92
Baryogenesis
explained in section 1.4, each scales as R(t)-3, where R(t) is the cosmological
scale factor. It is, therefore, customary to use the ratio
nB
t1= -
(4.4)
ny
to measure the asymmetry. ny is the photon number density given by the
Boltzmann distribution (see section 5.1)
ny = 2~(3)T3
(4.5)
n- 2
when the temperature is T. From the measured microwave background [4],
T = To = 2.725 ± 0.002 K at present and this gives
ny ~ 411 cm- 3 .
(4.6)
The present net baryon number density may be written in terms of the current
critical density, defined in (1.37).
3
2 n2
1 88h2 10-29
-3
PC=-2mp 0 =.
x
gcm
(4.7)
8nwhere h == Ho/lOO km 5- 1 Mpc-I measures the present Hubble constant,
mp == G;I/2 = 1.22 x 10 19 GeV is the Planck mass and [5]
h = 0071+0.04
(4.8)
. . -0.03'
Then
nB = OB Pc = 1.1 x 1O-'OBh 2 cm- 3
(4.9)
mB
and
,., = 2.65 x 1O- 8 0Bh 2
(4.10)
where 0 B == P B / Pc measures the baryon energy density as a fraction of the
critical density. The measured primordial deuterium and hydrogen abundances
require [5]
OBh 2 = 0.024 ± 0.001
(4.11 )
which gives
'1 = (6.36 ± 0.26) x 10- 10 •
(4.12)
The conservation of entropy in a comoving volume. when the universe is in
local thermal equilibrium, means that the entropy density s also scales as R(t)-3.
Thus. the baryon asymmetry may alternatively be measured by
nB
1/B == --;(4.13)