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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 epsilon and eta. The number of e-foldings (N) can be expressed in terms of epsilon using (63) and (78),

Equation 94 (94)

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.

Equation 95 (95)

Vk is the potential when the mode k leaves the horizon, Ve is the potential at the end of inflation, and rhoRH 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.

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