Arttu Rajantie: Stochastic effective theory for scalar fields in de Sitter spacetime

Scalar fields can have important cosmological consequences. It is believed that the accelerating expansion of the Universe during its early inflationary phase was driven by a scalar field called the inflaton, whose quantum fluctuations gave rise to the large scale structure of the Universe. However, from particle physics we know that there is at least one other elementary scalar field in the Universe – the Higgs field – and possibly many others. During inflation, these light scalar fields would have experienced similar amplification, leading to potentially observable effects such as phase transitions or production of dark matter or isocurvature perturbations. These observations can therefore be used to test and constrain the Standard Model of particle physics and its extensions well beyond the limits of particle accelerator experiments. However, there is a serious theoretical stumbling block: The usual perturbation theory techniques which work very well in flat spacetime are not applicable in the inflationary era because of the so-called infrared problem. In this talk, I will focus on a powerful alternative - the stochastic Starobinsky-Yokoyama approach - which is based on the observation that on large distances the scalar field behaves classically, with a noise term produced by short-wavelength quantum fluctuations. So far it has been mostly used to calculate the one-point probability distribution of the field, but its real power lies in describing the asymptotic long-distance behaviour of correlation functions through a spectral expansion. I demonstrate this by calculating observational constraints for scalar dark matter models and transition rates between different vacuum states. I also show how to extend the stochastic theory beyond the overdamped approximation used by Starobinsky and Yokoyama. The parameters of this effective theory are determined at one-loop order in perturbation theory, and do not suffer from the same infrared problems as a direct perturbative computation of observables. Therefore it provides a powerful and accurate way of computing cosmological observables.