Astro/Physics 224 Winter 2008Origin and Evolution of the UniverseDark Matter IFriday, February 1Joel PrimackUniversity of California, Santa CruzThe Planck Mass isThe Planck LengthThe Compton (i.e. quantum) wavelength equals the Schwarzschild radius when m = mPlis the smallest possible length. Here h is Planck’s constanth = 6.626068 × 10-34 m2 kg / s = 1.6 × 10-33 cm= 2.2 × 10-5 gThe Wedge of Material RealityFrom The View from the Center of the Universe © 2006In addition to the textbooks listed on the Syllabus for this course, a good place to start looking for up-to-date information is the Particle Data Group website http://pdg.lbl.gov For example, there are 2007 Mini-Reviews of Big Bang Nucleosynthesis including a discussion of 7Lihttp://pdg.lbl.gov/2007/reviews/bigbangnucrpp.pdf Big-Bang Cosmologyhttp://pdg.lbl.gov/2007/reviews/bigbangrpp.pdfCosmological Parametershttp://pdg.lbl.gov/2007/reviews/hubblerpp.pdfCMB http://pdg.lbl.gov/2007/reviews/microwaverpp.pdf and Dark Matter http://pdg.lbl.gov/2007/reviews/darkmatrpp.pdf(Re)combination: e- + p  HAs long as e- + p  H remains in equilibrium, the condition= 0 with 1 = e-, 2 = p, 3 = H, ensures that Neutrality ensures np = ne. Defining the free electron fractionthe equation above becomes, whichis known as the Saha equation. When T ~ ε, the rhs ~ 1015, so Xe is very close to 1 and very little recombination has yet occurred. As T drops, the free electron fraction also drops, and as it approaches 0 equilibrium cannot be maintained. To follow the freezeout of the electron fraction, it is necessary to use the Boltzmann equationε = 13.6 eVDodelson, Modern Cosmology, p. 72photon decouplingout of equilibriumfreezeout electron fractionDodelson, Modern Cosmology, p. 76Dark Matter AnnihilationThe weak shall inherit the universe!The weaker the cross section, the earlier freezeout occurs, and the larger the resulting dark matter density.Dark Matter AnnihilationThe abundance today of dark matter particles X of the WIMP variety is determined by their survival of annihilation in the early universe. Supersymmetric neutralinos can annihilate with each other (and sometimes with other particles: “co-annihilation”).Dark matter annihilation follows the same pattern as the previous discussions: initially the abundance of dark matter particles X is given by the equilibrium Boltzmann exponential exp(-mX/T), but as they start to disappear they have trouble finding each other and eventually their number density freezes out. The freezeout process can be followed using the Boltzmann equation, as discussed in Kolb and Turner, Dodelson, Mukhanov, and other textbooks. For a detailed discussion of Susy WIMPs, see the review article by Jungman, Kamionkowski, and Griest (1996). The result is that the abundance today of WIMPs X is given in most cases by (Dodelson’s Eqs. 3.59-60)Here xf ≈ 10 is the ratio of mX to the freezeout temperature Tf, and g*(mX) ≈ 100 is the density of states factor in the expression for the energy density of the universe when the temperature equals mXThe sum is over relativistic species i (see the graph of g(T) on the next slide). Note that more X’s survive, the weaker the cross section σ. For Susy WIMPs the natural values are σ ~ 10-39 cm2, so ΩX ≈ 1 naturally.This 2x increase corresponds to minimal supersymmetry with a ~1 TeV thresholdSupersymmetry is the basis of most attempts, such as superstring theory, to go beyond the current “Standard Model” of particle physics. Heinz Pagels and Joel Primack pointed out in a 1982 paper that the lightest supersymmetric partner particle is stable because of R-parity, and is thus a good candidate for the dark matter particles – weakly interacting massive particles (WIMPs).Michael Dine and others pointed out that the axion, a particle needed to save the strong interactions from violating CP symmetry, could also be the dark matter particle. Searches for both are underway.Supersymmetric WIMPsWhen the British physicist Paul Dirac first combined Special Relativity with quantum mechanics, he found that this predicted that for every ordinary particle like the electron, there must be another particle with the opposite electric charge – the anti-electron (positron). Similarly, corresponding to the proton there must be an anti-proton. Supersymmetry appears to be required to combine General Relativity (our modern theory of space, time, and gravity) with the other forces of nature (the electromagnetic, weak, and strong interactions). The consequence is another doubling of the number of particles, since supersymmetry predicts that for every particle that we now know, including the antiparticles, there must be another, thus far undiscovered particle with the same electric charge but with spin differing by half a unit.Supersymmetric WIMPsWhen the British physicist Paul Dirac first combined Special Relativity with quantum mechanics, he found that this predicted that for every ordinary particle like the electron, there must be another particle with the opposite electric charge – the anti-electron (positron). Similarly, corresponding to the proton there must be an anti-proton. Supersymmetry appears to be required to combine General Relativity (our modern theory of space, time, and gravity) with the other forces of nature (the electromagnetic, weak, and strong interactions). The consequence is another doubling of the number of particles, since supersymmetry predicts that for every particle that we now know, including the antiparticles, there must be another, thus far undiscovered particle with the same electric charge but with spin differing by half a unit. after doublingSupersymmetric WIMPs, continuedSpin is a fundamental property of elementary particles. Matter particles like electrons and quarks (protons and neutrons are each made up of three quarks) have spin ½, while force particles like photons, W,Z, and gluons have spin 1. The supersymmetric partners of electrons and quarks are called selectrons and squarks, and they have spin 0. The supersymmetric partners of the force particles are called the photino, Winos, Zino, and gluinos, and they have spin ½, so they might be matter particles. The lightest of these particles might be the photino. Whichever is lightest should be stable, so it is a natural candidate to be the dark matter WIMP. Supersymmetry does not predict its mass, but it must be more than 50 times as massive as the proton since it