Physical Foundations of Cosmology

9.8 Determining cosmic parameters 385

0

2

4

6

400 800 1200 l

Fig. 9.2.

9.8 Determining cosmic parameters

Assuming a Gaussian, adiabatic spectrum of initial density perturbations, as pre-
dicted by inflation, the principal cosmological parameters are: the amplitudeBand
slopenSof the primordial spectrum, the baryon densityξ≡ 17

(

(^) bh^275

)

, the cold

matter density (^) m,the vacuum density (^) and the Hubble parameterh 75 .We shall
consider how the spectrum changes as the parameters are varied around the best-fit
model, (^) b= 0 .04, (^) m= 0 .3, (^) = 0 .7 andH=70 km s−^1 Mpc−^1. Our formulae
above are valid for a wide variation in each parameter, more than sufficient to cover
the likely values, although some of the expressions break down if used in the limits
of very high or very low densities.
Keeping in mind the comments above on the physical origin of parameter de-
pendence of the coefficients in the formulae describing the fluctuations, the reader
can easily figure out why the main features of the spectrum depend in one way
or another on these parameters. Therefore we omit physical explanations for these
dependences in what follows.
The plateauFor a nearly scale-invariant spectrum, the anisotropy power spectrum
on large angular scales(l< 30 )is a nearly flat plateau. The amplitude and slope of