Soft Metric Fluctuations During Inflation

Abstract

The conservation of the long wavelength fluctuations of the metric plays a vital role in cosmology as the link between quantum fluctuations during inflation and late time observations. This is a well-known property of the classical evolution equations, but demonstrating that it is robust to quantum correction involves a number of technical arguments. In this paper, we will use effective field theory (EFT) techniques to demonstrate the all orders conservation of the super-horizon scalar and tensor fluctuations of the metric during inflation. We show how to construct an EFT for these soft modes, in analogy with Soft de Sitter Effective Theory. We pay particular attention to how the breaking of time-diffeomorphisms by the inflationary background introduces new time scales that alter the structure of the EFT. In this description, the all orders conservation of the metric fluctuations is a direct consequence of symmetries and power counting that cannot be altered by loop corrections. We further show that this holds when the inflaton (or metric fluctuations) is coupled to additional heavy fields, as in quasi-single field inflation. We match this behavior to several calculations in the ultraviolet (UV) theory and show how the Mellin representation enables a more transparent connection between the UV and the EFT descriptions.