Quantum Cosmological Correlations in an Inflating Universe: Can fermion and gauge fields loops give a scale free spectrum?

Abstract

This paper extends the calculation of quantum corrections to the cosmological correlation $<\zeta\zeta>$, which has been done by Weinberg for a loop of minimally coupled scalars, to other types of matter loops and a general and realistic potential. It is shown here that departures from scale invariance are never large even when Dirac, vector, and conformal scalar fields are present \emph{during} inflation. No fine tuning is needed, in the sense that effective masses or coupling constants can have arbitrary values. Even when the mass is as large as $M_{Pl}$, the one-loop result is still naturally smaller than the classical one. Thus, the results show that the existence of these fields \emph{during} inflation may not be ruled out and is consistent with natural reheating.