Astroparticle Physics

9.4 Thermal History of the First Ten Microseconds 2039.4 Thermal Historyof the First Ten Microseconds“An elementary particle that does notexist in particle theory should also notexist in cosmology.”AnonymousThe relations from the previous sections can now be used towork out the energy density and temperature of the universeas a function of time. As a start, one can use (9.40) to givethe energy density at the Planck time, although one needs tokeep in mind from the previous section that the assumptionof thermal equilibrium may not be valid. In any case theformula givesϱ(t Pl ) = 3m2 Pl32π1t 2 Pl= 332π m4 Pl ≈ 6×1074 GeV 4 , (9.44)where m Pl = 1/t Pl ≈ 1.2 × 10 19 GeV has been used. Onecan convert this to normal units by dividing by (¯hc) 3 ,ϱ(t Pl ) ≈ 6 × 10 74 GeV 4 ×1(0.2GeVfm) 3≈ 8 × 10 76 GeV/fm 3 . (9.45)This density corresponds to about 10 77 proton masses in thevolume of a single proton!Proceeding now more systematically, one can find thetimes and energy densities at which different temperatureswere reached. By combining this with the knowledge of particlephysics, one will see what types of particle interactionswere taking place at what time.To relate the temperature to the time, one needs the numberof degrees of freedom, g ∗ . Assuming that nature onlycontains the known particles of the Standard Model, thenfor T greater than several hundred GeV all of them can betreated as relativistic. From (9.20) one has g ∗ = 106.75.If, say, GUT bosons or supersymmetric particles also exist,then one would have a higher value. For the order-ofmagnitudevalues that one is interested in here this uncertaintyin g ∗ will not be critical.Table 9.2 shows values for the temperature and energydensity at several points within the first 10 microsecondsafter the Big Bang, where most of the values have beenrounded to the nearest order of magnitude.Planckian energy densitiescharacteristic temperaturesin the early universe