Quantum corrected power spectra of massless minimally coupled scalars during inflation: Effects of Yukawa coupling versus quartic self-interaction

Abstract

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.