Stochastic Samples versus Vacuum Expectation Values in Cosmology

Understand

Particle theorists typically use expectation values to study the quantum back-reaction on inflation, whereas many cosmologists stress the stochastic nature of the process.

• While expectation values certainly give misleading results for some things, such as the stress tensor, we argue that operators exist for which there is no essential problem.
• We quantify this by examining the stochastic properties of a noninteracting, massless, minimally coupled scalar on a locally de Sitter background.
• The square of the stochastic realization of this field seems to provide an example of great relevance for which expectation values are not misleading.