Big Bang nucleosynthesis as a probe of new physics Carlos A. Bertulani1Francis W. Hall1 and Benjamin I. Santoyo1 1Department of Physics and Astronomy Texas AM University-Commerce Commerce TX United States

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Big Bang nucleosynthesis as a probe of new physics

Carlos A. Bertulani1,∗,Francis W. Hall1,∗∗, and Benjamin I. Santoyo1,∗∗∗

1Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, TX, United States

Abstract. The Big Bang Nucleosynthesis (BBN) model is a cornerstone for the understanding of the evolution

of the early universe, making seminal predictions that are in outstanding agreement with the present observation

of light element abundances in the universe. Perhaps, the only remaining issue to be solved by theory is the

so-called “lithium abundance problem". Dedicated experimental eﬀorts to measure the relevant nuclear cross

sections used as input of the model have lead to an increased level of accuracy in the prediction of the light

element primordial abundances. The rise of indirect experimental techniques during the preceding few decades

has permitted the access of reaction information beyond the limitations of direct measurements. New theoretical

developments have also opened a fertile ground for tests of physics beyond the standard model of atomic,

nuclear, statistics, and particle physics. We review the latest contributions of our group for possible solutions of

the lithium problem.

1 Introduction

From about 10 seconds to 20 minutes after the Big Bang

the universe endured the production of light elements in

a process known as Big Bang Nucleosynthesis (BBN) [1–

14]. The temperature during this epoch decreased from

about 109K to 108K. BBN and its predictions depend

strongly on few quantities, namely, (a) the ratio of baryon-

to-photon number densities, η=nb/nγ, assumed to be uni-

form in space and time during BBN, (b) the number of

neutrinos families Nν, and (c) the neutron half-life τn. The

Cosmic Microwave Background (CMB) measurement ob-

tained with the Planck satellite yields η=(6.12 ±0.06) ×

10−10 [15]. Precise experiments at the CERN Large Elec-

tron–Positron Collider (LEP) have deduced the number of

neutrino families [16] as Nν=2.9840±0.0082, while neu-

tron lifetime measurements have obtained τn'877.75±28

s [17]. All these values are in excellent agreement with

the BBN model and its predictions of the abundance of

light elements. In particular, the BBN model predicts

η=(6.123 ±0.039) ×10−10, compatible with the most re-

cent measurements of the deuterium primordial abundance

[18]. Nowadays, it is possible to say that the BBN is a

parameter-free model, calculated using rather simple com-

puter programs and yielding consistent predictions for pri-

mordial abundances with inputs of experimental nuclear

cross sections.

During the BBN, the light elements D, 3He, 4He, and

7Li were produced and their abundances have been ob-

served in particular astrophysical environments thought to

∗e-mail: carlos.bertulani@tamuc.edu

∗∗e-mail: fhall2@leomail.tamuc.edu

∗∗∗e-mail: ben@santoyo.us

14 protons 2 neutrons

n/p = 1/7

12 protons = mass 12 helium = mass 4

25% He

75% H

Figure 1: Left: The observed nearly 25% of helium and

75% of hydrogen in the universe can be understood if the

neutron to proton ratio during the Big Bang nucleosynthe-

sis was equal to n/p=1/7.

be remnants of the BBN epoch. The BBN predictions de-

pend on the magnitude of the nuclear cross sections and

the nuclear reaction network in a medium where densities

and temperatures evolve within the model. One solves the

Friedmann’s equations for the expansion rate of the uni-

verse,

H2(t)= da/dt

a!2

=8πG

3ρ−k

a2+Λ

3,(1)

where H(t) is the evolving Hubble constant, ais a univer-

sal scale factor for distances, kis the “curvature” and Λis

the cosmological constant. The universe is assumed to be

homogeneous and isotropic (cosmological principle). The

Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is

adopted to describe distances between neighboring points

arXiv:2210.04071v3 [nucl-th] 9 Nov 2022

in the space-time,

ds2=dt2−a2(t)"dr2

1−kr2+r2dθ2+sin θdφ2#.(2)

Additionally, the ﬁrst law of thermodynamics invokes a

relation between density ρand pressure pin the form

dρ

dt =−3H(ρ+p).(3)

Moreover, charge-equilibrium implies that

nbX

ZjXj=ne+−ne−= Φ me

T, µe,(4)

where Xi=nimi/ρ is the mass fraction of the particle

species i, with mass miand number density ni. Nuclear

abundances Yiare deﬁned so that Xi=AiYiis the mass

fraction in the environment for a nuclide with charge Zi

and mass number Ai, with the normalization PiAiYi=1.

The function Φincorporates the densities of electrons,

positrons and neutrinos. Weak-decays also change the rel-

ative numbers of e+and e−through n↔prates.

All nuclear reaction rates include at most four diﬀerent

nuclides and are of the form

Ni(AiZi)+Nj(AjZj)↔Nk(AkZk)+Nl(AlZl),(5)

where Nmis the number of nuclide m, with Ai≥Ajand

Al≥Ak. The abundance changes are given in terms of

dYi/dt which is computed as

dYi

dt =X

j,k,l

Ni





−

YNi

iYNj

Ni!Nj![i j]k+YNl

lYNk

Nl!Nk![lk]j





,(6)

where [i j]kis the forward reaction rate and [lk]jis the re-

verse rate and abundance changes are summed over all for-

ward and reverse reactions involving nuclide i.

The reaction rates in a stellar environment with a tem-

perature Tis given by a Maxwell-Boltzmann average over

the relative velocity distribution of the pair [i j],

[i j]k=hσvi[i j]k=s8

πµ(kT )3Z∞

σ(E)Eexp −E

kT dE,

(7)

where µis the reduced mass of [i j], NAis Avogadro’s num-

ber, kis the Boltzmann constant, and the reaction cross

section and its energy dependence is denoted by σ(E).

Using k=0 and Λ = 0 for the epoch right af-

ter the baryogenensis, the standard BBN model described

above leads to the formation of deuterons about ∼3 min-

utes after the Big Bang. The p(n,γ)d reaction ﬂow for

deuteron formation is strongly dependent on the value of η.

Deuterons were immediately destroyed with the creation

of 3He nuclei by means of d(p,γ)3He and d(d,n)3He reac-

tions and the formation of tritium with the d(d,p)t reaction.

Subsequently, 4He were formed via the 3He(d,p)4He and

t(d,n)4He reactions. This chain of reactions yields a uni-

verse with about 75% of hydrogen and 25% of helium. As

the universe expanded and cooled down, nucleosynthesis

continued at a smaller rate, leading to very small amounts

of 7Li and 6Li. Heavier elements such as carbon, nitrogen

or oxygen were created in very tiny amounts, of the order

of <1016 relative abundance [19].

The prediction of 75% of hydrogen and 25% of helium

mass fraction in the universe is one of the major accom-

plishments of the Big Bang model [8]. It solely relies on

the the neutron-to-proton ratio being equal to n/p=1/7 at

the BBN epoch, as schematically shown in Fig. 1. The n/p

=1/7 value is obtained by solving the Big Bang standard

model (see Figure 1 of Ref. [8]).

The most relevant BBN reactions are listed in Table

1. The predicted mass and number fractions of light ele-

ments produced during the BBN are shown in Fig. 2 as a

function of time. One notices that elements up to 7Be and

7Li are predicted in reasonable amounts. But 7Be decays

by electron capture in about 53 days. Therefore, all 7Be

produced during the BBN is observed today as 7Li.

n↔p p(n,γ)d d(p,γ)3He d(d,p)t

d(d,n)3He 3He(n,p)t t(d,n)4He 3He(d,p)4He

3He(α, γ)7Be t(α, γ)7Li 7Be(n,p)7Li 7Li(p,α)4He

Table 1: Most relevant BBN reactions.

BBN predicts a 7Li/H of abundance of ∼10−10 and a

6Li/H abundance of ∼10−14. After the BBN era (&20

min), the universe cooled down and no more elements

were formed until the ﬁrst stars were born, about 100 mil-

lion years later. After the BBN and substantial formation

of stars, 6Li and 7Li could be produced in spallation pro-

cesses by cosmic rays formed by star ejecta. 7Li can also

be synthesized in novae or during AGB stars pulsations.

Astronomical observation suggest that the 7Li abundance

does not depend on “metallicity" (the content of elements

heavier than 4He) in metal-poor stars. These stars have

small Fe/H abundances and are observed in the galaxy

halo. The 7Li abundance in such stars is nearly constant, a

phenomenon known as the “Spite plateau” [20].

Low metallicity stars with masses M<Mand life

expectancies greater than the age of the universe have (in

principle) no convective zone near their surfaces. Lithium

present in their surfaces cannot be brought to deeper zones

and be destroyed where temperatures exceed 1 GK. The

depth of the convection zone decreases with the surface

temperature, and that is the reason why astronomers select

stars with Te f f >6000 K (warm) for such observations

(for more details, see Ref. [21]). Other observations of

low-metallicity stars apparently contradict the inferences

based on the Spite plateau [22, 23]. Using a variety of

observations and laboratory data on nuclear reactions, and

η=(6.07 ±0.07) ×10−10 [15], the BBN model predicts

a7Li abundance of Li/H=(4.16 −5.34) ×10−10 [25]

whereas observations from metal-poor halo stars obtains

Li/H=(1.58 +0.35 −0.28) ×10−10 [23, 24]. This value is

about 3 times smaller than the one predicted by the BBN

model and is the source of the so-called “lithium puzzle”.

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BigBangnucleosynthesisasaprobeofnewphysicsCarlosA.Bertulani1;,FrancisW.Hall1;,andBenjaminI.Santoyo1;1DepartmentofPhysicsandAstronomy,TexasA&MUniversity-Commerce,Commerce,TX,UnitedStatesAbstract.TheBigBangNucleosynthesis(BBN)modelisacornerstonefortheunderstandingoftheevolutionoftheearlyuniverse...

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Big Bang nucleosynthesis as a probe of new physics Carlos A. Bertulani1Francis W. Hall1 and Benjamin I. Santoyo1 1Department of Physics and Astronomy Texas AM University-Commerce Commerce TX United States

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