Effective Number Of Neutrinos Research Articles

Primordial Nucleosynthesis and Neutrino Physics Beyond the Standard Model

The present status of standard Big Bang Nucleosynthesis (BBN) is here reviewed by comparing the theoretical predictions with the observational estimates of light nuclei abundances. In particular, the analysis reports the expected ranges for baryon fraction and effective number of neutrinos as obtained by BBN only. The comparison is also performed in case of a more detailed analysis of neutrino decoupling by assuming initial degenerate neutrino distributions and oscillation mechanism as well.

Primordial Nucleosynthesis: an updated comparison of observational light nuclei abundances with theoretical predictions

An up to date review of Standard Big Bang Nucleosynthesis (BBN) predictions vs the astrophysical estimates of light nuclei abundances is here presented. In particular the analysis reports the expected ranges for baryon fraction and effective number of neutrinos as obtained by BBN only.

Non-standard neutrinos and Cosmology

Cosmology provides stringent constraints on neutrino masses, neutrino effective number and possible non standard interactions of both ordinary and possible extra neutrinos.

Constraining the universal lepton asymmetry

The relic cosmic background neutrinos accompanying the cosmic microwave background(CMB) photons may hide a universal lepton asymmetry orders of magnitudelarger than the universal baryon asymmetry. At present, the only direct way toprobe such an asymmetry is through its effect on the abundances of the lightelements produced during primordial nucleosynthesis. The relic light elementabundances also depend on the baryon asymmetry, parameterized by the baryondensity parameter () and on the early-universe expansion rate, parameterized by the expansion rate factor () or, equivalently, by the effective number of neutrinos (). We use data from the CMB (and large scale structure: LSS) along withthe observationally inferred relic abundances of deuterium and helium-4to provide new bounds on the universal lepton asymmetry, finding forηL, the analogof ηB,0.072 ± 0.053 if it isassumed that Nν = 3 and, 0.115 ± 0.095 along with Nν = 3.3−0.6+0.7, if Nν is free to vary.

Increasing the effective number of neutrinos with decaying particles

We present models of decaying particles for increasing the effective number of neutrinosNν after big bang nucleosynthesis but before the structure formation begins. We point outthat our scenario not only solves the discrepancy between the constraints onNν from these two epochs, but also provides a possible answer to deeper inconsistency in theestimation of the matter power spectrum amplitude at small scales, represented byσ8, between the WMAP and some small scale matter power measurements such as theLyman-α forest and weak lensing. We consider (a) saxion decay into two axions; (b) gravitino decayinto axino and axion; (c) Dirac right-handed sneutrino decay into gravitino andright-handed neutrino.

Relic neutrino decoupling including flavour oscillations

In the early universe, neutrinos are slightly coupled when electron–positron pairs annihilate transferring their entropy to photons. This process originates non-thermal distortions on the neutrino spectra which depend on neutrino flavour, larger for ν e than for ν μ or ν τ . We study the effect of three-neutrino flavour oscillations on the process of neutrino decoupling by solving the momentum-dependent kinetic equations for the neutrino spectra. We find that oscillations do not essentially modify the total change in the neutrino energy density, giving N eff = 3.046 in terms of the effective number of neutrinos, while the small effect over the production of primordial 4He is increased by O ( 20 % ) , up to 2.1 × 10 −4 . These results are stable within the presently favoured region of neutrino mixing parameters.

Avoiding BBN constraints on mirror models for sterile neutrinos

We point out that in models that explain the Los Alamos neutrino scintillation detector result for neutrino oscillations using the mirror neutrinos, the big bang nucleosynthesis constraints on the number of sterile neutrinos can be avoided by using the late time phase transition that only helps to mix the active and the sterile neutrinos. The main idea is to have a standard model singlet scalar field that mixes the visible and the mirror sector and has a low vacuum expectation value ($\ensuremath{\sim}100\text{ }\text{ }\mathrm{k}\mathrm{e}\mathrm{V}$) so that the active and sterile neutrinos remain unmixed at the big bang nucleosynthesis epoch. The model predicts different effective number of neutrinos at the epoch of recombination compared to the standard model and is therefore testable in experiments that measure cosmic microwave spectrum with a higher precision.

Primordial nucleosynthesis for the new cosmology: Determining uncertainties and examining concordance

Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) have a long history together in the standard cosmology. BBN accurately predicts the primordial light element abundances of deuterium, helium and lithium. The general concordance between the predicted and observed light element abundances provides a direct probe of the universal baryon density. Recent CMB anisotropy measurements, particularly the observations performed by the WMAP satellite, examine this concordance by independently measuring the cosmic baryon density. Key to this test of concordance is a quantitative understanding of the uncertainties in the BBN light element abundance predictions. These uncertainties are dominated by systematic errors in nuclear cross sections, however for helium-4 they are dominated by the uncertainties in the neutron lifetime and Newton's G. We critically analyze the cross section data, producing representations that describe this data and its uncertainties, taking into account the correlations among data, and explicitly treating the systematic errors between data sets. The procedure transforming these representations into thermal rates and errors is discussed. Using these updated nuclear inputs, we compute the new BBN abundance predictions, and quantitatively examine their concordance with observations. Depending on what deuterium observations are adopted, one gets the following constraints on the baryon density: ${\ensuremath{\Omega}}_{\mathrm{B}}{h}^{2}=0.0229\ifmmode\pm\else\textpm\fi{}0.0013$ or ${\ensuremath{\Omega}}_{\mathrm{B}}{h}^{2}{=0.0216}_{\ensuremath{-}0.0021}^{+0.0020}$ at 68% confidence, fixing ${N}_{\ensuremath{\nu},eff}=3.0.$ If we instead adopt the WMAP baryon density, we find the following deuterium-based constraints on the effective number of neutrinos during BBN: ${N}_{\ensuremath{\nu},eff}{=2.78}_{\ensuremath{-}0.76}^{+0.87}$ or ${N}_{\ensuremath{\nu},eff}{=3.65}_{\ensuremath{-}1.30}^{+1.46}$ at 68% confidence. Concerns over systematics in helium and lithium observations limit the confidence constraints based on this data provide. BBN theory uncertainties are dominated by the following nuclear reactions: ${d(d,n)}^{3}\mathrm{He},$ $d(d,p)t,$ $d(p,\ensuremath{\gamma}{)}^{3}\mathrm{He},$ ${}^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{7}\mathrm{Be}$ and ${}^{3}\mathrm{He}{(d,p)}^{4}\mathrm{He}.$ With new nuclear cross section data, light element abundance observations and the ever increasing resolution of the CMB anisotropy, tighter constraints can be placed on nuclear and particle astrophysics.

Effective number of neutrinos and baryon asymmetry from BBN and WMAP

We place constraints on the number of relativistic degrees of freedom and on the baryon asymmetry at the epoch of Big Bang Nucleosynthesis (BBN) and at recombination, using cosmic background radiation (CBR) data from the Wilkinson Microwave Anisotropy Probe (WMAP), complemented by the Hubble Space Telescope (HST) Key Project measurement of the Hubble constant, along with the latest compilation of deuterium abundances and Hii region measurements of the primordial helium abundance. The agreement between the derived values of these key cosmological and particle physics parameters at these widely separated (in time or redshift) epochs is remarkable. From the combination of CBR and BBN data, we find the 2σ ranges for the effective number of neutrinos Nν and for the baryon asymmetry (baryon to photon number ratio η) to be 1.7–3.0 and 5.53–6.76×10−10, respectively.

Addendum to “Update on neutrino mixing in the early universe”

In the light of the recent WMAP results we update the constraints on a class of nonstandard big bang nucleosynthesis (BBN) models with a simultaneous combination of nonstandard neutrino distributions and an extra effective number of neutrinos in the expansion rate. These models can be described in terms of the two parameters $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\mathrm{tot}},$ constrained by the primordial helium abundance ${Y}_{p}$ measurement, and $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\ensuremath{\rho}},$ constrained by a combination of cosmic microwave background and primordial deuterium data. Small deviations from standard big bang nucleosynthesis are suggested. Different nonstandard scenarios can be distinguished by a measurement of the difference $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{{f}_{\ensuremath{\nu}}}=\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\mathrm{tot}}\ensuremath{-}\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\ensuremath{\rho}}.$ From the current data we estimate $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{{f}_{\ensuremath{\nu}}}\ensuremath{\simeq}\ensuremath{-}{1.4}_{\ensuremath{-}1.4}^{+0.9},$ mildly disfavoring solutions with a low expansion rate, characterized by $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{{f}_{\ensuremath{\nu}}}=0$ and negative $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\ensuremath{\rho}}.$ Active-sterile neutrino mixing could be a viable explanation only for high values of ${Y}_{p}\ensuremath{\gtrsim}0.24.$ The existence of large positive neutrino chemical potentials ${\ensuremath{\xi}}_{i}\ensuremath{\sim}0.05,$ implying $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\ensuremath{\rho}}\ensuremath{\simeq}0,$ would be a possible explanation of the data within the analyzed class of nonstandard BBN models. Interestingly, it would also provide a way to evade the cosmological bounds for ``class A 3+1'' four neutrino mixing models. A scenario with a decaying sterile neutrino is also considered.

A precision calculation of the effective number of cosmological neutrinos

The neutrino energy density of the Universe can be conveniently parametrized in terms of the so-called effective number of neutrinos, Nνeff. This parameter enters in several cosmological observables. In particular it is an important input in those numerical codes, like CMBFAST, which are used to study the Cosmic Microwave Background anisotropy spectrum. By studying the neutrino decoupling with Boltzmann equations, one can show that this quantity differs from the number of massless neutrino species for an additional contribution due to a partial heating of neutrinos during the e± annihilations, leading to non-thermal features in their final distributions. In this Letter we review the different results obtained in the literature and perform a new analysis which takes into account, in a fully consistent way, the QED corrections at finite temperature to the photon and e± plasma equation of state. The value found for three massless active neutrinos is Nνeff=3.0395, in perfect agreement with the recommended value used in CMBFAST, Nνeff=3.04. We also discuss the case of additional relativistic relics and massive active neutrinos.

Constraining neutrino physics with big bang nucleosynthesis and cosmic microwave background radiation

We perform a likelihood analysis of the recent results on the anisotropy of cosmic microwave background radiation from the BOOMERanG and DASI experiments to show that they single out an effective number of neutrinos in good agreement with standard big bang nucleosynthesis. We also consider degenerate big bang nucleosynthesis to provide new bounds on effective relativistic degrees of freedom ${N}_{\ensuremath{\nu}}$ and, in particular, on the neutrino chemical potential ${\ensuremath{\xi}}_{\ensuremath{\alpha}}.$ When including supernova type Ia data we find, at $2\ensuremath{\sigma},$ ${N}_{\ensuremath{\nu}}<~7$ and $\ensuremath{-}0.01<~{\ensuremath{\xi}}_{e}<~0.22,$ $|{\ensuremath{\xi}}_{\ensuremath{\mu},\ensuremath{\tau}}|<~2.6.$

The standard and degenerate primordial nucleosynthesis versus recent experimental data

We report the results on Big Bang Nucleosynthesis (BBN) based on an updated code, with accuracy of the order of 0.1 % on 4He abundance, compared with the predictions of other recent similar analysis. We discuss the compatibility of the theoretical results, for vanishing neutrino chemical potentials, with the observational data. Bounds on the number of relativistic neutrinos and baryon abundance are obtained by a likelihood analysis. We also analyze the effect of large neutrino chemical potentials on primordial nucleosynthesis, motivated by the recent results on the Cosmic Microwave Background Radiation spectrum. The BBN exclusion plots for electron neutrino chemical potential and the effective number of relativistic neutrinos are reported. We find that the standard BBN seems to be only marginally in agreement with the recent BOOMERANG and MAXIMA-1 results, while the agreement is much better for degenerate BBN scenarios for large effective number of neutrinos, Nν ~ 10. For the low D data, standard BBN is still viable for η ~ (5÷6) 10−10.

Erratum: How neutrino oscillations can induce an effective neutrino number of less than three during big bang nucleosynthesis [Phys. Rev. D 56, 6653 (1997)

Ordinary-sterile neutrino oscillations can generate significant neutrino asymmetry in the early Universe. In this paper we extend this work by computing the evolution of neutrino asymmetries and light element abundances during the Big Bang Nucleosynthesis (BBN) epoch. We show that a significant electron-neutrino asymmetry can be generated in a way that is approximately independent of the oscillation parameters $\delta m^2$ and $\sin^2 2\theta$ for a range of parameters in an interesting class of models. The numerical value of the asymmetry leads to the prediction that the effective number of neutrino flavours during BBN is either about 2.5 or 3.4 depending on the sign of the asymmetry. Interestingly, one class of primordial deuterium abundance data favours an effective number of neutrino flavours during the epoch of BBN of less than 3.

How neutrino oscillations can induce an effective neutrino number of less than three during big bang nucleosynthesis

Ordinary-sterile neutrino oscillations can generate significant neutrino asymmetry in the early Universe. In this paper we extend this work by computing the evolution of neutrino asymmetries and light element abundances during the big bang nucleosynthesis (BBN) epoch. We show that a significant electron-neutrino asymmetry can be generated in a way that is approximately independent of the oscillation parameters $\ensuremath{\delta}{m}^{2}$ and ${\mathrm{sin}}^{2}2\ensuremath{\theta}$ for a range of parameters in an interesting class of models. The numerical value of the asymmetry leads to the prediction that the effective number of neutrino flavors during BBN is either about 2.5 or 3.4, depending on the sign of the asymmetry. Interestingly, one class of primordial deuterium abundance data favors an effective number of neutrino flavors during the epoch of BBN of less than 3.

Mass of tau neutrino in SO(10) GUTs

We investigate the allowed ranges of masses for an unstable tau neutrino in the context of SO(10) GUT-s. In light of the new nucleosynthesis results we obtain that there is a narrow window for m_{\nu_\tau} where the LEP, neutrino oscillation and nucleosynthesis data are compatible. This window, which depends on the effective number of neutrinos contributing to nucleosynthesis, has important cosmological consequences and will be tested by ongoing neutrino oscillation and LEP II experiments.

Big bang nucleosynthesis constraints on primordial magnetic fields

We reanalyze the effect of magnetic fields in BBN, incorporating several features which were omitted in previous analyses. We find that the effects of coherent magnetic fields on the weak interaction rates and the electron thermodynamic functions (${\ensuremath{\rho}}_{e}$, ${P}_{e}$, and $\frac{d{\ensuremath{\rho}}_{e}}{d{T}_{\ensuremath{\gamma}}}$) are unimportant in comparison with the contribution of the magnetic field energy density in BBN. As a consequence the effect of including magnetic fields in BBN is well approximated numerically by treating the additional energy density as an effective neutrino number. A conservative upper bound on the primordial magnetic field, parametrized as $\ensuremath{\zeta}=\frac{2e{B}_{\mathrm{rms}}}{({T}_{\ensuremath{\nu}}^{2})}$, is $\ensuremath{\zeta}<~2({\ensuremath{\rho}}_{B}<0.27{\ensuremath{\rho}}_{\ensuremath{\nu}})$. This bound can be stronger than the conventional bound coming from the Faraday rotation measures of distant quasars if the cosmological magnetic field is generated by a causal mechanism.

Big Bang Nucleosynthesis in Light of Discordant Deuterium Measurements

Two-dimensional concordance plots involving the baryon-to-photon ratio, η, and an effective number of light neutrinos, Nv, are used to discuss the overall consistency of standard big bang nucleosynthesis in light of recent determinations of the primordial deuterium (2H) abundance. Observations of high-redshift Lyα clouds have provided discordant 2H/H determinations: one cloud with a high value of 2H/H compared with the previously accepted range of (2H+3He)/H, and one system with a significantly lower value of 2H/H than those previously obtained. The high value of 2H/H agrees well with the current observationally inferred primordial abundances of 4He and 7Li for Nv = 3. The low value of 2H/H does not fit well with the current observationally inferred primordial abundance of 4He for Nv = 3. In addition, if the low value of 2H/H is indicative of the primordial deuterium abundance, then significant depletion of 7Li in old, hot Population II halo stars is probably required in order to obtain a concordant range of η, for any effective number of neutrino flavors. The use of conservative ranges for the primordial abundances of 2H, 4He, and 7Li allows the success of the standard picture for Nv=3.

The simplest scheme with massive neutrinos

The simplest possible extension of the “minimal three-family standard model”, where a single right-handed neutrino is added to the matter content of the model, is analyzed in some detail. The scheme has two massless and two massive Majorana neutrinos. A convenient parametrization of the lepton mixing matrix is proposed and all couplings of the neutrinos are calculated. It is found that the effective number of neutrinos, as determined by neutrino counting at the Z-peak, is bounded by three.

Neutrino counting at the Z-peak and right-handed neutrinos

We consider the implications of extending the minimal standard model, with n families of quarks and leptons, by introducing an arbitrary number of right-handed neutrinos, for neutrino-counting via the “invisible width” of the Z. It is shown that the effective number of neutrinos, 〈 n〉, satisfies, the inequality 〈 n〉 ⩽ n, where 〈 n〉 is defined by Γ( Z→neutrinos) ≡ 〈 n〉 Γ 0 and Γ 0 is the standard width for one massless neutrino. Thus, in the case of three families, the neutrino-counting can give a result which is less than three, if there are right-handed neutrinos.