Cosmic fluctuations from quantum effective action

Understand

Does the observable spectrum of cosmic fluctuations depend on detailed initial conditions? This addresses the question if the general inflationary paradigm is sufficient to predict within a given model the spectrum and amplitude of cosmic fluctuations, or if additional particular assumptions about the initial conditions are needed.

• The answer depends on the number of e-foldings $N_{in}$ between the beginning of inflation and horizon crossing of the observable fluctuations.
• We discuss an interacting inflaton field in an arbitrary homogeneous and isotropic geometry, employing the quantum effective action $\Gamma$.
• An exact time evolution equation for the correlation function involves the second functional derivative $\Gamma^{(2)}$.