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

Code

• github.com/a-paranjape/mlfundas
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Abstract

We consider approximating the linearly evolved 2-point correlation function (2pcf) of dark matter _ lin(r;) in a cosmological model with parameters as the linear combination _ lin(r;)_i\,b_i(r)\,w_i(), where the functions B= _i(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 _i\ 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 _ lin(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 above. The optimal NN trained on data in which only \_ m,h\ are varied in a flat CDM model produces a basis B comprising 9 functions capable of describing _ lin(r) to 0.6\% accuracy in curved wCDM models varying 7 parameters within 5\% of their fiducial, flat CDM values. Scales such as the peak, linear point and zero-crossing of _ lin(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 _ lin(r) in modified gravity models near our fiducial CDM model. Using our basis functions in model-agnostic BAO analyses can potentially lead to significant statistical gains.

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