Chapter 9: Short and Intermediate Wavelengths

The spectral energy density associated with the wavelengths crossing the effective horizon during the radiation epoch is specifically investigated in this chapter. Some of the relevant wavelengths of the spectrum are still larger than the Hubble radius after the end of inflation but they progressively reenter as the radiation plasma evolves. While, as expected, the long wavelengths have the same power spectrum they had during inflation, the short wavelengths exhibit strong Sakharov oscillations which practically disappear in the spectral energy density. As soon as the wavelengths reenter the Hubble radius their evolution is affected by various sources of damping that eventually suppress the high-frequency plateau of the spectral energy density. Indeed, for the short and intermediate frequency ranges examined here the evolution of the effective number of relativistic species and the neutrino free-streaming are the most prominent effects even if the former is less relevant than the latter. In the final part of this chapter the problem of the quantum mechanical normalization of the large-scale inhomogeneities is reexamined by specifically considering the possibility already discussed in Chapter 6 and illustrated in Fig. 6.9. The results illustrated here show, a posteriori, that different initial vacua only introduce a second-order correction on the leading-order expression of the scalar and tensor power spectra.