Accelerating Computation of the Nonlinear Mass by an Order of Magnitude
  The nonlinear mass is a characteristic scale in halo formation that has
wide-ranging applications across cosmology. Naively, computing it requires
repeated numerical integration to calculate the variance of the power spectrum
on different scales and determine which scales exceed the threshold for
nonlinear collapse. We accelerate this calculation by working in configuration
space and approximating the correlation function as a polynomial at $r <= 5$
$h^{-1}$ Mpc. This enables an analytic rather than numerical solution, accurate
across a variety of cosmologies to 0.1$-$1% (depending on redshift) and 10$-$20
times faster than the naive numerical method. We also present a further
acceleration (40$-$80 times faster than the naive method) in which we determine
the polynomial coefficients using a Taylor expansion in the cosmological
parameters rather than re-fitting a polynomial to the correlation function. Our
acceleration greatly reduces the cost of repeated calculation of the nonlinear
mass. This will be useful for MCMC analyses to constrain cosmological
parameters from the highly nonlinear regime, e.g. with data from upcoming
surveys.
