On a Stochastic Model of Inflationary Cosmology

Observational evidence for the accelerated expansion of the Universe raises a fundamental challenge to standard cosmological models. It is generally presumed that acceleration of cosmic expansion emerges from an unknown physical component called dark energy whose contributions in negative pressure and energy density are substantial. One of the unsettled questions posed by the dark energy hypothesis relates to the magnitude of the cosmological constant: the observed vacuum energy density is exceedingly small as compared to predictions of quantum field physics. In this work we develop a derivation of the cosmological constant based on classical diffusion theory. Dynamics of the dark energy is modeled using the Langevin equation of a damped harmonic field in steady contact with a chaotic reservoir of vacuum fluctuations. The field evolves in the Friedmann-Robertson-Walker metric and dissipation arises as a result of expansion. The asymptotic limit of this process corresponds to setting the self-interaction gravity scale as the largest temperature of the reservoir. Predictions on vacuum energy density and cosmological constant are shown to be consistent with current experimental bounds.