Astroparticle Physics

9.6 Problems 211investigation of CP-violating decays of K and B mesons.These experiments have not, however, revealed any effectincompatible with Standard Model predictions.The departure from thermal equilibrium could beachieved simply through the expansion of the universe,i.e., when the reaction rate needed to maintain equilibriumfalls below the expansion rate: Γ ≪ H . Alternatively, itcould result from a phase transition such as those associatedwith spontaneous symmetry breaking.So, the present situation with the baryon asymmetry ofthe universe is a collection of incomplete experimental observationsand partial theories which point towards the creationof a non-zero baryon density at some point in the earlyuniverse. The details of baryogenesis are still murky and remainan active topic of research. It provides one of the closestinterfaces between particle physics and cosmology. Untilthe details are worked out one needs to take the baryon densityof the universe or, equivalently, the baryon-to-photonratio, as a free parameter that must be obtained from observation,see also Fig. 9.2.deviationfrom thermal equilibriuminterfacebetween particle physicsand cosmologyFig. 9.2The matter–antimatter symmetryobserved at microscopic scalesappears to be broken at themacroscopic level9.6 Problems1. Derive the relation between the scale factor R and theenergy density ϱ for a universe dominated by non-relativisticmatter!2. Derive the relation between the scale factor R and timefor an early universe dominated by non-relativistic matter!3. The total energy density of the early universe varies withthe temperature like