Model-agnostic basis functions for the 2-point correlation function of dark matter in linear theory

Abstract

We consider approximating the linearly evolved 2-point correlation function (2pcf) of dark matter ξlin(r;θ) in a cosmological model with parameters θ as the linear combination ξlin(r;θ)≈∑ibi(r) wi(θ), where the functions ℬ = {bi(r)} form a model-agnostic basis for the linear 2pcf. This decomposition is important for model-agnostic analyses of the baryon acoustic oscillation (BAO) feature in the nonlinear 2pcf of galaxies that fix ℬ and leave the coefficients {wi} free. To date, such analyses have made simple but sub-optimal choices for ℬ, such as monomials. We develop a machine learning framework for systematically discovering a minimal basis ℬ that describes ξlin(r) near the BAO feature in a wide class of cosmological models. We use a custom architecture, denoted BiSequential, for a neural network (NN) that explicitly realizes the separation between r and θ above. The optimal NN trained on data in which only {Ωm,h} are varied in a flat ΛCDM model produces a basis ℬ comprising 9 functions capable of describing ξlin(r) to ∼0.6% accuracy in curved wCDM models varying 7 parameters within ∼5% of their fiducial, flat ΛCDM values. Scales such as the peak, linear point and zero-crossing of ξlin(r) are also recovered with very high accuracy. We compare our approach to other compression schemes in the literature, and speculate that ℬ may also encompass ξlin(r) in modified gravity models near our fiducial ΛCDM model. Replacing the ad hoc bases in model-agnostic BAO analyses with our basis functions can potentially lead to significant gains in constraining power.