Calculation of density fluctuations in the inflationary epoch - art. no. 043508

Starting from an initial state of thermal equilibrium, we derive an express ion for the quantum fluctuation in the energy density during the inflationa ry epoch in terms of the mode functions for the inflation field, The effect of this particular initial quantum state is not washed out in the final fo rmula, contrary to what is usually believed. Numerically, however, the effe ct is completely negligible, validating the use of the two paint function i n the vacuum state. We also point out the requirement of conventional quant um field theory during inflation, that the quantum fluctuation in a wavelen gth must be evaluated, at the latest, when the wavelength crosses the Hubbl e length, in contrast with the usual practice in the literature.