Astroparticle Physics

11.2 Discovery and Basic Properties of the CMB 231Assuming the particles that contribute to the energy densityare stable, one obtainsn i ∼ 1/R 3 ∼ T 3 . (11.3)Furthermore, since R ∼ t 2/3 , the expansion rate is nowgiven bytime dependence of R and Tunder matter dominationH = ṘR = 2 3t . (11.4)Combining (11.3) with (11.4) or R ∼ t 2/3 then leads toT 3 ∼ 1t 2 . (11.5)This is to be contrasted with the relation T 2 ∼ t −1 valid forthe era when the energy density was dominated by relativisticparticles.11.2 Discovery and Basic Propertiesof the CMB“What we have found is evidence for thebirth of the universe. It’s like looking atGod.”George SmootThe existence of the CMB was predicted by Gamow [22]in connection with Big Bang Nucleosynthesis. It was shownin Chap. 10 that BBN requires temperatures around T ≈0.08 MeV, which are reached at a time t ≈ 200 s. By knowingthe cross section for the first reaction, p + n → d + γ ,and the number density n of neutrons and protons, one canpredict the reaction rate Γ = n〈σv〉.In order for BBN to produce the observed amount of helium,one needs a sufficiently high rate for the deuteriumfusion reaction over the relevant time scale. This correspondsto requiring Γt to be at least on the order of unityat t ≈ 200 s, when the temperature passes through the relevantrange. This assumption determines the nucleon densityduring the BBN phase.Since the BBN era, the nucleon and photon densitieshave both followed n ∼ 1/R 3 ∼ T 3 . So, by comparing thenucleon density in the BBN era to what one finds today, thecurrent temperature of the photons can be predicted. Reasoningalong these lines, Alpher and Herman [23] estimateddeuterium fusionphoton temperatureestimation