  We, in the first part, contemplate a massless minimally coupled scalar which
is Yukawa-coupled to a massless Dirac fermion in a locally de Sitter background
of an inflating spacetime. We compute the scalar's quantum corrected mode
function, power spectrum, spectral index and the running of the spectral index
at one-loop order. We find that the spectrum is slightly blue-tilted; hence,
the amplitudes of fluctuations grow slightly toward the smaller scales. Then,
in the second part, we apply the computation method used in the first part to a
massless minimally coupled scalar with a quartic self-interaction in the same
background and obtain exact analytic expressions for the associated quantities
at one-loop order. In contrast to the Yukawa scalar, the spectrum in this case
is slightly red-tilted; hence, the amplitudes of fluctuations grow slightly
toward the larger scales.
