A Rigorous Proof of the Inflationary Spectrum

Fundamental formulae representing the density perturbation spectrums generated in inflationary scenarios are rigorously proved. Quantum fluctuations as initial conditions for structure generation in some inflationary era can be calculated in general scale. Thus, we could avoid the matching of the large and the small scale results at the horizon crossing epoch. This is possible because the perturbed scalar field equation in a special gauge has some remarkable nice properties. In the uniform-curvature gauge the contributions from the metric fluctuations effectively disappear in certain expansion stages, and also we can derive a simple general solution in the large scale limit.