrino oscillations have been analyzed yielding the following 95% CL bounds: $T_* > 2 MeV$ and $T_* > 4.1 MeV$ assuming radiative decay of the massive particles [ref] .
Two Micron-Size Dark Dimensions · Cosmological Constraints · 0.89
Compares with it 1 paper
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In the case of an early matter-dominated cosmology $w = 0$, the bound in Eq. [ref] can be restated as a bound on the reheating temperature as [equation] If the mass is not affected by non-perturbative effects and $χ= 0$, like for accidental ALPs, the expression above becomes independent on $m$ and yields the bound $≳3$GeV, which is about three orders of magnitude more stringent than what obtained in Refs. [ref] using BBN considerations.
Light axion-like dark matter must be present during inflation · Non-standard cosmological history · 0.80
Cites it as support 1 paper
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Such errors have also been reported in footnote 4 of Ref. [ref] .].
Neutrino decoupling beyond the Standard Model: CMB constraints on the Dark Matter mass with a fast and precise $N_{\rm eff}$ evaluation · Derivation of the temperature evolution equations · 0.97
Cites it as background 3 papers
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In supersymmetric extensions of the standard model, the overproduction of gravitinos can cause similar problems and have been a source of much investigation [ref] .
Non-thermal Dark Matter and the Moduli Problem in String Frameworks · Introduction · 0.99
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In the standard cosmological picture it is assumed that at early epoch, $T >> 1$ MeV, the energy density of the universe is mostly radiation dominated [ref] .
Long lived inert Higgs in fast expanding universe and its imprint on cosmic microwave background · Introduction · 0.90
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In the standard cosmological framework, one assumes that from the time scale of end of the inflation till the onset of the Big Bang Nucleosynthesis(BBN) at the temperature $T_BBN ∼few MeV$ the universe is mostly radiation dominated (RD) [ref] .
Axion-like particle (ALP) portal freeze-in dark matter confronting ALP search experiments · Introduction · 0.89
Discussion
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