Graviton one-loop effective action and inflationary dynamics

We consider the one-loop effective action due to gravitons in a FLRW background with constant epsilon=-(dH/dt)/H^2. By expanding around epsilon=0 (corresponding to an expansion around de Sitter space), we can study how the deviation from de Sitter space effects the quantum corrected Friedmann equations. We find that, at zeroth order in epsilon, one-loop effects induce only a finite shift in the coupling constants. At linear order in epsilon there is however a divergent contribution to the equations of motion. This contribution leads to a nontrivial term in the renormalized equations that depends logarithmically on H and thus cannot be absorbed in local counterterms. We find that deviations due to this term are unobservably small. Our study shows that quantum effects in quasi de Sitter space can be fundamentally different then in de Sitter space, albeit in the case under consideration the effect is unobservably small.