2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35704We address two basic issues in the theory of galaxy formation from fluctuations of quantum fields: 1) the nature and origin of noise and fluctuations and 2) the conditions for using a classical stochastic equation for their description. On the first issue, we derive the influence functional for a $λϕ^4 $ field in a zero-temperature bath in de Sitter universe and obtain the correlator for the colored noises of vacuum fluctuations. This exemplifies a new mechanism we propose for colored noise generation which can act as seeds for galaxy formation with non-Gaussian distributions. For the second issue, we present a (functional) master equation for the inflaton field in de Sitter universe. By examining the form of the noise kernel we study the decoherence of the long-wavelength sector and the conditions for it to behave classically.Plain Tex, 32 pages. This is a reprint of a 1992 conference talk published in 1993. It is related to two later papers on similar subjects by E. Calzetta and B. L. Hu, gr-qc/9312036 [Phys. Rev. D49, 6636 (1994)] and gr-qc/9505046 [Phys. Rev. D52, (Dec. 15, 1995)]General Relativity and Quantum Cosmologytext