Astroparticle Physics

244 11 The Cosmic Microwave Backgroundparticle physicsin the early universeThese experiments provide another close bridge betweencosmology and the particle physics of the early universe.In addition to helping pin down important cosmological parameters,the CMB may provide the most important cluesneeded to understand particle interactions at ultrahigh energyscales – energies that will never be attained by manmadeparticle accelerators. This theme will be further exploredin the next chapter on inflation.11.7 Problems1. What is the probability that a photon from the Big Bangundergoes a scattering after having passed the surface oflast scattering?2. Estimate a limit for the cosmological constant!3. The Friedmann equation extended by the cosmologicalconstant is nothing but a relation between differentforms of energy:m2 Ṙ2} {{ }kinetic(+− GmMR − 1 6 mΛc2 R 2 )} {{ }potential=−kc 2 m 2} {{ }total energy(m is the mass of a galaxy at the edge of a galactic clusterof mass M).Work out the pressure as a function of R related to theclassical potential energy in comparison to the pressurecaused by the term containing the cosmological constant.4. Work out the average energy of blackbody microwavephotons! For the integration of the Planck distributionrefer to Chap. 27 in [35] or Formulae 3.411 in [36] orcheck with the web page:http://jove.prohosting.com/~skripty/page_998.htm.For the Riemann zeta function look athttp://mathworld.wolfram.com/RiemannZetaFunction.html.5. Estimate the energy density of the cosmic microwavebackground radiation at present and at the time of lastscattering.6. Why is the decoupling temperature for photons at lastscattering (0.3 eV) much lower compared to the ionizationenergy of hydrogen (13.6 eV)?