A time-variable tensor metric perturbation similarly leaves an imprint in the
temperature anisotropy [Sachs & Wolfe, 1967]. A tensor metric perturbation
can be viewed as a standing gravitational wave and produces a quadrupolar distortion
in the spatial metric. If its amplitude changes, it leaves a quadrupolar
distortion in the CMB temperature distribution [Polnarev, 1985]. Inflation predicts a nearly scale-invariant
spectrum of gravitational waves. Their amplitude depends strongly on the energy
scale of inflation,(power
[Rubakov et al, 1982,Fabbri & Pollock, 1983]) and its relationship
to the curvature fluctuations discriminates between particular models
for inflation. Detection of gravitational waves in the CMB therefore
provides our best hope to study the particle physics of inflation.
Figure: Gravitational waves and the energy scale of inflation
. Left: temperature and polarization spectra from an initial scale invariant gravitational wave spectrum with power
. Right: 95% confidence upper limits statistically achievable on
and the scalar tilt
by the MAP and Planck satellites as well as an ideal experiment out to
in the presence of gravitational lensing
-modes.
Gravitational waves, like scalar fields, obey the Klein-Gordon equation in
a flat universe and their amplitudes begin oscillating and decaying once the
perturbation crosses the horizon. While this process occurs even before recombination,
rapid Thomson scattering destroys any quadrupole anisotropy that develops (see
§3.6). This fact dicates the general
structure of the contributions to the power spectrum (see Figure 4,
left panel): they are enhanced at the present quadrupole and sharply suppressed at multipole larger
than that of the first peak [Abbott & Wise, 1984,Starobinskii, 1985,Crittenden et al, 1993]. As is the case
for the ISW effect, confinement to the low multipoles
means that the isolation of gravitational waves is severely limited by
cosmic variance.
The signature of gravitational waves in the polarization
is more distinct. Because gravitational waves cause a quadrupole temperature
anisotropy at the end of recombination, they also generate a polarization. The
quadrupole generated by a gravitational wave has its main angular variation
transverse to the wavevector itself [Hu & White, 1997a]. The resulting polarization
that results has components directed both along or orthogonal to the wavevector
and at 45 degree angles to it. Gravitational waves therefore generate a
nearly equal amount of
and
mode polarization when viewed at a distance that is much greater than
a wavelength of the fluctuation [Kamionkowski et al, 1997,Zaldarriaga & Seljak, 1997]. The
-component presents a promising means of measuring the gravitational
waves from inflation and hence the energy scale of inflation (see Figure 4,
right panel). Models of inflation correspond to points in the
plane [Dodelson et al, 1997]. Therefore, the
anticipated constraints will discriminate among different models of inflation,
probing fundamental physics at scales well beyond those accessible in accelerators.