  Starting from an initial state of thermal equilibrium, we derive an
expression for the quantum fluctuation in the energy density during the
inflationary epoch in terms of the mode functions for the inflaton field. The
effect of this particular initial state is not washed out in the final formula,
contrary to what is usually believed. Numerically, however, the effect is
completely negligible, validating the use of the two point function in the
vacuum state. We also point out the requirement of conventional quantum field
theory during inflation, that the quantum fluctuation in a wavelength must be
evaluated, at the latest, when the wavelength crosses the Hubble length, in
contrast to the usual practice in the literature.
