Ultraviolet Divergences in Cosmological Correlations

Understand

A method is developed for dealing with ultraviolet divergences in calculations of cosmological correlations, which does not depend on dimensional regularization.

• An extended version of the WKB approximation is used to analyze the divergences in these calculations, and these divergences are controlled by the introduction of Pauli--Villars regulator fields.
• This approach is illustrated in the theory of a scalar field with arbitrary self-interactions in a fixed flat-space Robertson--Walker metric with arbitrary scale factor $a(t)$.
• Explicit formulas are given for the counterterms needed to cancel all dependence on the regulator properties, and an explicit prescription is given for calculating finite regulator-independent correlation functions.