By J M Overduin, P S Wesson
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Additional info for Dark Sky Dark Matter
The unbroken curve is a least-squares ﬁt to the data, while the dashed lines represent upper and lower limits. 11) where we have introduced a new shorthand for the comoving luminosity density of sources: Ä(z) ≡ n(z)L(z). 24). Numerous studies have shown that the product of n(z) and L(z) is approximately conserved with redshift, even when the two quantities themselves appear to be evolving markedly. So it would be reasonable to take Ä(z) = Ä0 = constant. However, the latest analyses have been able to beneﬁt from new observational work at deeper redshifts, and a new consensus is emerging that Ä(z) does rise slowly but steadily with z, peaking in the range 2 º z º 3, and falling away sharply thereafter .
Second, the vacuum term was regarded with particular suspicion for reasons to be discussed in chapter 4. Third, a period of inﬂation was asserted to have driven tot (t) to unity. ) And ﬁnally, the EdS model was favoured on grounds of simplicity. These arguments are no longer compelling today, and the determination of r,0 , m,0 and ,0 (along with H0 ) has shifted largely back into the domain of observation. 5). 6 The static analogue This is a good place to pause and take stock of our results so far.
34) for ρ . If we now assume that only one of these three components is dominant at a given time, then we can make Light at the end of the Universe? 32) to obtain R˙ R 2 −4 8π G ρr,0 (R/R0 ) −3 = × ρm,0 (R/R0 ) 3 ρ (radiation) (matter) (vacuum). These differential equations are separable and have solutions 1/2 (radiation) R(t) (t/t0 )2/3 = (t/t0 ) (matter) R0 exp[H0(t − t0 )] (vacuum). 61) We emphasize that these results assume (i) spatial ﬂatness and (ii) a singlecomponent cosmic ﬂuid which must have the critical density.
Dark Sky Dark Matter by J M Overduin, P S Wesson