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CALTECH AY 21 - Light Element Nucleosynthesis

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eaa.iop.orgDOI: 10.1888/0333750888/2130 Light Element NucleosynthesisGary Steigman FromEncyclopedia of Astronomy & AstrophysicsP. Murdin © IOP Publishing Ltd 2006 ISBN: 0333750888Downloaded on Tue Jan 31 17:16:57 GMT 2006 [127.0.0.1]Institute of Physics PublishingBristol and PhiladelphiaTerms and ConditionsLight Element NucleosynthesisENCYCLOPEDIA OF ASTRONOMY AND ASTROPHYSICSLight Element NucleosynthesisThe early universe was hot and dense behaving as a cosmicnuclear reactor during the first 20 min of its evolution. Itwas, however, a ‘defective’ nuclear reactor, expanding andcooling very rapidly. As a result, only a handful of thelightest nuclides were synthesized before the density andtemperature dropped too low for the nuclear reaction ratesto compete with the universal expansion rate (seeUNIVERSE:THERMAL HISTORY). After hydrogen (1H ≡ protons) the nextmost abundant element to emerge from the Big Bang ishelium (4He ≡ alpha particles). Isotopes of these nuclides(deuterium and helium-3) are the next most abundantprimordially. Then there is a large gap to the muchlower abundance of lithium-7. The relative abundancesof all other primordially-produced nuclei are very low,much smaller than their locally observed (or, currentlyobservable) abundances. After a brief description of theearly evolution of the universe emphasizing those aspectsmost relevant to primordial, or ‘big bang’ nucleosynthesis(BBN), the predicted abundances of the light nuclides willbe presented as a function of the one ‘free’ parameter(in the simplest, ‘standard’ model: SBBN), the nucleon(or ‘baryon’) abundance. Then, each element willbe considered in turn in a confrontation between thepredictionsof SBBN and the observational data. At present(summer 1999) there is remarkable agreement betweenthe SBBN predictions of the abundances of four nuclides(D,3He,4He and7Li) and their primordial abundancesinferred from the observations. However, there are somehints that this concordance of the hot big bang modelmay be imperfect, so we will also explore some variationson the theme of the standard model with regard to theirmodifications of the predicted primordial abundances ofthe light elements.In the simplest, standard, hot big bang model thecurrently observed large-scale isotropy and homogeneityof the universe is assumed to apply during earlier epochsin its evolution (seeCOSMOLOGY: STANDARD MODEL). Given thecurrently observed universal expansion and the matterand radiation (CBR: ‘cosmic background radiation’, the2.7 K ‘black body radiation’) content, it is a straightforwardapplication of classical physics to extrapolate back toearlier epochs in the history of the universe (seeCOSMICMICROWAVE BACKGROUND). At a time of order 0.1 s after theexpansion began the universe was filled with a hot, denseplasma of particles. The most abundant were photons,electron–positron pairs, particle–antiparticle pairs of allknown ‘flavors’ of neutrinos (νe, νµand ντ) and traceamounts of neutrons and protons (‘nucleons’ or ‘baryons’).At such early times the thermal energy of these particleswas very high, of order a few MeV. With the exceptionof the nucleons, it is known or assumed that all theother particles present were extremely relativistic at thistime. Given their high energies (and velocities close to,or exactly equal to, the speed of light) and high densities,the electroweak interactions among these particles weresufficiently rapid to have established thermal equilibrium.As a result, the numbers and distributions (of momentumand energy) of all these particles are accurately predictedby well-known physics.Nucleosynthesis in the early universeThe primordial yields of light elements are determinedby the competition between the expansion rate of theuniverse (the Hubble parameter H ) and the rates ofthe weak and nuclear reactions (seeHUBBLE CONSTANT).It is the weak interaction, interconverting neutrons andprotons, that largely determines the amount of4He whichmay be synthesized, while detailed nuclear reaction ratesregulate the production (and destruction) of the other lightelements. In the standard model of cosmology the earlyexpansion rate is fixed by the total energy density ρ,H2= 8πGρ/3 (1)where G is Newton’s gravitational constant. In thestandard model of particle physics the early energy densityis dominated by the lightest, relativistic particles. For theepoch when the universe is a few tenths of a second oldand older, and the temperature is less than a few MeV,ρ = ργ+ ρe+Nνρν(2)where ργ, ρeand ρνare the energy densities in photons,electrons and positrons, and massless neutrinos andantineutrinos (one species), respectively; Nνis the numberof massless (or, very light: mν 1 MeV) neutrino specieswhich, in standard BBN, is exactly 3. In consideringvariations on the theme of the standard model, it isuseful to allow Nνto differ from 3 to account for thepresence of ‘new’ particles and/or any suppression of thestandard particles (e.g. if the τ neutrino should have a largemass). Since the energy density in relativistic particlesscales as the fourth power of the temperature, the earlyexpansion rate scales as the square of the temperaturewith a coefficient that depends on the number of differentrelativistic species. The more such species, the faster theuniverse expands, the earlier (higher temperature) will theweak and nuclear reactions drop out of equilibrium. It isuseful to write the total energy density in terms of thephoton energy density and g, the equivalent number ofrelativistic degrees of freedom (i.e. helicity states, modulothe different contributions to the energy density fromfermions and bosons),ρ ≡ (g/2)ργ. (3)In the standard model at T ∼ 1 MeV, gSM= 43/4.Account may be taken of additional degrees of freedomby comparing their contribution to ρ with that of oneadditional light neutrino species:ρ ≡ ρTOT− ρSM≡ Nνρν. (4)If the early energy density deviates from that of thestandard model, the early expansion rate (or, equivalently,Copyright © Nature Publishing Group 2001Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998and Institute of Physics Publishing 2001Dirac House, Temple Back, Bristol, BS1 6BE, UK1Light Element NucleosynthesisENCYCLOPEDIA OF ASTRONOMY AND ASTROPHYSICSthe age at a fixed temperature) will change as well. The‘speed-up’ factor ξ ≡ H/HSMmay be related to Nνbyξ =


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