100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

Understanding Our Universe: Current Status and Open Issues 195Matter DominatedInflationReheatingRadiation DominatedCMBRReinflation30DFlog distance (cm)1020100−10Hubble RadiusBCMB Photon WavelengthDark EnergyScaleL ΛL ΛL P−20−30C A E−60 −50 −40 −30 −20 −10 0 10 20 30log a10Fig. 4. The geometrical structure of a universe with two length scales L P and L Λcorresponding to the Planck length and the cosmological constant. See text for detaileddescription of the figure.NowL P1/L 4 Λ = ρ Λ. Thus L P determines the highest possible energy density inthe universe while L Λ determines the lowest possible energy density in thisuniverse. As the energy density of normal matter drops below this value, thethermal ambience of the deSitter phase will remain constant and providethe irreducible ‘vacuum noise’. Note that the dark energy density is thethe geometric mean ρ DE = √ ρ Λ ρ P between the two energy densities. Ifwe define a dark energy length scale L DE such that ρ DE = 1/L 4 DE thenL DE = √ L P L Λ is the geometric mean of the two length scales in theuniverse. The figure 4 also shows the L DE by broken horizontal lines.While the two deSitter phases can last forever in principle, there is anatural cut off length scale in both of them which makes the region ofphysical relevance to be finite. 32 In the the case of re-inflation in the lateuniverse, this happens (at point F) when the temperature of the CMBRradiation drops below the deSitter temperature. The universe will be essentiallydominated by the vacuum thermal noise of the deSitter phase for