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, with the $w$CDM class of models tested, $\delta (k,a)$ 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 {/scshape RelFit} using only five relatively inexpensive $w$CDM simulations (box length $L=256h^{-1}$ Mpc, $N={1024}^3$ particles, initialised at $z_i=49$). In a 6-parameter space spanning {ω_m, A_s,n_s,w,ω_b, h}, the output relative power spectra of RELFIT are consistent with the predictions of the {/scshape 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.