Nonlinear noise in cosmology

Abstract

This paper derives and analyzes exact, nonlocal Langevin equations appropriate in a cosmological setting to describe the interaction of some collective degree of freedom with a surrounding "environment." Formally, these equations are much more general, involving as they do a more or less arbitrary "system," characterized by some time-dependent potential, which is coupled via a nonlinear, time-dependent interaction to a "bath" of oscillators with time-dependent frequencies. The analysis reveals that, even in a Markov limit, which can often be justified, the time dependences and nonlinearities can induce new and potentially significant effects, such as systematic and stochastic mass renormalizations and state-dependent "memory" functions, aside from the standard "friction" of a heuristic Langevin description. One specific example is discussed in detail, namely, the case of an inflaton field, characterized by a Landau-Ginzburg potential, that is coupled quadratically to a bath of scalar "radiation." The principal conclusion derived from this example is that nonlinearities and time-dependent couplings do not preclude the possibility of deriving a fluctuation-dissipation theorem, and do not change the form of the late-time steady state solution for the system, but can significantly shorten the time scale for the approach towards the steady state.