Physical Foundations of Cosmology

210 The very early universe

particular, atTQCD200 MeV,we have

ma(T)∼ma

(

QCD/T

) 4

. (4.219)

For realistic values off, the axion mass becomes of order the Hubble constant at
these high temperatures. UsingH∗in (4.201), we findma(T∗)=H∗when

T∗∼g ̃∗−^1 /^12 m^1 a/^6 ^2 QCD/^3

and

m∗∼g ̃^1 ∗/^3 m^1 a/^3 ^4 QCD/^3. (4.220)

Substituting this value form∗into (4.213) and taking into account thatain=fθin,
we finally obtain the following expression for the axion contribution to the total
energy density:

(^) ah^275 ∼O( 1 )

(

6 × 10 −^6 eV

ma

) 7 / 6

θ ̄in^2 ∼O( 1 )

(

f

1012 GeV

) 7 / 6

θ ̄in^2. (4.221)

The axion is periodic inθ ̄=a/fand therefore the natural value forθ ̄inis∼O( 1 ).
Thus, ifma∼ 10 −^5 eV, the axions can constitute the dominant component of dark
matter. Because all couplings of the axion scale as 1/f,axions interact only very
weakly with ordinary matter and, in spite of their small mass, are cold particles. At
first glance, only axions with masses within a very narrow window near 10−^5 eV
seem to be cosmologically interesting. However, one can argue thatθ ̄in1 is not
so unnatural in inflationary cosmology. This allows the universe to close even with
axions of much smaller mass.
Particle theories beyond the Standard Model also provide us with other candi-
dates for dark matter, among which are the gravitino, the axino (the superpartner of
the axion), and the remnant of the inflaton. Their contributions can be determined
using approaches similar to those outlined above.

4.6.2 Baryogenesis

The universe is asymmetric: there are more baryons than antibaryons. While an-
tibaryons are produced in accelerators or in cosmic rays, “antigalaxies” are not
observed. The relative excess of the baryonsB≡(nb−nb ̄)/s∼ 10 −^10 is exactly
what we need to explain the abundance of light elements and the observations of
CMB fluctuations (see Chapter 9). In past the baryon asymmetry could be inter-
preted as simply due to the initial conditions in the universe. However, in the light
inflationary cosmology, now widely accepted, this “solution” completely fails. We
will see in the following chapter that an inflationary stage erases any pre-existing