Astroparticle Physics

9.5 The Baryon Asymmetry of the Universe 209where these are rough approximations with the missing factorsof order unity. Using these ingredients one can expressthe asymmetry asA ≈ n b,0n γ,0. (9.52)Further, the baryon-number-to-photon ratio can be defined:baryon-to-photon ratioη = n b − n¯bn γ. (9.53)One expects this ratio to remain constant as long as there areno further baryon-number-violating processes and there areno extra influences on the photon temperature beyond theHubble expansion. So one can also assume that η refers tothe current value, (n b,0 − n¯b,0 )/n γ,0 ≈ n b,0 /n γ,0 , although– strictly speaking – one should call this η 0 . So one finallyobtains that the baryon–antibaryon asymmetry A is roughlyequal to the current baryon-to-photonratio η. A more carefulanalysis which keeps track of all the missing factors givesA ≈ 6η.The current photon density n γ,0 is well determined fromthe CMB temperature to be 410.4 cm −3 . In principle onecould determine n b,0 by adding up all of the baryons thatone finds in the universe. This in fact is expected to be anunderestimate, since some matter such as gas and dust willnot be visible and these will also obscure stars further away.A more accurate determination of η comes from the modelof Big Bang Nucleosynthesis combined with measurementsof the ratio of abundances of deuterium to hydrogen. Fromthis one finds η ≈ 5 × 10 −10 . So, finally, the baryon asymmetrycan be expressed ascurrent photon densitynucleosynthesisA ≈ 6η ≈ 3 × 10 −9 . (9.54)This means that at early times, for every billion antiquarksthere were a billion and three quarks. The matter in the universeone sees today is just the tiny amount left over afteressentially all of the antibaryons annihilated.9.5.3 The Sakharov ConditionsIn 1967 Andrei Sakharov pointed out that three conditionsmust exist in order for a universe with non-zero baryon numberto evolve from an initially baryon-symmetric state [16].Nature must provide: