Quantally fed steady-state domain distributions in stochastic inflation

Within the framework of stochastic in inflationary cosmology we derive stea dy-state distributions P-c(V) of domains in comoving coordinates, under the assumption of slow-rolling and for two specific choices of the coarse-grai ned inflaton potential V(Phi). We model the process as a Starobinsky-like e quation in V-space plus a time-independent source term P-w(V) which carries (phenomenologically) quantum-mechanical information drawn from either of t wo known solutions of the Wheeler-De Witt equation: Hartle-Hawking's and Vi lenkin's wave functions. The presence of the source term leads to the exist ence of nontrivial steady-state distributions P-c(w)(V). The relative effic iencies of both mechanisms at different scales are compared for the propose d potentials.