Responses in Large-Scale Structure

Understand

We introduce a rigorous definition of general power-spectrum responses as resummed vertices with two hard and $n$ soft momenta in cosmological perturbation theory.

• These responses measure the impact of long-wavelength perturbations on the local small-scale power spectrum.
• The kinematic structure of the responses (i.e., their angular dependence) can be decomposed unambiguously through a "bias" expansion of the local power spectrum, with a fixed number of physical response coefficients, which are only a function of the hard wavenumber $k$.
• Further, the responses up to $n$-th order completely describe the $(n+2)$-point function in the squeezed limit, i.e.