Physics 129 LECTURE 12 February 18, 2014 More Early Universe Cosmology n Big Bang Nucleosynthesis Review n Baryogenesis - Sakharov Conditions n Four Scenarios for Satisfying the Sakharov Conditions n Leptogenesis Converted to Baryogenesis n Baryogenesis by Coherent Motion of Scalar Fields n Cold Dark Matter Candidates n Axions: Needed to Avoid Strong CP Violation n WIMP Abundance from Annihilation: The Weak Shall Dominate the Universe n Searching for WIMPs: Direct & Indirect Detection, Production at the LHC n Warm Dark Matter - Sterile Neutrinos: Needed for Neutron Star Kicks? Seen? Tuesday, February 18, 14 Nucleosynthesis and 6 baryogenesis 144 Nucleosynthesis and baryogenesis 6.1 Primordial nucleosynthesis The expectedIn continuation helium of mass this fraction, discussion with of the the early mass universe, of the heliumwe next nucleusturn our attention set equal toto 4 the times synthesis that of of the the proton nuclei is of then the light given elements— by 4He, 2H, 3He, and 7Li. The agreement between the predicted and measured abundances of these elements 4N 2r provided earlyY support forHe the Big Bang hypothesis.0.24 (6.9) As discussed in= Section(4NHe 5.10,NH) once= (1 the universer) ≈ had cooled to a temperature + + kT < 100 MeV, or after a time t > 10 4 s, essentially all the hadrons, with The mass fraction Y has been measured in a variety− of celestial sites, including the sole exception of neutrons and protons and their antiparticles, would have stellar atmospheres, planetary nebulae, globular clusters, gas clouds, and so on, disappeared by decay. The nucleons and antinucleons would have been present with valuesin equal in the numbers range and have nearly, but not quite completely, annihilated to Y 0.238 0.006 (6.10) radiation. As described in= the next± section, once the temperature had fallen Problemsbelow in evaluatingkT 20 MeV, both a the tiny predicted residue and of about measured one billionth values mean of the that original = agreementnumbers between of protons theory and (6.9) neutrons and observation must have (6.10) survived is still to uncertain form the stuff at the of the 5% level.material Nevertheless, universe this we level inhabit of agreement today. The was relative an early numbers and very of theseimportant surviving successprotons for the and Big neutrons Bang model. would It should have been be pointed determined out here by the that weak the observed reactions helium mass fraction is far greater than that which could have been produced ve n e− p (6.1) in hydrogen burning in main sequence+ stars;↔ their+ contribution adds only 0.01 to the ratio Y (see Problem 6.4). ve p e+ n (6.2) An important feature of nucleosynthesis¯ + ↔ in the+ Big Bang scenario is that n p e− ve (6.3) it accounts not only for 4He but also for→ the+ light+¯ elements D, 3He, and 7Li, which occurSince at in the small temperatures but significant considered, amounts, the far nucleons more in are fact non-relativistic, than would have then just survivedas if in they the analysis hadBig only Bang of been Section producedNucleosynthesis 5.12, in the thermonuclear equilibrium Review ratio interactions of neutrons in stellar to protons interiors.will The be lithiumgoverned and by deuterium the ratio of abundances the Boltzmann give factors, so that Before freezeout of n ↔ p conversion by neutrinos, Nn Li Q 10 2 exp −(1.23; 0.01Q ) M10n −Mp c 1.293 MeV(6.11) (6.4) N = H =kT ± = × − = p ! " D # 5 $ At freezeout Tf = 0.80 MeV; substituting(2.6 0.4 T)f into10 −the above equation gives(6.12) Nn/Np = 50.20. The rate or width !Hfor the first two reactions (6.1) and (6.2) must vary as T Because the deuterium binding= energy± is only× 2.22 MeV and there are about 109 photons 144 Nucleosynthesis and baryogenesis purely on dimensional grounds. The Fermi constant GF from (1.9) or Table for every nucleon, deuterium nuclei2 are photodissociated as fast as the2 form until T = 0.05 The curves1.5 has in dimensions Fig. 6.1 showsE− , so the the abundances cross-section expectedσ (dimension from primordialE− ) must vary MeV, which for2 N2 ν = 3 corresponds to t = 300 s = 5 min. This is when Big Bang 3 nucleosynthesis,as GFT and calculated the incident on the flux basisφ, proportional of the cross-sections to the neutrino involved, density, and as T . nucleosynthesisTheplotted expectedHence in terms helium the begins. of width the mass (present !At fraction,thatσφ day)time,gets with baryon because a T the5 factor. to mass photonof neutron On of the densitythe helium otherdecay ratio. hand nucleuswith The the a resultlifetime expansion set of 885 s, r = Nn/Np = 0.135. Almost all= the neutrons are bound into 14He,/2 2 which gives a promordial equal(6.12) to onrate 4 times the of deuterium–hydrogen the that radiation-dominated of the proton is ratio then universe leadsgiven to by is aH valueg of∗ theT baryonfrom (5.59). density Hence helium abundance3 by mass1/2 of ∼ in the range!/H T /(g∗) and as the universe expands and the temperature falls, the above∼ reactionsρ will go(44.0N outHe of0.4 equilibrium) 102r28 kg when m W3 /H < 1, where(6.13)W !/h. Y B − 0.24− (6.9)= In fact, as described= (4=N inHe Chapter±NH) 5,=× at(1kT <r) 3≈ MeV neutrinos are already going¯ + + and a contributionout of equilibrium to the closure with electrons parameter in the process e e v v, since this The mass fraction Y has been measured in a variety of celestial+ − sites, including All the nucleosynthesishas an even smaller in stars cross-section adds only than about (6.2) 0.01 because to Y+ of (Perkins the↔ smaller problem+¯ target 6.4). mass. stellar atmospheres, planetary" nebulae,B 0.044 globular0.005 clusters, gas clouds, and so (6.14) on, = ± Thewith two values most in accurate the range ways of measuring the primordial abundance of baryons are the 3 relativecorresponding heights of to the a numberfirst two peaks density in of the baryons CMB angularNB power0.24 spectrum0.03 m and. the D/H ratio Y 0.238 0.006 = ± (6.10)− in Comparingnear-primordial with thehydrogen; number both density= give of Ω± microwaveb = 0.044. photonsCompared (5.52), with this the yieldsnumber density of photons,Problemsfor the baryon–photonthis in gives evaluating the baryon/photon ratio both the predicted ratio of and measured values mean that agreement between theory (6.9) and observation (6.10) is still uncertain at the 5% level. Nevertheless,NB thisN levelB ofNB agreement was an early and10 very important success for the Big Bang model.− It should( be6.1 pointed0.6) out10 here− that the observed(6.15) Nγ ≈ Nγ = ± × helium mass fraction is far! greater than" that which could have been produced Tuesday, February 18, 14 10 inA hydrogen slightly different burning in value main of sequence(6.5 0.4 stars;) their10− contributionis found from adds the only analysis 0.01 toof the microwave ratio Y (see anisotropies Problem 6.4). by the± WMAP× (Wilkinson Microwave Anisotropy Probe),An important described feature in Chapter of nucleosynthesis 8. This value for in the the Big baryon–photon Bang scenario ratio is would that 4 3 7 itimply accounts for the not helium only for fraction,He butY also0.248, for the about light 5% elements larger D, thanHe, the and observedLi, whichvalue occur in (6.10). in small but significant= amounts, far more in fact than would have survived if they had only been produced in thermonuclear interactions in stellar interiors. The lithium and deuterium abundances give Li 10 (1.23 0.01) 10− (6.11) H = ± × D 5 (2.6 0.4) 10− (6.12) H = ± × The curves in Fig. 6.1 shows the abundances expected from primordial nucleosynthesis, calculated on the basis of the cross-sections involved, and plotted in terms of the (present day) baryon to photon density ratio. The result (6.12) on the deuterium–hydrogen ratio leads to a value of the baryon density in the range 28 3 ρB (4.0 0.4) 10− kg m− (6.13) = ± × and a contribution to the closure parameter "B 0.044 0.005 (6.14) = ± 3 corresponding to a number density of baryons NB 0.24 0.03 m− . Comparing with the number density of microwave photons= (5.52),± this yields for the baryon–photon ratio NB NB NB 10 − (6.1 0.6) 10− (6.15) Nγ ≈ ! Nγ " = ± × 10 A slightly different value of (6.5 0.4) 10− is found from the analysis of microwave anisotropies by the± WMAP× (Wilkinson Microwave Anisotropy Probe), described in Chapter 8. This value for the baryon–photon ratio would imply for the helium fraction, Y 0.248, about 5% larger than the observed value in (6.10). = Baryogenesis Generates Matter - Antimatter Asymmetry Perkins Example_ 6.1 calculates the baryon-antibaryon ratio after annihilation freezes out if there were equal amounts initially of baryons and antibaryons, and gets the answer _ -18 -9 NB/Nγ = NB/Nγ = 0.72x10 instead of the observed value NB/Nγ = 0.6x10 . It follows that there must have been an initial asymmetry between matter and antimatter. Since Cosmic Inflation ended with matter-antimatter symmetry, something must have happened after the end of Inflation to generate the asymmetry. The Three Sakharov Requirements As we discussed, CP violation in the Weak interactions was discovered in 1964, and in 1967 Andrei Sakharov showed that the following conditions are necessary in order to generate baryon-antibaryon asymmetry: n Baryon-number violation n Out of thermal equilibrium n C and CP violation The first requirement is obvious, and it occurs naturally in Grand Unified Theories (GUTs).