Alternate Definitions of Loop Corrections to the Primordial Power Spectra

Understand

We consider two different definitions for loop corrections to the primordial power spectra.

• One of these is to simply correct the mode functions in the tree order relations using the linearized effective field equations.
• The second definition involves the spatial Fourier transform of the 2-point correlator.
• Although the two definitions agree at tree order, we show that they disagree at one loop using the Schwinger-Keldysh formalism, so there are at least two plausible ways of loop correcting the tree order result.