One-loop Corrections to Scalar and Tensor Perturbations during Inflation   in Stochastic Gravity
  Based on the stochastic gravity, we study the loop corrections to the scalar and tensor perturbations during inflation. Since the loop corrections to scalar perturbations suffer infrared (IR) divergence, we consider the IR regularization to obtain the finite value. We find that the loop corrections to the scalar perturbations are amplified by the e-folding; in other words there appear the logarithmic correction, just as discussed by M.Sloth et al. On the other hand, we find that the tensor perturbations do not suffer from infrared divergence. 
Yuko Urakawa and Kei-ichi Maeda