Introduction to Cosmology

196 Cosmic Microwave Background

0.0 0.1 0.2 0.3 0.4 0.5 0.6

ΩM

• 2.0


• 1.5


• 1.0


• 0.5

W

Figure 8.7The 1휎and 2휎cosmological constraints in훺m,Wspace using PanSTARRS1 super-
nova data [13], Planck CMB data [6], BAO [14] andH 0 data [6] with statistical and systematic
errors propagated. Reproduced with permission of Armin Rest for the PanSTARRS1 Collabo-
ration. (See plate section for color version.)

In the present matter-dominated Universe, the pressure푝mis completely negligible
and we can set푤=0, as can be seen.
In Figure 8.7 the confidence regions in훺m, w space are plotted for the combined
PanSTARRS1 supernova data [13], Planck CMB data [6], baryonic oscillation BAO
data [14] and퐻 0 data [6].
From Equation (8.60) and the values for훺mand훺휆above, we find

푞 0 =− 0. 53 ± 0. 02. (8.62)

The reason for the very small error is that the errors of훺mand훺휆are completely
anti-correlated. The parameter values given in this section have been used to construct
the scales in Figure 6.5. The values are collected in Table A.6 in the Appendix.

Problems

1. Derive an equation for푇eqfrom the condition in Equation (8.3).


2. Show that the quantity푄^2 +푈^2 is an invariant under the rotation of an angle휙
   in the (푥,푦)-plane, where푄and푈are the Stokes parameters defined in Equa-
   tion (8.26).