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Model-agnostic basis functions for the 2-point correlation function of dark matter in linear theory
Aseem Paranjape, Ravi K. Sheth
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)≈∑ᵢ bᵢ(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 $w$CDM 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. Using our basis functions in model-agnostic BAO analyses can potentially lead to significant statistical gains.
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