Fitting functions on the cheap: the relative nonlinear matter power
  spectrum
  We propose an alternative approach to the construction of fitting functions
to the nonlinear matter power spectrum extracted from $N$-body simulations
based on the relative matter power spectrum $\delta(k,a)$, defined as the
fractional deviation in the absolute matter power spectrum produced by a target
cosmology away from a reference $\Lambda$CDM prediction. From the computational
perspective, $\delta(k,a)$ is fairly insensitive to the specifics of the
simulation settings, and numerical convergence at the 1%-level can be readily
achieved without the need for huge computing capacity. Furthermore,
$\delta(k,a)$ exhibits several interesting properties that enable a piece-wise
construction of the full fitting function, whereby component fitting functions
are sought for single-parameter variations and then multiplied together to form
the final product. Then, to obtain 1%-accurate absolute power spectrum
predictions for any target cosmology only requires that the community as a
whole invests in producing one single ultra-precise reference $\Lambda$CDM
absolute power spectrum, to be combined with the fitting function to produce
the desired result. To illustrate the power of this approach, we have
constructed the fitting function RelFit using only five relatively inexpensive
$w$CDM simulations (box length $L=256 h^{-1}$Mpc, $N=1024^3$ particles,
initialised at $z_i=49$). In a 6-parameter space spanning
$\{\omega_m,A_s,n_s,w,\omega_b,h\}$, the output relative power spectra of
RelFit are consistent with the predictions of the CosmicEmu emulator to 1% or
better for a wide range of cosmologies up to $k\simeq 10$/Mpc. Thus, our
approach could provide an inexpensive and democratically accessible route to
fulfilling the 1%-level accuracy demands of the upcoming generation of
large-scale structure probes, especially in the exploration of "non-standard"
or "exotic" cosmologies on nonlinear scales.
