Fitting functions on the cheap: the relative nonlinear matter power spectrum

Abstract

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 δ(k,a), defined as the fractional deviation in the absolute matter power spectrum produced by a target cosmology away from a reference ΛCDM prediction. From the computational perspective, δ(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 wCDM class of models tested, δ(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 ΛCDM 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 wCDM simulations (box length L=256 h−1 Mpc, N=10243 particles, initialised at zi=49). In a 6-parameter space spanning {ωm, As,ns,w,ωb, 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 0k ≃ 1/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.