Stochastic Inflation and Dimensional Reduction
  We present a replica field-theoretic approach to stochastic inflation in which a manifestation of dimensional reduction is found. The scale above which the latter dominates grows exponentially fast with time and thus affects largest super-horizon scales. We find inevitable modifications of the spectral index on those scales. An explicit relation between the noise correlator and the non-gaussianity parameter f_NL is found. 
Florian Kuhnel and Dominik J. Schwarz