Stochastic quantization of scalar fields in de Sitter spacetime

We consider the stochastic quantization method for scalar fields defined in a curved manifold. The two-point function associated with a massive self-interacting scalar field is evaluated, up to the first-order level in the coupling constant λ, for the case of the de Sitter Euclidean metric. Its value for the asymptotic limit of the Markov parameter τ → ∞ is exhibited. We discuss in detail the covariant stochastic regularization, which renders the one-loop two-point correlation function finite in the de Sitter Euclidean metric.