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

We consider approximating the linearly evolved 2-point correlation function (2pcf) of dark matter xirm lin(r;boldsymbolθ) in a cosmological model with parameters boldsymbolθ as the linear combination xirm lin(r;boldsymbolθ)≈sumi,bi(r),wi(boldsymbolθ), where the functions B=bi(r) form a textitmodel-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 textitminimal basis B that describes xirm lin(r) near the BAO feature in a wide class of cosmological models. We use a custom architecture, denoted textttBiSequential, for a neural network (NN) that explicitly realizes the separation between r and boldsymbolθ above. The optimal NN trained on data in which only Omegarm m,h are varied in a textitflat LambdaCDM model produces a basis B comprising 9 functions capable of describing xirm lin(r) to ~0.6% accuracy in textitcurved wCDM models varying 7 parameters within ~5% of their fiducial, flat LambdaCDM values. Scales such as the peak, linear point and zero-crossing of xirm 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 xirm lin(r) in modified gravity models near our fiducial LambdaCDM model. Using our basis functions in model-agnostic BAO analyses can potentially lead to significant statistical gains.