**C. Summary**

Scalar perturbations are the most easily detected form of
perturbation. The scalar nature of these fluctuations arise from
the fact that the perturbations are of mass fields in the
primordial era, that is, before the time of decoupling. Different
models of inflation and the corresponding reheating mechanisms
differ in their predictions of mass variation. Regardless, these
variations of the early universe eventually give rise to the
structural formation of galaxy clusters, which can help
distinguish the various theories of inflation and structure
formation. Tensor perturbations are also detectable and these
perturbations result from fluctuations in the space-time metric in
the primordial era. Again, these perturbations are very small and
would be very hard to detect. However, certain models of
inflation predict wavelengths that could be detected by laser
interferometry gravitational wave detectors, such as
LIGO ^{(30)}
If these waves were
detected it would help eliminate many inflation models and help
narrow the region of viable theories. Furthermore, inflation is
the only theory that can currently account for a gravitational
wave spectrum. The detection of the spectrum would be a great
success for the inflation theory.

Both of these types of perturbations contribute to the 10^{-5}
temperature fluctuation in the cosmic background. The biggest
challenge for experimentalists is to separate the scalar and
tensor contributions to the temperature fluctuations. In practice
this is very difficult, if not impossible, and it becomes more
practical to consider the polarization of the CBR.

For the inflationist, the goal of CRB measurements is to
distinguish between the various models of inflation. A good way
to begin, is to express many of the relations obtained thus far,
in terms of and
. The number of e-foldings
(*N*) can be expressed in terms of
using
(63) and (78),

Another useful relation, which may be found in the literature
[61],
gives a measure of when a given perturbations of
wave length *k* passes through the horizon and is therefore
`frozen out'. This can be expressed as the number of e-foldings
*N(k)* from the end of inflation.

*V*_{k} is the potential when the mode *k* leaves the
horizon,
*V*_{e} is the potential at the end of inflation, and
_{RH}
is the energy density after reheating. This expression may appear
formidable, however it can be used to begin understanding density
fluctuations. For example, the modes *k* entering the horizon
today, left the horizon at *N(k)* = 50-70. The
uncertainty in this range manifests the lack of knowledge of the
inflaton potential. Thus, once again different inflaton models
make different predictions.

With the rapid advances in observational cosmology, cosmologists are able to use the abundance of data that is being obtained by the Hubble Space Telescope, balloon experiments, satellites (such as Chandra), etc. to narrow the parameters of the universe. Then with these values and the relations that have been presented in this section, one can use inflation to predict new physics for the pre-inflation or Planckian epoch. Ultimately this physics will need a quantum theory of gravity or supersting theory, but determination of the inflaton potential and the resulting large-scale structure will set stringent limits in which to test the predictions of these new theories. In this way, inflation offers the link between the innerspace of the quantum realm and the outerspace of the large-scale structure of the universe. The marvelous universe in which we live, the beauty that surrounds us, and even ourselves, will be the result of a quantum fluctuation or perhaps a chaotic mishap.