eaa.iop.org DOI: 10.1888/0333750888/2130 Light Element Nucleosynthesis Gary Steigman From Encyclopedia of Astronomy & Astrophysics P. Murdin © IOP Publishing Ltd 2006 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, 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 1 Light Element Nucleosynthesis E NCYCLOPEDIA OF A STRONOMY AND A STROPHYSICS 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.