  A commonly used perturbative method for computing large-scale clustering of
tracers of mass density, like galaxies, is to model the tracer density field as
a Taylor series in the local smoothed mass density fluctuations, possibly
adding a stochastic component. I suggest a set of parameter redefinitions,
eliminating problematic perturbative correction terms, that should represent a
modest improvement, at least, to this method. As presented here, my method can
be used to compute the power spectrum and bispectrum to 4th order in initial
density perturbations, and higher order extensions should be straightforward.
While the model is technically unchanged at this order, just reparameterized,
the renormalized model is more elegant, and should have better convergence
behavior, for three reasons: First, in the usual approach the effects of
beyond-linear-order bias parameters can be seen at asymptotically large scales,
while after renormalization the linear model is preserved in the large-scale
limit, i.e., the effects of higher order bias parameters are restricted to
relatively high k. Second, while the standard approach includes smoothing to
suppress large perturbative correction terms, resulting in dependence on the
arbitrary cutoff scale, no cutoff-sensitive terms appear explicitly after my
redefinitions (and, relatedly, my correction terms are less sensitive to
high-k, non-linear, power). Third, the 3rd order bias parameter disappears
entirely, so my model has one fewer free parameter than usual (this parameter
was redundant at the order considered). This model predicts a small
modification of the baryonic acoustic oscillation (BAO) signal, in real space,
supporting the robustness of BAO as a probe of dark energy, and providing a
complete perturbative description over the relevant range of scales.
