Light Element Nucleosynthesis Encyclopedia of Astronomy

eaa.iop.org DOI: 10.1888/0333750888/2130

Light Element Nucleosynthesis Gary Steigman

From Encyclopedia of Astronomy & Astrophysics P. Murdin

ISBN: 0333750888

Institute of Physics Publishing Bristol and Philadelphia

Downloaded on Tue Jan 31 17:16:57 GMT 2006 [127.0.0.1]

Terms and Conditions Light Element Nucleosynthesis E NCYCLOPEDIA OF A STRONOMY AND A STROPHYSICS

Light Element Nucleosynthesis As a result, the numbers and distributions (of momentum and energy) of all these particles are accurately predicted The early universe was hot and dense behaving as a cosmic by well-known physics. nuclear reactor during the first 20 min of its evolution. It was, however, a ‘defective’ nuclear reactor, expanding and Nucleosynthesis in the early universe cooling very rapidly. As a result, only a handful of the The primordial yields of light elements are determined lightest nuclides were synthesized before the density and by the competition between the expansion rate of the temperature dropped too low for the nuclear reaction rates universe (the Hubble parameter H ) and the rates of to compete with the universal expansion rate (see UNIVERSE: the weak and nuclear reactions (see HUBBLE CONSTANT). 1 THERMAL HISTORY). After hydrogen ( H ≡ protons) the next It is the weak interaction, interconverting neutrons and most abundant element to emerge from the Big Bang is protons, that largely determines the amount of 4He which helium (4He ≡ alpha particles). Isotopes of these nuclides may be synthesized, while detailed nuclear reaction rates (deuterium and helium-3) are the next most abundant regulate the production (and destruction) of the other light primordially. Then there is a large gap to the much elements. In the standard model of cosmology the early lower abundance of lithium-7. The relative abundances expansion rate is fixed by the total energy density ρ, of all other primordially-produced nuclei are very low, H 2 = πGρ/ much smaller than their locally observed (or, currently 8 3 (1) observable) abundances. After a brief description of the G early evolution of the universe emphasizing those aspects where is Newton’s gravitational constant. In the most relevant to primordial, or ‘big bang’ nucleosynthesis standard model of particle physics the early energy density (BBN), the predicted abundances of the light nuclides will is dominated by the lightest, relativistic particles. For the be presented as a function of the one ‘free’ parameter epoch when the universe is a few tenths of a second old (in the simplest, ‘standard’ model: SBBN), the nucleon and older, and the temperature is less than a few MeV, (or ‘baryon’) abundance. Then, each element will ρ = ργ + ρ +Nν ρν (2) be considered in turn in a confrontation between the e predictions of SBBN and the observational data. At present where ργ , ρ and ρν are the energy densities in photons, (summer 1999) there is remarkable agreement between e electrons and positrons, and massless neutrinos and the SBBN predictions of the abundances of four nuclides antineutrinos (one species), respectively; Nν is the number (D, 3He, 4He and 7Li) and their primordial abundances of massless (or, very light: mν 1 MeV) neutrino species inferred from the observations. However, there are some which, in standard BBN, is exactly 3. In considering hints that this concordance of the hot big bang model variations on the theme of the standard model, it is may be imperfect, so we will also explore some variations useful to allow Nν to differ from 3 to account for the on the theme of the standard model with regard to their presence of ‘new’ particles and/or any suppression of the modifications of the predicted primordial abundances of standard particles (e.g. if the τ neutrino should have a large the light elements. mass). Since the energy density in relativistic particles In the simplest, standard, hot big bang model the scales as the fourth power of the temperature, the early currently observed large-scale isotropy and homogeneity expansion rate scales as the square of the temperature of the universe is assumed to apply during earlier epochs with a coefficient that depends on the number of different in its evolution (see COSMOLOGY: STANDARD MODEL). Given the relativistic species. The more such species, the faster the currently observed universal expansion and the matter universe expands, the earlier (higher temperature) will the and radiation (CBR: ‘cosmic background radiation’, the weak and nuclear reactions drop out of equilibrium. It is 2.7 K ‘black body radiation’) content, it is a straightforward useful to write the total energy density in terms of the application of classical physics to extrapolate back to photon energy density and g, the equivalent number of earlier epochs in the history of the universe (see COSMIC relativistic degrees of freedom (i.e. helicity states, modulo MICROWAVE BACKGROUND). At a time of order 0.1 s after the the different contributions to the energy density from expansion began the universe was filled with a hot, dense fermions and bosons), plasma of particles. The most abundant were photons, electron–positron pairs, particle–antiparticle pairs of all ρ ≡ (g/2)ργ . (3) ν ν ν known ‘flavors’ of neutrinos ( e, µ and τ ) and trace T ∼ g = / amounts of neutrons and protons (‘nucleons’ or ‘baryons’). In the standard model at 1 MeV, SM 43 4. At such early times the thermal energy of these particles Account may be taken of additional degrees of freedom was very high, of order a few MeV. With the exception by comparing their contribution to ρ with that of one of the nucleons, it is known or assumed that all the additional light neutrino species: other particles present were extremely relativistic at this ρ ≡ ρ − ρ ≡ N ρ . time. Given their high energies (and velocities close to, TOT SM ν ν (4) or exactly equal to, the speed of light) and high densities, the electroweak interactions among these particles were If the early energy density deviates from that of the sufficiently rapid to have established thermal equilibrium. standard model, the early expansion rate (or, equivalently,

0 the age at a ﬁxed temperature) will change as well. The 10 ξ ≡ H/H N ‘speed-up’ factor SM may be related to ν by -1 10 Y ξ = (ρ/ρ )1/2 = ( N / )1/2. p SM 1+7 ν 43 (5)

-2 As we will see shortly, the 4He abundance is very 10 sensitive to the early expansion rate while the abundances -3 2 of the other light nuclides depend mainly on the nuclear 10 H reaction rates which scale with the nucleon (baryon) density. Since the baryon density is always changing -4 10 as the universe expands, it is convenient to distinguish between models with different baryon densities using a 7 -5 10 , y 3 dimensionless parameter which either is conserved or, 3 He , y changes in a known and calculable fashion. From the 2

, y -6 very early universe until now the number of baryons in p 10 Y a comoving volume has been preserved and the same is roughly true for photons since the end of BBN. Therefore, -7 n 10 the ratio of number densities of baryons ( B) and photons (nγ ) provides just such a measure of the universal baryon -8 abundance: 10

10 η ≡ (n /nγ ) η ≡ η. -9 B 0 10 10 (6) 10 7 Li The universal density of photons at present (throughout -10 this article the present epoch is indicated by the subscript 10 = . ‘0’) is dominated by those in the CBR (for T0 2 73 K, − n = 3 -11 γ 0 412 cm ) so that the baryon density parameter 10 ≡ (ρ /ρ ) -12 -11 -10 -9 -8 -7 B B c 0, the ratio of the present baryon density 10 10 10 10 10 10 ρ ρ η ( B) to the present critical density ( c), may be related to η ≡ and the present value of the Hubble parameter H0 100h km s−1 Mpc−1, Figure 1. The predicted primordial abundances as a function of 4 η. Yp is the He mass fraction while y2P, y3P, y7P are the number η = h2. 3 4 10 273 B (7) density ratios to hydrogen of D, He and He respectively.

It should be noted that prior to electron–positron annihilation there were fewer photons in every comoving steps necessary in order to go from ‘here and now’ to ‘there volume (by a factor very close to 4/11); this is and then’ when using the data to infer the true primordial automatically accounted for in all numerical BBN codes. abundances. Then we will be in a position to assess the It is simply a matter of consensus and convenience that the consistency of the standard model. baryon abundance is quoted in terms of its present value. 4 In SBBN (i.e. Nν = 3) the abundances of the light Weak equilibrium and the He abundance nuclides synthesized primordially depend on only one Consider now those early epochs when the universe was ‘free’ parameter, η. SBBN is thus ‘overconstrained’ since only a few tenths of a second old and the radiation one value (or, a narrow range of values set by the filling it was at a temperature (thermal energy) of a few observational and theoretical reaction rate uncertainties) MeV. According to the standard model, at those early of η must account consistently for the primordial times the universe was a hot, dense ‘soup’ of relativistic abundances of D, 3He, 4He and 7Li. At the same time particles (photons, e± pairs, three ‘flavors’ (e, µ, τ)of this value or range of η must be consistent with current neutrino–antineutrino pairs) along with a trace amount estimates of (or, bounds to) the present baryon density. (at the level of a few parts in 1010) of neutrons and For these reasons BBN is one of the key pillars supporting protons. At such high temperatures and densities both the the edifice of the standard model of cosmology and it is the weak and the nuclear reaction rates are sufficiently rapid only one which offers a glimpse of the earliest evolution (compared with the early universe expansion rate) that all of the universe. In the following we will first identify particles have come to equilibrium. A key consequence the key landmarks in the first 20 min in the evolution of of equilibrium is that the earlier history of the evolution the universe in order to identify the physical processes of the universe is irrelevant for an understanding of responsible for determining the primordial abundances BBN. When the temperature drops below a few MeV the of the light nuclides. Then, after presenting the SBBN weakly interacting neutrinos effectively decouple from the predictions (as a function of η; see figure 1) we will review photons and e± pairs, but they still play an important role the current status of the observational data, as well as the in regulating the neutron-to-proton ratio.

0.26 At high temperatures, neutrons and protons are continuously interconverting via the weak interactions: + ↔ ν ν ↔ − ↔ − ν 0.25 n+e p+¯e,n+ e p+e , and n p+e +¯e. When the interconversion rate is faster than the expansion rate, the neutron-to-proton ratio tracks its equilibrium 0.24 value, decreasing exponentially with temperature (n/p = Y −m/T m = . e , where 1 29 MeV is the neutron–proton 0.23 mass difference). A comparison of the weak rates with the universal expansion rate reveals that equilibrium may be 0.22 maintained until the temperature drops below ∼0.8 MeV. When the interconversion rate becomes less than the n/p 0.21 expansion rate, the ratio effectively ‘freezes out’ (at 110 a value of ≈1/6), thereafter decreasing slowly, mainly as a result of free neutron decay. η10 Although n/p freeze-out occurs at a temperature below the deuterium binding energy, E = 2.2 MeV, B 4 σ the first link in the nucleosynthetic chain, p + n → Figure 2. The predicted He abundance (solid curve) and the 2 theoretical uncertainty [2]. The horizontal lines show the range D+γ , is ineffective in jump-starting BBN since the −E /T indicated by the observational data. photodestruction rate of deuterium (∝ nγ e B ) is much ∝ n larger than the deuterium production rate ( B) owing 9 to the very large universal photon-to-baryon ratio ( 10 ). Nν and on particle physics beyond the standard model Thus, the universe must ‘wait’ until there are so few [1]. sufficiently energetic photons that deuterium becomes It should be noted that the uncertainty in the BBN- effectively stable against photodissociation. This occurs predicted mass fraction of 4He is very small and almost for temperatures 80 keV, at which time neutrons are entirely dominated by the (small) uncertainty in the n–p 4 rapidly incorporated into He with an efficiency of interconversion rates. These rates may be ‘normalized’ 99.99%. This efficiency is driven by the tight binding τ through the neutron lifetime, n, whose current standard 4 of the He nucleus, along with the roadblock to further value is 887 ± 2 s (actually, 886.7 ± 1.9 s). To very nucleosynthesis imposed by the absence of a stable nucleus τ good accuracy, a 1 s uncertainty in n corresponds to T n/p − at mass 5. By this time ( 80 keV), the ratio an uncertainty in Y of order 2 × 10 4. At this tiny ∼ / p has dropped to 1 7, and simple counting (2 neutrons level of uncertainty it is important to include finite-mass, 4 4 in every He nucleus) yields an estimated primordial He zero- and finite-temperature radiative corrections, and mass fraction (n/p) Coulomb corrections to the weak rates. However, within Y ≈ 2 ≈ . . P n/p 0 25 (8) the last few years it has emerged that the largest error 1+ Y in the BBN-prediction of p was due to a too large time- As a result of its large binding energy and the gap at mass step in the numerical code. With this now under control, 5, the primordial abundance of 4He is relatively insensitive it is estimated that the residual theoretical uncertainty τ to the nuclear reaction rates and, therefore, to the baryon (in addition to that from the uncertainty in n)isofthe abundance (η). As may be seen in figure 1, while η varies by order of 2 parts in 104. Indeed, a comparison of two 4 Y orders of magnitude, the predicted He mass fraction, p, major, independent BBN codes reveals agreement in the ≤ η ≤ Y . ± . changes by factors of only a few. Indeed, for 1 10 10, predicted values of p to 0 0001 0 0001 over the entire . ≤ Y ≤ . ≤ η ≤ 0 22 P 0 25. As may be seen in figures 1 and 2, there range 1 10 10. In figure 2 is shown the BBN-predicted Y η 4 Y η is a very slight increase in p with . This is mainly due He mass fraction, p, as a function of ; the thickness of ± σ η to BBN beginning earlier, when there are more neutrons the band is the 2 theoretical uncertainty. For 10 2 4 σ Y × −4 available to form He, if the baryon-to-photon ratio is the 1 theoretical uncertainty in p is 6 10 .Aswe Y η Y higher. The increase in p with is logarithmic; over most will soon see, the current observational uncertainties in p η Y ≈ . η/η of the interesting range in , p 0 01 . are much larger (see, also, figure 2). The 4He abundance is, however, sensitive to the competition between the universal expansion rate (H ) Deuterium—the ideal baryometer and the weak interaction rate (interconverting neutrons As may be seen in figure 1, the deuterium abundance (the and protons). If the early universe should expand ratio, by number, of deuterium to hydrogen: hereinafter, ≡ y faster than predicted for the standard model, the weak (D/H)P 2P) is a monotonic, rapidly decreasing function interactions will drop out of equilibrium earlier, at a higher of the baryon abundance η. The reason for this behavior is temperature, when the n/p ratio is higher. In this case, easily understood. Once BBN begins in earnest, when the more neutrons will be available to be incorporated into temperature drops below ∼80 keV, D is rapidly burned 4 Y 3 3 4 He and p will increase. Numerical calculations show to H, He and He. The higher the baryon abundance, N Y ≈ . N η that, for a modest speed-up ( ν 1), p 0 013 ν . the faster the burning and the less D survives. For 10 in Y η y ∼ . Hence, constraints on p (and ) lead directly to bounds on the ‘interesting’ range 1–10, 2P decreases with the 1 6

-2 10 evolution, 3He will survive in the cooler stellar exteriors while being destroyed in the hotter interiors. For the more abundant lower-mass stars which are cooler, a larger -3 10 fraction of prestellar 3He (along with the 3He produced

D/H from prestellar D) survives. Indeed, for sufﬁciently low-

-4 mass stars (less than a few solar masses) incomplete 10 burning actually leads to a buildup of newly synthesized 3He (to be contrasted with the prestellar D and 3He) which

10 -5 may—or may not—be returned to the interstellar medium. In fact, some PLANETARY NEBULAE are observed to be highly enriched in 3He. So, the evolution of 3He is complex -6 10 with stellar destruction competing with primordial and 110 stellar production. Indeed, if all low-mass stars were as prolific producers of 3He as indicated by some planetary η10 nebulae, the solar system and local interstellar medium abundances of 3He should far exceed those inferred from Figure 3. The predicted D/H abundance (solid curve) and the observations. Thus, at least some low-mass stars must be 2σ theoretical uncertainty [2]. The horizontal lines show the net destroyers of 3He. Given this necessarily complex and range indicated by the observational data for both high D/H (upper two lines) and low D/H (lower two lines). uncertain picture of production, destruction and survival, it is difficult to use current observational data to infer the primordial abundance of 3He. Unless and until 3He η y power of . As a result, a 10% error in 2P corresponds is observed in high-redshift (i.e. early universe), low- η y to only a 6% error in . This strong dependence of 2P metallicity (i.e. nearly unevolved) systems, it will provide η on 10, combined with the simplicity of the evolution of only a weak check on the consistency of BBN. D/H in the epochs following BBN, is responsible for the unique role of deuterium as a baryometer [3]. Because Lithium-7– the lithium valley almost all the relevant reaction cross sections are measured The trend of the BBN-predicted primordial abundance of 7 η in the laboratory at energies comparable with those of lithium (almost entirely Li) with is more ‘interesting’ BBN, the theoretical uncertainties in the BBN-predicted than that of the other light nuclides (see figures 1 and 4). η ≈ abundance of deuterium is quite small, 8–10% for most of The ‘lithium valley’, centered near 10 2–3, is the result the interesting η range shown in figure 3. of the competition between production and destruction in Deuterium and helium-4 are complementary,forming the two paths to mass 7 synthesis. At relatively low baryon η 7 the crucial link in testing the consistency of BBN in the abundance ( 10 2) mass 7 is mainly synthesized as Li via 3 4 → 7 γ standard model. While the primordial D abundance H+ He Li + . As the baryon abundance increases at η 7 ,γ) α is very sensitive to the baryon density, the primordial low , Li is destroyed rapidly by (p 2 reactions, hence ≡ y η 4He abundance is relatively insensitive to η. Deuterium the decrease in (Li/H)P 7P with increasing seen (at low η provides a bound on the universal baryon density while ) in figures 1 and 4. Were this the only route to primordial helium-4 constrains the early expansion rate of the synthesis of mass 7, this monotonic trend would continue, universe, offering bounds on particle physics beyond the similar to those for D and 3He. However, mass 7 may standard model. also be synthesized via 3He + 4He → 7Be + γ . The 7Be will later capture an electron to become 7Li. This channel Helium-3—complicated evolution is very important because it is much easier to destroy 7Li As may be seen in figure 1, the predicted primordial than 7Be. As a result, for relatively high baryon abundance 3 η abundance of He behaves similarly to that of D, ( 10 3) the latter channel dominates mass 7 production η y η decreasing monotonically with . Again, the reason is and 7P increases with increasing . the same: 3He is being burned to the more tightly bound As may been seen in figure 4, the BBN-predicted 4 y 3 nucleus He. The higher the nucleon abundance, the faster uncertainties for 7P are much larger than those for D, He 3 4 ≤ η ≤ σ the burning and the less He survives. In contrast to the or He. In the interval 1 10 10 the 1 uncertainties behavior of D/H versus η, the decrease of 3He/H with are typically ∼20%, although in a narrow range of η near increasing η is much slower. This is simply a reflection the bottom of the ‘valley’ they are somewhat smaller (∼12– of the much tighter binding of 3He compared with D. 15%). Although the BBN predictions for the abundance of 3He have similarly small uncertainties (8–10%) to those of D, From here and now to there and then it is much more difficult to exploit the observations of To test the consistency of SBBN requires that we confront 3He to test and constrain BBN. The complication is the the predictions with the primordial abundances of the evolutionary history of the 3He abundance since BBN. light nuclides which, however, are not observed but, Although any deuterium cycled through stars is rather, are inferred from observations. The path from the burned to 3He during the stars’ pre-main-sequence observational data to the primordial abundances is long

-8 10 for chemical evolution. On the other hand, as noted earlier, the status of helium-3 is in contrast to that of the other light elements. For this reason, 3He will not be used quantitatively in this article. 10 -9 The currently very favorable observational and evolutionary situation for the nuclides produced during

Li/H BBN is counterbalanced by the likely presence of 10 -10 systematic errors in the path from observations to primordial abundances. By their very nature, such errors are difficult—if not impossible—to quantify. In the key case of deuterium there is a very limited set of the most 10 -11 110useful data. As a result, and although cosmological abundance determinations have taken their place in the current ‘precision’ era of cosmology, it is far from clear that η10 the present abundance determinations are truly ‘accurate’. Thus, the usual caveat emptor applies to any conclusions 7 σ Figure 4. The predicted Li abundance (solid curve) and the 2 drawn from the subsequent comparison between the theoretical uncertainty [2]. The horizontal lines show the range indicated by the observational data. predictions and the data. With this caution in mind the current status of the data will be surveyed in order to infer ‘reasonable’ ranges for the primordial abundances of the and twisted and often fraught with peril. In addition key light elements. to the usual statistical and systematic uncertainties, it is crucial to forge a connection from ‘here and now’ to ‘there Deuterium and then’, i.e. to relate the derived abundances to their Since deuterium is completely burned away whenever it primordial values. It is indeed fortunate that each of is cycled through stars, and there are no astrophysical the key elements is observed in different astrophysical sites capable of producing deuterium in anywhere near sites using very different astronomical techniques. Also, its observed abundance [3], any D abundance derived the corrections for chemical evolution differ among them from observational data provides a lower bound to its and, even more important, they can be minimized. For primordial abundance. Thus, without having to correct example, deuterium (and hydrogen) is mainly observed in for Galactic evolution, the ‘here-and-now’ deuterium cool, neutral gas (so-called H I REGIONS) via UV absorption abundance inferred from UV observations along 12 lines from the atomic ground state (the Lyman series), while of sight in the local interstellar medium (LISM) bounds radio telescopes allow helium-3 to be studied utilizing the ‘there-and-then’ primordial abundance from below ≥ ( / ) = ( . ± . ) × −5 the analog of the hydrogen 21 cm line for singly ionized ((D/H)P D H LISM 1 5 0 1 10 ). As may be 3He in regions of hot, ionized gas (so called H II regions). seen from figures 1 and 2, any lower bound to primordial Helium-4 is probed using the emission from its optical D will provide an upper bound to the baryon-to-photon recombination lines formed in H II regions. In contrast, ratio [4]. lithium is observed in the absorption spectra of warm, Solar system observations of 3He permit an indepen- low-mass halo stars. With such different sites, with dent, albeit indirect, determination of the pre-solar-system the mix of absorption–emission, and with the variety of deuterium abundance [5]. This estimate of the Galac- telescopes and different detectors involved, the possibility tic abundance some 4.5 Gyr ago, while somewhat higher of correlated errors biasing the comparison with the than the LISM value, has a larger uncertainty (D/H = − predictions of BBN is unlikely. This favorable situation (2.1±0.5)×10 5 [6]). Within the uncertainty it is consistent extends to the obligatory evolutionary corrections. with the LISM value suggesting there has been only mod- For example, although until recently observations of est destruction of deuterium in the last 4.5 Gyr. There is deuterium were limited to the solar system and the also a recent measurement of deuterium in the atmosphere Galaxy, mandating uncertain evolutionary corrections to of Jupiter using the Galileo Probe Mass Spectrometer [7] −5 infer the pregalactic abundance, the Keck and HUBBLE SPACE (D/H = (2.6 ± 0.7) × 10 (see GALILEO MISSION TO JUPITER)). TELESCOPEs have begun to open the window to deuterium To further exploit the solar system and/or LISM in high-redshift, low-metallicity,nearly primordial regions deuterium determinations to constrain or estimate the (Lyman-α clouds). Observations of 4He in chemically primordial abundance would require corrections for unevolved, low-metallicity (∼1/50 of solar) extragalactic the Galactic evolution of D; see GALACTIC EVOLUTION. H II regions permit the evolutionary correction to be Although the simplicity of the evolution of deuterium (it reduced to the level of the statistical uncertainties. The is only destroyed) suggests that such correction might abundances of lithium inferred from observations of be very nearly independent of the details of specific the very metal-poor halo stars (one-thousandth of solar chemical evolution models, large differences remain abundance and even lower) require almost no correction between different estimates. It is therefore fortunate that

Copyright © Nature Publishing Group 2001 Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998 and Institute of Physics Publishing 2001 Dirac House, Temple Back, Bristol, BS1 6BE, UK 5 Light Element Nucleosynthesis E NCYCLOPEDIA OF A STRONOMY AND A STROPHYSICS data on D/H in high-redshift (nearly primordial), low- metallicities of order 1/50–1/30 of solar, the extrapolation metallicity (nearly unevolved) Lyman-α absorbers have from the lowest-metallicity regions to truly primordial become available in recent years [8, 9]. It is expected introduces an uncertainty no larger than the statistical that such systems still retain their original, primordial error. deuterium, undiluted by the deuterium-depleted debris Using published data [13, 14] for 40 low-metallicity Y = . ± . of any significant stellar evolution. That is the good regions, one group [15] finds P 0 234 0 003. news. The bad news is that, at present, D abundance In contrast, from an independent data set of 45 low- Y = . ± determinations are claimed for only three such systems, metallicity regions another group [16] infers P 0 244 and that the abundances inferred for two of them (along 0.002. Clearly, these results are statistically inconsistent. with a limit to the abundance for a third) appear to It is crucial that high priority be assigned to further H II be inconsistent with the abundance estimated for the region observations to estimate or avoid the systematic Y remaining one. Here we have a prime illustration errors. Until then, since the error budget for P is of ‘precise’, but possibly inaccurate, cosmological data. probably dominated by systematic rather than statistical Y Indeed, there is a serious obstacle inherent to using uncertainties, in what follows a generous range for p will . ≤ Y ≤ . absorption spectra to measure the deuterium abundance be adopted: 0 228 P 0 248. since the isotope-shifted deuterium absorption lines are indistinguishable from the corresponding lines in suitably Lithium-7 velocity-shifted (−81 km s−1) hydrogen. Such ‘interlopers’ Cosmologically interesting lithium is observed in the may have been responsible for some of the early claims spectra of nearly 100 very metal poor halo stars [17, 18] [8] of a ‘high’ deuterium abundance [10]. Indeed, an (see GALACTIC METAL-POOR HALO). These stars are so metal interloper may be responsible for the one surviving high- poor they provide a sample of more nearly primordial D claim [11]. At present it seems that only three good material than anything observed anywhere else in the candidates for nearly primordial deuterium have emerged universe; the most metal-poor among them have heavy- from ground- and space-based observations. It may element abundances less than one-thousandth of the be premature to constrain cosmology on the basis of solar metallicity. However, these halo stars are also such sparse data. Nonetheless, the two ‘low-D’ systems the oldest objects in the Galaxy and, as such, have suggest a primordial deuterium abundance consistent had the most time to modify their surface abundances. with estimates of the pre-Galactic value inferred from So, even though any correction for Galactic evolution ( / ) = ( . ± . ) × −5 LISM and solar system data ( D H P 3 4 0 25 10 modifying their lithium abundances may be smaller than [12]). Toillustrate the confrontation of cosmological theory the statistical uncertainties of a given measurement, the with observational data, this D abundance will be adopted systematic uncertainty associated with the dilution and/or in the following. However, the consequences of choosing destruction of surface lithium in these very old stars could (( / ) = ( ± ) × −5 the ‘high-D’ abundance D H P 20 5 10 [11]) dominate the error budget. There could be additional will also be discussed. errors associated with the modeling of the surface layers of these cool, low-metallicity, low-mass stars needed to Helium-4 derive abundances from absorption-line spectra. It is also As the second most abundant nuclide in the universe (after possible that some of the Li observed in these stars is hydrogen), the abundance of 4He can be determined to non-primordial (e.g. that some of the observed Li may high accuracy at sites throughout the universe. However, have been produced post-BBN by spallation reactions (the as stars evolve they burn hydrogen to helium and the breakup of C, N and O nuclei into nuclei of Li, Be and B) 4 6 7 He in the debris of STELLAR EVOLUTION contaminates any or fusion reactions (α + α to form Li and Li) in cosmic- primordial 4He. Since any attempt to correct for stellar ray collisions with gas in the ISM). In a recent analysis evolution will be inherently uncertain, it is sensible [19], it is argued that as much as ∼0.2 dex of the observed to concentrate on the data from low-metallicity sites. lithium abundance, A(Li) ≡ 12+log(Li/H), could be post- Extragalactic regions of hot, ionized gas (H II regions) primordial in origin. provide such sites, where the helium is revealed via The very large data set of lithium abundances emission lines formed when singly and doubly ionized measured in the warmer (T>5800 K), more metal- helium recombines. As with deuterium, current data poor ([Fe/H] < −1.3) halo stars defines a plateau (the provide ambiguous estimates of the primordial helium ‘Spite-plateau’ [17]) in the lithium abundance–metallicity abundance. Since the differences (Y = 0.010) are larger plane. Depending on the choice of stellar-temperature than the statistical uncertainties (±0.003), systematic scale and stellar atmosphere model, the abundance level errors probably dominate. Among the currently most of the plateau is A(Li) = 2.2 ± 0.1, with very little likely sources of such errors are uncertain corrections for dispersion in abundances around this plateau value. The collisional excitation in helium, uncertain corrections for small dispersion provides an important constraint on unseen neutral helium and/or hydrogen, and underlying models which attempt to connect the present surface stellar absorption (leading to an underestimate of the lithium abundances in these stars to the original lithium true strength of the helium emission lines). In contrast, abundance in the gas out of which these stars were formed since the most metal poor of the observed regions have some 10–15 Gyr ago. ‘Standard’ (i.e. non-rotating) stellar

Copyright © Nature Publishing Group 2001 Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998 and Institute of Physics Publishing 2001 Dirac House, Temple Back, Bristol, BS1 6BE, UK 6 Light Element Nucleosynthesis E NCYCLOPEDIA OF A STRONOMY AND A STROPHYSICS models predict almost no lithium depletion and, therefore, From the two well-observed, high-redshift absorption are consistent with no dispersion about the Spite plateau. line systems with ‘low D’, the estimate adopted for the = ( . − . ) × Although early work on mixing in models of rotating stars primordial D abundance is (D/H)P 2 9 4 0 − was very uncertain, recently stellar models have been 10 5 (see figure 3). Also shown for comparison in constructed which reproduce the angular momentum figure 3 is the allowed range of the primordial deuterium evolution observed for the much younger, low-mass open abundance suggested by the ‘high-D’ abundance inferred cluster stars. These models have been applied to the study from observations of one lower-redshift absorption-line of lithium depletion in main sequence halo stars. A well- system. With allowance for the ∼8% uncertainty in the defined lithium plateau with modest scatter and a small theoretically predicted abundance, the favored range (low η η = . ± . population of ‘outliers’ (overdepleted stars), consistent D) for is quite narrow: 10 5 1 0 36. It is clear from with the current data, is predicted for depletion factors figure 4 that, for the baryon abundance in this range, the between 0.2 dex and 0.4 dex [20]. BBN-predicted lithium abundance is entirely consistent To err on the side of caution, a generous range with the Spite plateau value, even if the plateau were ∼ . for the plateau abundance, 2.1 ≤ A(Li) ≤ 2.3, is raised by 0 2 dex to allow for modest stellar destruction– adopted. If depletion is absent, this range is consistent dilution or lowered by a similar amount owing to post- η with the primordial lithium ‘valley’ (see figure 4). For BBN production. For this narrow range in the predicted 4 η ≈ Y ≈ depletion ≥0.2 dex, the consistent primordial lithium He mass fraction varies very little. For 10 5, p . η/η abundances bifurcate and move up into the ‘foothills’, 0 010 , so that, including the error in the predicted Y = . ± . although a non-negligible contribution from post-BBN abundance, p 0 247 0 001. As may be verified lithium could move the primordial abundance back down from figure 2, this is within (albeit at the high end of) again (figure 4). the range allowed by the data from the low-metallicity, extragalactic H II regions. Given the current uncertainties Confrontation of theory with data in the primordial abundances, SBBN is consistent with ‘low-D, high-η’. In the context of the ‘standard’ model (three families The significance of this concordance cannot be of massless, or light, two-component neutrinos), the underestimated. A glance at figure 1 provides a reminder predictions of BBN (SBBN) depend on only one free of the enormous ranges for the predicted primordial parameter, the nucleon-to-photon ratio η. The key test of abundances. That the simplest hot, big bang cosmological the standard, hot, big bang cosmology is to assess whether model can account for (‘predict’) three independent there exists a unique value or range of η for which the abundances (four with 3He; although 3He has not been predictions of the primordial abundances are consistent employed in this comparison, its predicted abundance is with the light-element abundances inferred from the consistent with extant observational data) by adjusting observational data. From a statistical point of view it only one free parameter (η) is a striking success. The might be preferable to perform a simultaneous fit of the theory, which is in principle falsifiable, has passed the inferred primordial abundances of D, 3He, 4He and 7Li to η test. It need not have. Indeed, future observational the SBBN predictions. In this manner the ‘best fit’ , along data coupled to better understanding of systematic errors with its probability distribution may be found, and the may provide new challenges. For example, if in the ‘goodness of fit’ assessed [21]. However, since systematic future it should be determined that the primordial helium uncertainties most likely dominate observational errors at Y = . mass fraction were lower than p 0 245, this would present, the value of this approach is compromised. An be inconsistent (within the errors) with the ‘low-D, high- alternative approach is adopted here. η’ range derived above. Similarly, if the best estimate As emphasized earlier, deuterium is an ideal for the D-determined η range changed, the comparison baryometer. As a first step the primordial abundance performed above should be repeated. With this in mind, of deuterium inferred from observations at high redshift what of the ‘high-D, low-η’ range which has been set aside will be compared with the SBBN prediction to identify a in the current comparison? η consistent range for . Then, given this range, the SBBN If, in contrast to the deuterium abundance adopted abundances of 4He and 7Li are predicted and these are = ( above, the true value were higher, (D/H)P 10– compared with the corresponding primordial abundances 30) × 10−5, the SBBN-favored range in η would be lower derived from the observational data. The challenge is to (see figure 3). Accounting for the ∼8% uncertainty in η η = . ± . see whether the D-identified range for leads to consistent the theoretically predicted abundance, 10 1 7 0 28. 4 7 η . predictions for He and Li. Recall that, because of its Inspection of figures 2–4 reveals that, as long as 10 1 1– complicated evolutionary history, it is difficult to use 1.3, consistency with 4He and 7Li can be obtained. Hence, 3 He to test and constrain SBBN. Furthermore, another for ‘high D’ as well, the standard model passes the key consistency test is to compare the SBBN-inferred η range cosmological test. with the present baryon density derived from non-BBN observations and theory. Is our model for the very early Comparison of BBN with non-BBN baryon density estimates evolution of the universe consistent with the present Having established the internal consistency of primordial universe? nucleosynthesis in the standard model, it is necessary to

It is a daunting task to attempt to inventory the 4 baryons in the universe. Since many (most?) baryons may be ‘dark’, such approaches can best set lower bounds to the Lo-D present ratio of baryons to photons. One such estimate 0.228 < Y < 0.248 η η ≥ obs [22] suggests a very weak lower bound on of 10 0.25, entirely consistent with the BBN estimates above. Others [23] have used more subjective (although cautious) Nν 3 estimates of the uncertainties, finding a much higher lower η ≥ . bound to the global budget of baryons: 10 1 5, which is still consistent with the ‘low-η’ range identified using the high-D results. A possible challenge to the ‘low-η’ case comes from an analysis [24] which employed observational constraints 2 on the Hubble parameter, the age of the universe, the structure-formation ‘shape’ parameter and the x-ray cluster gas fraction to provide non-BBN constraints on the η ≥ present density of baryons, finding that 10 5 may be η ≤ η favored over 10 2. Even so, a significant low- , high-D 1 range still survives. 12345678910 η 10 Cosmology constrains particle physics Limits on particle physics beyond its standard model Figure 5. The number of equivalent massless neutrinos are mostly sensitive to the bounds imposed on the 4He Nν ≡ 3+Nν (see equation (4)) as a function of η. The region allowed by an assumed primordial 4He mass fraction in the abundance (see also STANDARD MODEL OF PARTICLE PHYSICS). As 4 range 0.228–0.248 lies between the two solid curves. The vertical described earlier, the He abundance is predominantly bands bounded by the dashed lines show generous bounds on η determined by the neutron-to-proton ratio just prior from ‘high’ and ‘low’ deuterium. to nucleosynthesis. This ratio is determined by the competition between the weak interaction rates and the universal expansion rate. The latter can be modified Summary from its standard model prediction by the presence of The standard, hot, big bang cosmological model is simple ‘new’ particles beyond those known or expected on the (assuming isotropy, homogeneity, Newtonian–Einsteinian basis of the standard model of particle physics. For gravity, standard particle physics, etc) and, probably, example, additional neutrino ‘flavors’ (Nν > 0), or other simplistic. In broad brush it offers a remarkably successful new particles, would increase the total energy density framework for understanding observations of the present of the universe, thus increasing the expansion rate (see and recent universe. It may seem hubris to expect that equations (4) and (5)), leaving more neutrons to form more this model could provide a realistic description of the 4He. For Nν sufficiently small, the predicted primordial universe during the first 20 min or so in its evolution when helium abundance scales nearly linearly with Nν : Y ≈ the temperature and density were enormously larger than . N Y 0 013 ν . As a result, an upper bound to p coupled with today. According to the standard model, during these η Y a lower bound to (since p increases with increasing first 20 min the entire universe was a nuclear reactor, baryon abundance) will lead to an upper bound to Nν turning neutrons and protons into the light nuclides. This and a constraint on particle physics [1]. prediction presents the opportunity to use observations The constraints on Nν = 3+Nν as a function of here and now to test the theory there and then. As the baryon-to-photon ratio η are shown in figure 5. For described in this article, SBBN predicts observable ‘low D, high η’ there is little room for any ‘extra’ particles: primordial abundances for just four light nuclides, D, Nν 0.3. This would eliminate a new neutrino flavor 3He, 4He and 7Li, as a function of only one adjustable (Nν = 1) or a new scalar particle (Nν = 4/7) provided parameter, η, the nucleon-to-photon ratio, which is a they were massless or light (m 1 MeV) and interacted measure of the universal baryon abundance. Even though at least as strongly as the ‘ordinary’ neutrinos. In contrast, it is currently difficult to use the extant observational much weaker constraints are found for ‘high D, low η’ data to bound the primordial abundance of 3He, SBBN is where Nν as large as 5 (Nν ≤ 2) may be allowed (see still overconstrained, yielding three predicted abundances figure 5). for one free parameter. Furthermore, the baryon density