We suggest an approach to perturbative calculations of large-scale clustering
in the Universe that includes from the start the stream crossing (multiple
velocities for mass elements at a single position) that is lost in traditional
calculations. Starting from a functional integral over displacement, the
perturbative series expansion is in deviations from (truncated) Zel'dovich
evolution, with terms that can be computed exactly even for stream-crossed
displacements. We evaluate the one-loop formulas for displacement and density
power spectra numerically in 1D, finding dramatic improvement in agreement with
N-body simulations compared to the Zel'dovich power spectrum (which is exact in
1D up to stream crossing). Beyond 1D, our approach could represent an
improvement over previous expansions even aside from the inclusion of stream
crossing, but we have not investigated this numerically. In the process we show
how to achieve effective-theory-like regulation of small-scale fluctuations
without free parameters.Comment: added pedagogical explanation of key math trick in appendi
