Introduction to Cosmology

194 Cosmic Microwave Background

0.0 0.2 0.4 0.6 0.8 1.0

ΩM

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Ω

λ

Decelerating

Accelerating

No Big

Bang

Figure 8.6The 1휎and 2휎cosmological constraints in훺m,훺휆space 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.)

The number of neutrino families is푁휈= 3. 30 ± 0 .27 in good agreement with the stan-
dard model number 3.
Inserting the values of훺bandℎin Equation (6.96) we obtain the ratio of baryons
to photons

휂=( 6. 06 ± 0. 08 )× 10 −^10. (8.53)

Inserting the value ofℎin Equation (8.12), we obtain the present value of the radi-
ation density parameter,

훺r=^5.^456 ×^10 −^5. (8.54)

Timescales. From this value for훺rone can determine the time of equality of radia-
tion and matter density,푡eq. From Equations (5.13) and (5.29), the equation determin-
ing the evolution of the scale is

퐻(푎)^2 =퐻 02 [( 1 −훺 0 )푎−^2 +훺(푎)] =퐻 02 [( 1 −훺 0 )푎−^2 +훺m푎−^3 +훺r푎−^4 +훺휆].

At the present time (푎=1)훺m>훺rbut, as we move back in time and푎gets smaller, the
term훺r푎−^4 will come to dominate. The epoch of matter–radiation equality would have