9.9 Gravitational waves 391index. The dark energy may comprise quintessence, rather than vacuum energy.
In this case, we must introduce a new parameter, the equation of state of the dark
energyw(or perhaps a functionw(z)). Correlated changes in (^) m,h 75 andwcan
produce canceling effects that leave the plateau and the first three peaks virtually
unchanged. Thus, the temperature autocorrelation function is a powerful tool, but
it is not all-powerful.
To explore the range of possible models fully we need to use all the information
the power spectrum offers, in combination with other cosmological observations.
For example, the heights, locations and shapes of the peaks also depend on the dis-
sipation scaleslfandlS,which in turn depend on combinations of the cosmological
parameters. For the current best-fit model, for whichlS∼1000, dissipation does
not influence the first peak significantly, but it becomes increasingly important for
the higher-order peaks. Hence, using more peaks in the analysis further constrains
models.
9.9 Gravitational waves
An important physical effect that we have neglected thus far is that of gravitational
waves, one of the basic predictions of inflationary cosmology. As discussed in
Section 7.1, to describe gravitational waves we use the metric
ds^2 =a^2(
dη^2 −(δik+hik)dxidxk)
. (9.114)
The gravitational waves correspond to the traceless, divergence-free part ofhik.
They produce perturbations in the microwave background by inducing the redshifts
and blueshifts of the photons. Using the equationpαpα= 0 ,we can express the
zero component of the photon’s 4-momentum as
p 0 =p^0 =p
a^2(
1 −
1
2
hiklilk)
, (9.115)
where as beforep≡
(
#pi^2) 1 / 2
,li≡−pi/pand we have kept only the first order
terms in metric perturbations. The photon geodesic equations for the metric (9.114)
take the following forms:
dxi
dη=li+O(h),dpj
dη=−
1
2
p∂hik
∂xjlilk. (9.116)Taking into account that the distribution function f depends only on the single
variable
y=
ω
T=
p 0
T√
g 00=
p
T 0 a(
1 −
δT
T−
1
2
hiklilk