1

24. Big Bang Nucleosynthesis

24. Big Bang Nucleosynthesis
Revised August 2023 by B.D. Fields (Astronomy, Illinois U.; Physics, Illinois U.), P. Molaro (INAFOATS Trieste; IFPU) and S. Sarkar (Rudolf Peierls, Oxford U.).

24.1 Abstract
Big-Bang nucleosynthesis (BBN) offers the deepest reliable probe of the early Universe, being
based on well-understood Standard Model physics [1]. Predictions of the abundances of the lightelements, D, 3 He, 4 He, and 7 Li, synthesized at the end of the first three minutes, are in good overall
agreement with the primordial abundances inferred from observational data, thus validating thestandard hot Big-Bang cosmology (see [2–5] for reviews). This is particularly impressive given thatthese abundances span nine orders of magnitude – from 4 He/H∼ 0.08 down to 7 Li/H∼ 10−10 (ratios
by number). Thus BBN provides powerful constraints on possible deviations from the standard
cosmology, and on new physics beyond the Standard Model [6–9].

24.2 Theory
The synthesis of the light elements is sensitive to physical conditions in the early radiationdominated era at a temperature T ∼ 1 MeV, corresponding to an age t ∼ 1 s. At higher
temperatures, weak interactions were in thermal equilibrium, thus fixing the ratio of the neutron
and proton number densities to be n/p = e−Q/T , where Q = 1.293 MeV is the neutron-proton
mass difference. As the temperature dropped, the neutron-proton inter-conversion
rate per nucleon,√Γn↔p ∼ G2F T 5 , fell faster than the Hubble expansion rate, H ∼ g∗ GN T 2 , where g∗ counts thenumber of relativistic particle species determining the energy density in radiation (see ‘Big Bang
Cosmology’ — Sec. 22 of this Review). This resulted in departure from chemical equilibrium (freezeout) at Tfr ∼ (g∗ GN /G4F )1/6 ' 1 MeV. The neutron fraction at this time, n/p = e−Q/Tfr ' 1/6,
is thus sensitive to every known physical interaction, since Q is determined by both strong andelectromagnetic interactions while Tfr depends on the weak as well as gravitational interactions.
Moreover, the sensitivity to the Hubble expansion rate affords a probe of, e.g., the number ofrelativistic neutrino species [10]. After freeze-out, the neutrons were free to β-decay, so the neutron
fraction dropped to n/p ' 1/7 by the time nuclear reactions began. A simplified analytic model offreeze-out yields the n/p ratio to an accuracy of ∼ 1% [11, 12].
The rates of these reactions depend on the density of baryons (strictly speaking, nucleons),
which is usually expressed normalized to the relic blackbody photon density as η ≡ nb /nγ . As
we shall see, all the light-element abundances can be explained with η10 ≡ η × 1010 in the range
6.143 ± 0.190. With nγ fixed by the present CMB temperature 2.7255 K (see ‘Cosmic Microwave
Background’ — Sec. 29 of this Review), this can be stated as the allowed range for the baryon massdensity today, ρb = (4.2 ± 0.1) × 10−31 g cm−3 , or as the baryonic fraction of the critical density,Ωb = ρb /ρcrit ' η10 h−2 /274 = (0.02244 ± 0.00069)h−2 , where h ≡ H0 /100 km s−1 Mpc−1 is thepresent Hubble parameter (see ‘The Cosmological Parameters’ — Sec. 25 of this Review).
The nucleosynthesis chain begins with the formation of deuterium in the process p(n, γ)D.
However, photo-dissociation by the high number density of photons delays production of deuterium(and other complex nuclei) until well after T drops below the binding energy of deuterium, ∆D =2.23 MeV. The quantity η −1 e−∆D /T , i.e., the number of photons per baryon above the deuterium
photo-dissociation threshold, falls below unity at T ' 0.1 MeV; nuclei can then begin to form
without being immediately photo-dissociated again. Only 2-body reactions, such as D(p, γ)3 He and3 He(D, p)4 He are important because the density by this time has become rather low – comparable
to that of air!
Nearly all neutrons end up bound in the most stable light element 4 He. Heavier nuclei do not
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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24. Big Bang Nucleosynthesis

form in any significant quantity both because of the absence of stable nuclei with mass number 5 or
8 (which impedes nucleosynthesis via n4 He, p4 He or 4 He4 He reactions), and the large Coulomb barriers for reactions such as 3 He(4 He, γ)7 Li and 3 He(4 He, γ)7 Be. Hence the primordial mass fractionof 4 He, Yp ≡ ρ(4 He)/ρb , can be estimated by the simple counting argumentYp =2(n/p)' 0.25
1 + n/p(24.1)

where strictly speaking this gives the baryon fraction in 4 He, which is what we will quote throughout.
This differs slightly from the mass fraction due to small binding energy corrections.
There is little sensitivity here to the actual nuclear reaction rates for the production of 4 He.
Nuclear rates are, however, critically important in determining the other ‘left-over’ abundances: D
and 3 He at the level of a few times 10−5 by number relative to H, and 7 Li/H at the level of about
10−10 (when η10 is in the range 1–10). These values can be understood in terms of approximate
analytic arguments [12, 13].
The elemental abundances shown in Fig. 24.1 as a function of η10 were calculated using an
updated version [14] of the Wagoner code [1]; other versions [15–17] too are publicly available. The
4 He curve includes small corrections due to radiative processes at zero and finite temperatures [18],non-equilibrium neutrino heating during e± annihilation [19], and finite nucleon mass effects [20];the range primarily reflects the 2σ uncertainty in the neutron lifetime. The spread in the curves
for D, 3 He, and 7 Li corresponds to the 2σ uncertainties in nuclear cross sections, as estimated byMonte Carlo methods [21–24]. The input nuclear data have been carefully reassessed [2, 14, 21–31],
leading to improved precision for the abundance predictions. In particular, the uncertainty in 7 Li/H
at interesting values of η has been reduced recently by a factor ∼ 2, a consequence of a similar
reduction in the error budget [32] for the dominant mass-7 production channel 3 He(4 He, γ)7 Be.
Polynomial fits to the predicted abundances and the error correlation matrix have been given in
refs. [23, 33]. The boxes in Fig 24.1 show the observationally inferred primordial abundances with
their associated uncertainties, as discussed below.
The nuclear reaction cross sections important for BBN have all been measured at the relevantenergies. Recently however there have been substantial advances in the precision of light element
observations (e.g., D/H) and in the determination of cosmological parameters (e.g., from Planck).
This motivates corresponding improvement in BBN predictions and thus in the key reaction crosssections. Recent measurements of D(p, γ)3 He by the LUNA collaboration have significantly improved the precision of D/H predictions [34]. Even so, the nuclear uncertainties still leave D/H
prediction errors larger than those of the observations [14, 30, 31]. The D(D, n)3 He and D(D, p)3 H
reactions now not only dominate the uncertainty budget, but they can give significantly different
D/H predictions depending on whether one uses just the empirical determination of the cross sections, or also uses theory to guide the functional form. Clearly, more experimental data is needed.
An additional experimental parameter important in determining the light element abundancesis the neutron lifetime, τn , which normalizes (the inverse of) Γn↔p . Its value has been revised
downwards to τn = 879.4 ± 0.6 s (see N Baryons Listing).

24.3 Observations: the Light Element Abundances
BBN theory predicts the universal abundances of D, 3 He, 4 He, and 7 Li which are essentially fixed
by t ∼ 180 s. However, abundances are derived at much later epochs, after stellar nucleosynthesis
commenced. Stars produce heavy elements such as C, N, O, and Fe (“metals”), while the ejected
remains of stellar processing alters the light element abundances from their primordial values. Thus,
one seeks astrophysical sites with low metal abundances to measure light element abundances thatare closer to primordial.
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24. Big Bang Nucleosynthesis

3

BBN is the only significant source of deuterium which is entirely destroyed when it is cycled
into stars [35]. Thus, any detection provides a lower limit to primordial D/H|p , and an upper
limit on η10 . The best proxy to the primordial value of D is its measure in distant and chemicallyunprocessed matter, where stellar processing (astration) is minimal [35, 36]. This has become
possible with the advent of large telescopes, but after nearly three decades of observational efforts
we have only 11 determinations listed in Table 24.1 [37–43].
High-resolution spectra reveal the presence of D in high-redshift, low-metallicity quasar absorption systems via its isotope-shifted Lyman-α absorption features, though, unfortunately, theseare often obscured or contaminated by the hydrogen features of the Lyman-α forest. A few DLA
systems show D lines resolved up to the higher members of the Lyman series. Recent determinations [38, 40] and re-analyses [41–43] provide strikingly improved precision over earlier work. D/Hshows
no correlation with metallicity, redshift, or the neutral hydrogen column density N (HI) (=Rnlos HI ds) integrated over the line-of-sight through the absorber. Metallicities of the absorbers are(0.001 − 0.03)× Solar, and the level astration is estimated at the 0.1-1 % level [36]. In the Galaxy
DI/HI measurements are anti-correlated with metal abundances, which suggests that interstellar
D partly resides in dust particles [45]. However, in the absorbers where deuterium is measured,
the dust content is small, as implied by Solar proportions of the abundances of refractory and non
refractory elements. Thus, the neutral atomic ratio DI/HI ≡ D/H should match the underlying
isotope ratio, and be truly representative of the primordial value D/H|p . The weighted mean of
the 11 most precise measurements in Table 24.1 is D/H|p × 106 = (25.47 ± 0.25). However, thesemeasurements provide χ2 /(N − 1) = 1.295,
p showing that some error is underestimated. We thusincrease the uncertainty by a factor S = χ2 /(N − 1) = 1.137 and the recommended value is:
D/H|p × 106 = (25.47 ± 0.29).

(24.2)

Considering also the previous determinations of [46–50], the weighted mean of 16 measurements
is D/H|p × 106 = (25.36 ± 0.26), while different selections provide D/H|p × 106 = (25.27 ± 0.30) [43]or D/H|p × 106 = (25.45 ± 0.25) [42]. These are all consistent with each other, even without the S
correction.
Table 24.1: D/H measurements. For systems with multiple measurements we used the most recent one which is generally more precise.
QSO
SDSS J1419+0829
HS 0105+1619
QSO B0913+0715
SDSS J1358+0349
SDSS J1358+6522
SDSS J1558−0031
PKS 1937−1009
QSO J1444+2919
PKS 1937−1009
QSO 1009+2956
QSO 1243+307

zem
3.03
2.65
2.78
2.89
3.17
2.82
3.78
2.66
3.78
2.63
2.55

zabs
3.049
2.536
2.618
2.853
3.067
2.702
3.256
2.437
3.572
2.504
2.525

log N ((HI))
20.392±0.003
19.426±0.006
20.312±0.008
20.524±0.006
20.495±0.008
20.75±0.03
18.09±0.03
19.983±0.010
17.925±0.006
17.362±0.005
19.761±0.026[X/H]-1.92[O/H]-1.77[O/H]-2.40[O/H]-2.80[O/H]-2.33[O/H]-1.55[O/H]-1.87[O/H]-2.04[O/H]-2.26[O/H]-2.50[Si/H]-2.77[O/H](D/H) × 106
25.06 ± 0.52
25.76 ± 1.54
25.29 ± 1.05
26.18 ± 0.72
25.82 ± 0.71
24.04 ± 1.44
24.49 ± 2.80
+3.3
19.68 −2.8
26.24 ± 0.48
+4.1
24.77 −3.5
23.88 ± 0.82

Ref
[37]
[37]
[37]
[38]
[37]
[37]
[39]
[40]
[41]
[42]
[43]

25.47 ± 0.29

Weighted mean, with S = 1.137

The primordial 4 He abundance is best determined through recombination emission lines of
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24. Big Bang Nucleosynthesis

4

D/H

4

He mass fraction

0.27

baryon density parameter ΩBh2
10−2

0.26
0.25
0.24
0.23
10−3
C
M
B

3

He/H

10−4

10−5

7

Li/H

10−9

10−10
10−10

10−9
baryon-to-photon ratio η = nb/nγ

Figure 24.1: The primordial abundances of 4 He, D, 3 He, and 7 Li as predicted by the standard
model of Big-Bang nucleosynthesis — the bands show the 95% CL range [44]. Boxes indicate theobserved light element abundances. The narrow vertical band indicates the CMB measure of thecosmic baryon density, while the wider band indicates the BBN D+4 He concordance range (bothat 95% CL).

He and H in the most metal-poor extragalactic HII (ionized) regions, viz. blue compact galaxies,
generally found at low redshift. There is now a large body of data on 4 He and CNO in these galaxies,
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24. Big Bang Nucleosynthesis

5with over 1000 such systems in the Sloan Digital Sky Survey alone [51]. These data confirm thatthe stellar contribution to the helium abundance is positively correlated with metal production,
so extrapolation to zero metallicity gives the primordial 4 He abundance Yp . However, HII regions
are complex systems and several physical parameters enter in the He/H determination, notably
the electron density and temperature, as well as reddening. Thus, systematic effects dominate theuncertainties in the abundance determination [52,53]. A major step forward has been the inclusionof the He λ10830 infrared emission line which shows a strong dependence on the electron density
and is thus useful to break the degeneracy with the temperature, allowing for a more robust helium
abundance determination. In recent works the underlying 4 He stellar absorption, and/or the newly
derived values of the HeI-recombination and H-excitation-collisional coefficients are adressed andthe 4 He abundances have increased significantly. Some recent results are reported in Table 24.2.
Table 24.2: Recent primordial 4 He measurements in extragalactic HII
regions.
Yp (4 He)
0.24530.24510.243
0.24620.2436
0.24480.2448±1σstat0.00340.00190.005
0.00220.00400.0027±1σsys±1σtot0.00180.00260.00180.00330.0033# systems
16
1
16
120
54
7
17

Ref
[54]
[55]
[56]
[57]
[58]
[59]
[60]

There is a reassuring convergence towards the value of Yp = 0.245 between detailed analysesof specific extragalactic HII regions with other (statistically more significant) analyses of manysystems. Thus our recommended 4 He abundance is:
Yp = 0.245 ± 0.003.

(24.3)

The central value is close to the mean/weighted average of the values in Table 24.2, however wecaution that combining these partially overlapping data sets is not straightforward. The uncertainty
reflects the combined statistical and systematic errors, with the latter, estimated to be ±0.002 [59],being dominant.
The best suited objects for the determination of primordial 7 Li are metal-poor stars in the
Galactic halo, which have metallicities going down to 10−6 of the Solar value [61]. Observations havelong shown [62–65] that 7 Li does not vary significantly in halo dwarfs with metallicities <∼ 1/30 ofSolar — the Spite plateau [62,66]. Recent observations show a puzzling drop in the Li/H abundancein metal-poor stars with [Fe/H] < −3.0 [67–69]. This becomes particularly acute at the very low
metallicity end where only one star out of the seven dwarfs with metallicities [Fe/H] <∼ −4.5 shows a
7 Li abundance close to the Spite Plateau, while in the others where it ought to be present it is either
lower or totally absent [61,70]. The reason for the increase in scatter at low metallicity is unknown
and prevents derivation of the primordial 7 Li value by extrapolation to zero metallicity [68, 69].
To estimate the primordial 7 Li value we consider only stars with metallicity in the range −2.8 <[Fe/H] < −1.5 [69], where no scatter in excess of the observational errors is observed. This yields:
Li/H|p = (1.6 ± 0.3) × 10−10 .
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(24.4)

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24. Big Bang Nucleosynthesis

Strictly speaking the suggested primordial 7 Li abundance should be considered a lower bound rather
than a measure. In fact, 7 Li in Pop II stars may have been partially destroyed due to mixing of
the outer layers with the hotter interior [71]. Such processes can be constrained by the absenceof significant scatter in 7 Li versus Tef f [64], but 7 Li depletion by a factor as large as ∼ 1.8 may
have occurred [64, 72]. Stellar determination of Li abundances typically sum over both 6 Li and 7 Li
isotopes. however, high-precision measurements indicate 6 Li/7 Li ≤ 0.05, thus confirming that 7 Li
is dominant [73].
The primordial abundance of 3 He has the poorest observational determination of all of thelight nuclides. The only data available come from the Solar system and from solar-metallicity
HII regions in the Galaxy [74]. Therefore, inferring the primordial 3 He abundance is problematic,
compounded by the fact that stellar nucleosynthesis models for 3 He are in conflict with observations.
Consequently, we consider it inappropriate to use 3 He (and also D+3 He) as a cosmological probe.

24.4 Concordance, Dark Matter, and the CMB
We now use the observed light element abundances to test the theory. We first consider standard
BBN, which is based on Standard Model physics alone, so Nν = 3 and the only free parameter is thebaryon-to-photon ratio η. (The implications of BBN for physics beyond the Standard Model will beconsidered below). Thus, any abundance measurement determines η, and additional measurements
overconstrain the theory and thereby provide a consistency check.
While the η ranges spanned by the boxes in Fig 24.1 do not all overlap, they are all within afactor ∼ 2 of each other. In particular, the lithium abundance corresponds to η values that areinconsistent with that of the (now very precise) D/H abundance as well as the less-constraining
4 He abundance. This discrepancy marks the lithium problem. The problem could simply reflect
difficulty in determining the primordial lithium abundance, or could hint at a more fundamental
omission in the theory. The possibility that lithium reveals new physics is addressed in detail in thenext section. If however we exclude the lithium constraint because its inferred abundance suffersfrom systematic uncertainties, then D/H and 4 He are in agreement. The concordant η range isessentially determined by D/H, and yields [75]
η10 = 6.040 ± 0.118(24.5)

where the errors are 1σ. Despite the lithium problem, the overall concordance remains remarkable:using only well-established microphysics we can extrapolate back to t ∼ 1 s to predict light element
abundances spanning nine orders of magnitude, in approximate agreement with observation. Thisis a major success for the standard cosmology, and inspires confidence in extrapolation back to such
early times.
This concordance provides a measure of the baryon content:Ωb h2 = 0.02205 ± 0.00043(24.6)

where again errors are 1σ, a result that plays a key role in our understanding of the matter budgetof the Universe. First of all Ωb  1, i.e., baryons cannot close the Universe [76]. Furthermore, thecosmic density of (optically) luminous matter is Ωlum ' 0.0024h−1 [77], so that Ωb  Ωlum : mostbaryons are optically dark, probably in the form of a diffuse intergalactic medium [78]. Finally,
given that Ωm ∼ 0.3 (see the ‘Dark Matter’ and ‘Cosmological Parameters’ reviews), we infer thatmost matter in the Universe is not only dark, but also takes some non-baryonic (more precisely,
non-nucleonic) form.
The BBN prediction for the cosmic baryon density can be tested through precision measurements of CMB temperature fluctuations (see the ‘Cosmic Microwave Background’ review). One can
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24. Big Bang Nucleosynthesis

determine η from the amplitudes of the acoustic peaks in the CMB angular power spectrum [79],making it possible to compare two measures of η using very different physics, at two widely separated
epochs. In the standard cosmology, there is no change in η between BBN and CMB decoupling,
thus, a comparison of ηBBN and ηCMB is a key test. Agreement would endorse the standard picture,
while disagreement could point to new physics during/between the BBN and CMB epochs.
The analysis described in the Cosmic Microwave Background review (Sec.29), based on Planck
TT, TE, EE + lowE data and lensing, yields Ωb h2 = 0.02237 ± 0.00015 [80], which corresponds
to η10 = 6.12 ± 0.04 [81]. This result depends weakly on the primordial helium abundance, andthe fiducial Planck analysis uses BBN theory to fix Yp (η). Without BBN theory, the Planck
TT, TE, EE + lowE data plus lensing give Ωb h2 = 0.02230 ± 0.00021, corresponding to η10 =6.104 ± 0.058. As shown in Fig. 24.1, this CMB estimate of the baryon density (narrow verticalband) is consistent with the BBN range, i.e., in good agreement with the value inferred from highredshift D/H measurements and local 4 He determinations; together these observations span diverse
environments from redshifts z ∼ 1000 to the present. Combining the CMB and BBN sharpens thebaryon measures to η10 = 6.115 ± 0.038 and Ωb h2 = 0.02233 ± 0.00014 [75].
The 4 He abundance is proportional to the n/p ratio when the weak-interaction rate falls behindthe Hubble expansion rate at Tfr ∼ 1 MeV. The presence of additional neutrino flavors (or of any
other relativistic species) at this time increases g∗ , hence the expansion rate, leading to a larger valueof Tfr , n/p, and therefore Yp [10, 82]. In the Standard Model at T = 1 MeV, g∗ = 5.5 + 74 Nν , whereNν is the effective number of (nearly) massless neutrino flavors. The helium curves in 24.1 werecomputed taking Nν = 3; small corrections for non-equilibrium neutrino heating [19] are includedin the thermal evolution and lead to an effective Nν = 3.044 compared to assuming instantaneous
neutrino freezeout (see ‘Big Bang Cosmology’ — Sec. 22 of this Review). The computed 4 He
abundance scales as ∆ Yp ' 0.013∆Nν [11]. Clearly the central value for Nν from BBN will dependon η, which is independently determined (with weaker sensitivity to Nν ) by the adopted D or 7 Li
abundance. For example, if the best value for the observed primordial 4 He abundance is 0.249,
then, for η10 ∼ 6, the central value for Nν is very close to 3. A maximum likelihood analysis onη and Nν based on 4 He and D abundances nearly identical to those above finds the (correlated)
68% CL ranges to be η10 = 6.088 ± 0.054 and Nν = 2.898 ± 0.141 [44, 75, 83]. Identical results are
obtained using a simpler method to extract such bounds based on χ2 statistics, given a set of input
abundances [84].
The CMB damping tail is sensitive to the primordial 4 He abundance independently of both BBN
and local 4 He measurements [85]. The Planck analysis using TT, TE, EE+lowE and lensing but not+0.24
the BBN Yp (η) relation gives a 4 He mass fraction 0.239+0.024−0.025 , and nucleon fraction Yp = 0.240−0.25 ,both at 95% CL [80]. This is consistent with the HII region helium abundance determination.
Moreover, this value is consistent with the Standard (Nν = 3) BBN prediction for Yp with the
Planck-determined baryon density. This concordance represents a successful CMB-only test of
BBN.
The precision determination of the baryon density using the CMB motivates using this as an
input to BBN calculations. Within the context of the Standard Model, BBN then becomes azero-parameter theory, and the light element abundances are completely determined to within theuncertainties in ηCMB and the BBN theoretical errors. Comparison with the observed abundancesthen can be used to test the astrophysics of post-BBN light element evolution [86]. Alternatively,
one can consider possible physics beyond the Standard Model (e.g., which might change the expansion rate during BBN) and then use all of the abundances to test such models; this is discussed
in 24.6 below.
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24. Big Bang Nucleosynthesis

24.5 The Lithium Problem and its Possible Resolution
As Fig. 24.1 shows, stellar Li/H measurements are inconsistent with the D/H (and CMB)
measurements, given the error budgets we have quoted. For instance, the value of Li/H|p =(4.72 ± 0.7) × 10−10 [44] is a factor 3.1 higher than in eq.24.4 which is a 4.4 σ discrepancy.
Stars that have been accreted by the Milky Way Gyrs ago from external galaxies show thesame abundances as those in the Milky Way, showing that the Li problem is universal [87–89].
The question then becomes pressing as to whether this mismatch comes from systematic errors in
the observed abundances, and/or uncertainties in stellar astrophysics or nuclear inputs, or whether
there might be new physics at work [9]. Nuclear inputs (cross sections) for BBN reactions are constrained by extensive laboratory measurements; to increase 7 Be destruction requires enhancementof otherwise subdominant processes that can be attained by missed resonances in a few reactions
such as 7 Be(d, p)2α if the compound nuclear state properties are particularly favorable [29, 90–92].
However, experimental searches have now closed off these possibilities [93–95], making a nuclear fix
increasingly unlikely.
Another means to solve the lithium problem is by in situ destruction over the long lifetimes of
the host halo stars. Stellar depletion mechanisms include diffusion, rotationally induced mixing, or
pre-main-sequence depletion. These effects certainly occur, but to reduce lithium to the required
levels generally requires some ad hoc mechanism and fine tuning of the initial stellar parameters[72, 96–98]. General features of diffusive models are a dispersion in the Li abundances and apronounced downturn in the Li abundances at the hot end of the Li plateau. Some extra turbulenceneeds to be invoked to limit diffusion in the hotter stars and to restore uniform Li abundance along
the Spite plateau [98]. Li abundances for over 100 000 field stars have been obtained in the GALAH(Galactic Archeology with HERMES) survey. Warm stars with [Fe/H] in between -1.0 and -0.5 form
an elevated plateau consistent with the BBN prediction and it has been suggested that this could
have been also true for the more metal poor stars which have evolved further [99]. Li destructionin the pre-Main sequence phase has been also proposed [97].
Recent 6 Li measurements have cast new light on the lithium problem. BBN production of 6 Li
is negligible [100]; instead it is created much later by energetic cosmic-ray p and 4 He interactions
with interstellar gas, in fusion reactions such as 4 He + 4 He → 6,7 Li + · · · . and spallation reactions
on interstellar carbon, nitrogen, and oxygen such as pcr + 16 O → 6,7 Li9 Be10,11 B + · · · . Thus 6 Li,
beryllium, and boron are co-produced, and the detection of Be and B in metal-poor stars thus
requires cosmic-ray 6 Li was present when these stars were formed. 6 Li detections were reported forsome of these stars [101–103], and because the weakly-bound 6 Li nucleus is more easily destroyed
than 7 Li, the survival of 6 Li implied that 7 Li destruction should be small. But new observations
place strong upper limits on 6 Li/H in the plateau stars where this isotope had long been reported
to exist [104]. This removes the 6 Li argument against stellar depletion. Indeed, detailed models of
cosmic-ray lithium production can quantify the 6 Li depletion, and may suggest the 7 Li destruction
could be sufficient to explain the mismatch between the observed Li abundance and the expected
BBN 7 Li [105]. This line of argument supports the predictions of stellar depletion as the possible
resolution of the lithium problem [72, 96–98]. Additional 6 Li limits or detections, in concert withmodel calculations, can firm up this conclusion.
Observations of interstellar lithium in low-metallicity systems probe lithium abundances not
subject to stellar depletion. Measurements of interstellar Li/H in the Small Magellanic Cloudlie near the primordial level, but also are consistent with Milky Way stellar abundances at thatmetallicity (∼ 1/4 solar) [106]. Additional such measurements in more metal-poor systems would
be of great interest.
It remains possible that the lithium problem points to new physics. Nucleosynthesis models inwhich the baryon-to-photon ratio is inhomogeneous can alter abundances for a given ηBBN , but will
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924. Big Bang Nucleosynthesis

overproduce 7 Li [107]. Entropy generation by some non-standard process could have decreased η
between the BBN era and CMB decoupling, however the lack of spectral distortions in the CMB
rules out any significant energy injection up to a redshift z ∼ 107 [108]. The most intriguing
resolution of the lithium problem thus involves new physics during BBN [7–9]
We summarize the general features of such solutions here, and later consider examples in thecontext of specific particle physics models. Many proposed solutions introduce perturbations tolight-element formation during BBN; while all element abundances may suffer perturbations, theinterplay of 7 Li and D is often the most important i.e. observations of D often provide the strongest
constraints on the allowed perturbations to 7 Li. In this connection it is important to note that thenew, very precise determination of D/H will significantly constrain the ability of such models toameliorate or solve the lithium problem.
A well studied class of models invokes the injection of suprathermal hadronic or electromagnetic particles due to decays of dark matter particles. The effects are complex and depend on thenature of the decaying particles and their branchings and spectra. However, the models that mostsuccessfully solve the lithium problem generally feature non-thermal nucleons, which dissociate alllight elements. Dissociation of even a small fraction of 4 He introduces a large abundance of freeneutrons, which quickly thermalize. The thermal neutrons drive the 7 Be(n, p)7 Li conversion of
7 Be. The resulting 7 Li has a lower Coulomb barrier relative to 7 Be and is readily destroyed via
7 Li(p, α)4 He [109, 110]]. But 4 He dissociation also produces D directly as well as via nonthermal
neutron n(p, γ)d reactions. This introduces a tension between Li/H reduction and D/H enhancement that becomes increasingly restrictive with the increasing precision of deuterium observations.
Indeed, this now forces particle injection scenarios to make very small 7 Li perturbations — far shortof the level needed. An exception is a recent model wherein MeV-scale decays by construction avoid
4 He dissociation and associated D/H overproduction, instead borrowing neutrons by dissociating
only deuterons [111].
Another important class of models retains the standard cosmic particle content, but changes
their interactions via time variations in the fundamental constants [112–118]. Here too, the details
are model-dependent, but scenarios that solve or alleviate the lithium problem often feature perturbations to the deuteron binding energy. A weaker D binding leads to the D bottleneck being
overcome later, so that element formation commences at a lower temperature and lower density.
This leads in turn to slower nuclear rates that freeze out earlier. The net result is a higher final
D/H, due to less efficient processing into 4 He, but also lower Li, due to suppressed production via
3 He(α, γ)7 Be.
The cosmological lithium problem remains an unresolved issue in BBN. Nevertheless, the remarkable concordance between the CMB and the D (as well as 4 He) abundance, is a non-trivial
success, and provides important constraints on the early Universe.

24.6 Beyond the Standard Model
Given the simple physics underlying BBN, it is remarkable that it still provides the most effective
test for the cosmological viability of ideas concerning physics beyond the Standard Model. Althoughbaryogenesis and inflation must have occurred at higher temperatures in the early Universe, we
do not as yet have ‘standard models’ for these, so BBN still marks the boundary between theestablished and the speculative in Big Bang cosmology. It might appear possible to push theboundary backto the quark-hadron transition at T ∼ ΛQCD , or electroweak symmetry breaking√
at T ∼ 1/ GF ; however, so far no observable relics of these epochs have been identified, either
theoretically or observationally. Thus, although the Standard Model provides a precise descriptionof physics up to the Fermi scale, cosmology cannot be traced in detail before the BBN era.
The CMB power spectrum in the damping tail is independently sensitive to Nν (e.g. [119]).
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24. Big Bang Nucleosynthesis

The CMB value NνCMB probes the cosmic radiation content at (re)combination, so a discrepancy
would imply new physics or astrophysics. Indeed, observations by the South Pole Telescope implied
NνCMB = 3.85 ± 0.62 [120], prompting discussion of dark radiation such as sterile neutrinos [121].
+0.36
However, Planck 2018 results give NνCMB = 2.92+0.37, 95% CL, when using Planck TT, TE,
EE+lowE, a result quite consistent with 3 Standard Model neutrinos [80] (and adjusting for the
CMB’s measurement of Neff = 3.044 due to neutrino heading effects [122–124]). Indeed, the BBN
and CMB constraints on Nν are independent and of similar precision, so that it is now possible tolimit any change in this parameter (and/or the baryon-to-photon ratio) between nucleosynthesis
and recombination [75]. This can, for example, constrain models with late particle decays, or withearly dark energy.
Just as one can use the measured helium abundance to place limits on g∗ [82, 113, 125–127],
any changes in the strong, weak, electromagnetic, or gravitational coupling constants, arising e.g.,
from the dynamics of new dimensions, can be similarly constrained [128], as can any speed-up of
the expansion rate in, e.g., scalar-tensor theories of gravity [129].
The limits on Nν can be translated into limits on other types of particles or particle masses
that would affect the expansion rate of the Universe during nucleosynthesis. For example, consider
sterile neutrinos with only right-handed interactions of strength GR < GF . Such particles would
decouple at higher temperature than (left-handed) neutrinos, so their number density (∝ T 3 )relative to neutrinos would be reduced by any subsequent entropy release, e.g., due to annihilationsof massive particles that become non-relativistic between the two decoupling temperatures. Thus,(relativistic) particles with less than full strength weak interactions contribute less to the energy
density than particles that remain in equilibrium up to the time of nucleosynthesis [130]. If we
impose Nν < 4 as an illustrative constraint, then the three right-handed neutrinos must have atemperature 3(TνR /TνL )4 < 1. Since the temperature of the decoupled νR is determined by entropy
conservation (see ‘Big Bang Cosmology’ — Sec. 22 of this Review), TνR /TνL = [(43/4)/g∗ (Td )]1/3 <
0.76, where Td is the decoupling temperature of the νR . This requires g∗ (Td ) > 24, so decouplingmust have occurred at Td > 140 MeV. The decoupling temperature is related to GR through(GR /GF )2 ∼ (Td /3 MeV)−3 , where 3 MeV is the decoupling temperature for νL s. This yields a limit
GR . 10−2 GF . The above argument sets lower limits on the masses of new Z 0 gauge bosons to whichright-handed neutrinos would be coupled in models of superstrings [131], or extended technicolour[132]. Similarly a Dirac magnetic moment for neutrinos, which would allow the right-handed states
to be produced through scattering and thus increase g∗ , can be significantly constrained [133], as
can any new interactions for neutrinos that have a similar effect [134–136]. Right-handed states
can be populated directly by helicity-flip scattering if the neutrino mass is large enough, and thisproperty has been used to infer a bound of mντ . 1 MeV (taking Nν < 4) [137]. If there is mixing
between active and sterile neutrinos then the effect on BBN is more complicated [138, 139].
BBN limits on the cosmic expansion rate constrain supersymmetric scenarios in which theneutralino or gravitino are very light, so that they contribute to g∗ [140]. A gravitino in the mass
range ∼ 10−4 − 10 eV will affect the expansion rate of the Universe similarly to a light neutralino(which is however now probably ruled out by collider data, especially the decays of the Higgs-likeboson). The net contribution to Nν then ranges between 0.74 and 1.69, depending on the gravitino
and slepton masses [141].
The limit on the expansion rate during BBN can also be translated into bounds on the mass/lifetime of non-relativistic particles that decay during BBN. This results in an even faster speed-up
rate, and typically also changes the entropy [142–144]. If the decays include Standard Modelparticles, the resulting electromagnetic [145] [86, 131, 146] and/or hadronic [147, 148] cascades canstrongly perturb the light elements, which leads to even stronger constraints. Such arguments havebeen applied to rule out an MeV mass for ντ , which decays during nucleosynthesis [149].
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24. Big Bang Nucleosynthesis

Decaying-particle arguments have proved very effective in probing supersymmetry. Lightelement abundances generally are complementary to accelerator data in constraining SUSY parameter space, with BBN reaching to values kinematically inaccessible to the LHC. Much recent
interest has focused on the case in which the next-to-lightest supersymmetric particle is metastableand decays during or after BBN. The constraints on unstable particles discussed above imply stringent bounds on the allowed abundance of such particles [109]; if the metastable particle is charged(e.g., the stau), then it is possible for it to form atom-like electromagnetic bound states with nuclei, and the resulting impact on light elements can be quite complex [8, 90, 150]. Moreover, SUSY
decays can destroy 7 Li and/or produce 6 Li, leading to a possible supersymmetric solution to thelithium problems noted above [151] (see [7] for a review).
These arguments impose powerful constraints on supersymmetric inflationary cosmology [86,131, 146–148], particularly thermal leptogenesis [152]. These limits can be evaded only if the gravitino is massive enough to decay before BBN, i.e., m3/2 & 50 TeV [153] (which would be unnatural), or if it is in fact the lightest supersymmetric particle and thus stable [131, 146, 154, 155].
Similar constraints apply to moduli – very weakly coupled fields in string theory that obtain anelectroweak-scale mass from supersymmetry breaking [156].
Finally, we mention that BBN places powerful constraints on the possibility that there are
new large dimensions in nature, perhaps enabling the scale of quantum gravity to be as low as theelectroweak scale [157]. Thus, Standard Model fields may be localized on a brane, while gravity alone
propagates in the bulk. It has been further noted that the new dimensions may be non-compact,even infinite [158], and the cosmology of such models has attracted considerable attention. The
expansion rate in the early Universe can be significantly modified, so BBN is able to set interesting
constraints on such possibilities [159, 160].
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