The standard and degenerate primordial nucleosynthesis versus recent experimental data

Abstract

We report the results on Big Bang Nucleosynthesis (BBN) based on an updated code, with accuracy of the order of 0.1% on He4 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, N_\nu \sim 10. Comment: LaTeX2e, 41 pages, 20 figures. Minor changes and 4 figures slightly modified

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arXiv:astro-ph/0005571v2 31 Jul 2000
DSF 13/2000
astro-ph/0005571
The standard and degenerate primordial
nucleosynthesis versus recent experimental data
S. Esposito, G. Mangano, G. Miele, and O. Pisanti,
Dipartimento di Scienze Fisiche, Universit´ a di Napoli ”Federico II”, and INFN, Sezione
di Napoli, Complesso Universitario di Monte Sant’Angelo, Via Cintia, I-80126 Napoli,
Italy
Abstract
We report the results on Big Bang Nucleosynthesis (BBN) based on an updated
code, with accuracy of the order of 0.1% on4He 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.
PACS number(s): 98.80.Cq; 98.80.Ft
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1Introduction
The synthesis of light nuclei in the early universe, the Big Bang Nucleosynthesis (BBN),
represents one of the most striking evidence in favour of standard cosmology, and since
its proposal [1], it has been extensively used as one of the best laboratories where to test
cosmological models and/or elementary particle physics. The appealing feature of BBN
is that, in its standard version, it relies on quite solid theoretical grounds, which makes
the predictions for D,3He,4He and7Li abundances, whose primordial values are only
partially modified by the subsequent stellar activity, quite robust.
Recently, the experimental accuracy in measurements of the light primordial nuclide
abundances, mainly4He, has been highly improved, reaching a precision of the order
of 1%. Similar improvements have been also obtained for both Deuterium (D) and7Li
relative abundances, YD≡ D/H and Y7Li≡
the experimental techniques does not yet correspond to a clear picture of the primordial
7Li/H, but, unfortunately, the refinement of
nuclide densities. This is mainly due to an uncomplete understanding of systematic
errors. In particular, measuring the primordial4He mass fraction, Yp, from regression to
zero metallicity in Blue Compact Galaxies, two independent surveys obtained two results,
a low value [2],
Y(l)
p
= 0.234±0.003,(1.1)
and a sensibly larger one [3],
Y(h)
p
= 0.244±0.002,(1.2)
which are compatible at 2σ level only.
As in a recent analysis [4], we here adopt a more conservative value, with a larger
error (hereafter we always use 1σ errors)
Yp= 0.238±0.005.(1.3)
A similar dichotomy holds in D measurements as well, where the study of distant Quasars
Absorption line Systems (QAS), is thought to represent a reliable way to estimate the pri-
mordial Deuterium. In this case, observations in different QAS leads to the incompatible
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results [5, 6, 4]
Y(l)
D
= (3.4±0.3)10−5
= (2.0±0.5)10−4
,(1.4)
Y(h)
D
.(1.5)
Finally, a reliable estimate for7Li primordial abundance is provided by the Spite plateau,
observed in the halo of POP II stars [7, 8]. The observations give the primordial abundance
[9],
Y7Li= (1.73±0.21)10−10
.(1.6)
From the theoretical point of view, the BBN predictions are obtained by numerically
solving a set of coupled Boltzmann equations, which trace the abundances of the different
nuclides in the framework of standard Big Bang cosmology [10]. The collisional integrals
of the above equations contain all n ↔ p weak reaction rates and a large nuclear reaction
network [11].
The increasing precision in measuring the primordial abundance has recently pushed
the theoretical community to make an effort to develop new generation BBN codes [12, 13],
with a comparable level of accuracy. In a recent series of papers, in the framework
of the standard cosmological model, the present authors [14] and other groups [12] have
performed a comprehensive and accurate analysis of all the physical effects which influence
4He mass fraction up to 0.1%.
Since almost all neutrons present at the onset of nucleosynthesis are fixed into4He,
its abundance is mainly function of the neutron versus proton abundances, at the time of
n ↔ p weak interactions freeze out, which takes place for T ∼ 1MeV . To improve the
accuracy on the4He prediction it is demanding to reach an accuracy level of the order of
1% in the estimate of the n ↔ p rates, well beyond the simple Born approximation. This
has been performed by considering a number of additional contributions, which, ordered
according to their relative weight, are the following:
i) electromagnetic radiative and Coulomb corrections [15, 16];
ii) finite nucleon mass corrections [17, 14];
iii) thermal radiative effects induced by the presence of a surrounding plasma of e±and
γ [18, 14];
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iv) corrections to the equation of state of the e±, γ plasma due to thermal mass renor-
malization [19, 12, 13];
v) the residual neutrino coupling to the plasma during e+e−annihilation, affecting the
neutrino to photon temperature ratio [20, 12, 13].
Unfortunately, a similar systematic analysis of all corrections up to the desired level
of accuracy cannot be performed for the other input parameters of the theory. The
theoretical estimates do depend in fact on the values of the neutron lifetime, as well as
on several nuclear reaction cross sections, which are poorly known in the energy range
relevant for BBN. This introduces a certain level of uncertainty on the light element
abundances. This aspect has been studied in two different approaches, either using Monte
Carlo methods [21] to sample the error distributions of the relevant reaction cross sections,
or, alternatively, using a linear error propagation [22], with comparable results.
In this paper, we further refine our previous predictions by using a new version of our
numerical code, where the full dependence of the BBN equations on the electron chemical
potential is accurately implemented. Furthermore, for the standard scenario (vanishing
neutrino chemical potentials) we perform an accurate likelihood analysis in the space of
the two free parameters of the model, the effective number of neutrinos, Nν, and the
baryon to photon ratio η.
While the value of electron chemical potential is bounded, by neutrality, by the value
of η, this is not the case for neutrino–antineutrino asymmetries which, in principle, can
be quite large. The influence of the neutrino chemical potentials on BBN predictions
(degenerate BBN) has been considered in the past [23].One relevant aspect of this
analysis, which is worth stressing, is that degenerate BBN allows for a better agreement
with observations at values of η larger than, say, 6·10−10, while standard BBN prefers
smaller values, η ∼ (2÷6)·10−10. We will discuss this in detail in the paper. This feature is
particularly relevant in view of the recent analysis of the BOOMERANG and MAXIMA-1
results [24] on the acoustic peak of the Cosmic Microwave Background Radiation (CMBR),
which seems to favour a value for the baryonic asymmetry η of the order of 10−9, larger, as
we said, than what expected in the framework of standard BBN. This discrepancy may be
looked as a signal in favour of a large neutrino–antineutrino asymmetry. It seems therefore
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demanding to re–analyze the degenerate scenario, making profit of the now available more
precise BBN codes. We have performed this study, and the main result is that degenerate
BBN and CMBR data seems to be compatible for large values of the effective number of
neutrinos, Nν≥ 10 and η ≤ 10−9.
The paper is organized as follows. In section 2 we briefly describe the BBN set of
differential equations, recast in a suitable form for a numerical solution. The light element
abundances obtained from our code, for standard BBN, are then presented in section 3 as
a functions of τn, Nνand η. Section 4 is devoted to degenerate BBN and to the bounds
on neutrino chemical potentials coming from nucleosynthesis and CMBR data. Finally,
in section 4, we give our conclusions.
2The BBN set of equations
Consider Nnucspecies of nuclides, whose number densities, ni, are normalized with respect
to the total number density of baryons, nB,1
Xi=ni
nB
i = 1,..,Nnuc
.(2.1)
Alternatively, we will also make use in the following of the notation:
X1= Xn
,X2= Xp= XH
,X3= XD
,
X5= X3He
,X6= X4He
,X8= X7Li
.(2.2)
The set of differential equations ruling primordial nucleosynthesis is given by [1, 13]:
˙R
R
= H =
?
8π
3M2
P
ρT
,(2.3)
˙ nB
nB
˙ ρT
= −3H
= −3H (ρT+ pT)
˙Xi =
j,k,l
nB
T3
, (2.4)
,(2.5)
?
Ni

Γkl→ijXNl
?
l
XNk
k
Nl!Nk!
− Γij→kl
XNi
i
Ni!Nj!
XNj
j

≡ Γi(Xj),(2.6)
L(me
T,φe) =
j
ZjXj
,(2.7)
1We will use the same notations of our previous paper [13], which we refer to for further details.
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