On the Soft Limit of the Large Scale Structure Power Spectrum: UV Dependence

Understand

We derive a non-perturbative equation for the large scale structure power spectrum of long-wavelength modes.

• Thereby, we use an operator product expansion together with relations between the three-point function and power spectrum in the soft limit.
• The resulting equation encodes the coupling to ultraviolet (UV) modes in two time-dependent coefficients, which may be obtained from response functions to (anisotropic) parameters, such as spatial curvature, in a modified cosmology.
• We argue that both depend weakly on fluctuations deep in the UV.