Model-agnostic basis functions for the 2-point correlation function of dark matter in linear theory
This work addresses the need for improved basis functions in baryon acoustic oscillation analyses for cosmology, offering potential statistical gains but is incremental in method.
The paper tackled the problem of approximating the linearly evolved 2-point correlation function of dark matter using a model-agnostic basis, achieving a description accuracy of ~0.6% with 9 basis functions across varied cosmological models.
We consider approximating the linearly evolved 2-point correlation function (2pcf) of dark matter $ξ_{\rm lin}(r;\boldsymbolθ)$ in a cosmological model with parameters $\boldsymbolθ$ as the linear combination $ξ_{\rm lin}(r;\boldsymbolθ)\approx\sum_i\,b_i(r)\,w_i(\boldsymbolθ)$, where the functions $\mathcal{B}=\{b_i(r)\}$ form a $\textit{model-agnostic basis}$ 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 $\mathcal{B}$ and leave the coefficients $\{w_i\}$ free. To date, such analyses have made simple but sub-optimal choices for $\mathcal{B}$, such as monomials. We develop a machine learning framework for systematically discovering a $\textit{minimal}$ basis $\mathcal{B}$ that describes $ξ_{\rm lin}(r)$ near the BAO feature in a wide class of cosmological models. We use a custom architecture, denoted $\texttt{BiSequential}$, for a neural network (NN) that explicitly realizes the separation between $r$ and $\boldsymbolθ$ above. The optimal NN trained on data in which only $\{Ω_{\rm m},h\}$ are varied in a $\textit{flat}$ $Λ$CDM model produces a basis $\mathcal{B}$ comprising $9$ functions capable of describing $ξ_{\rm lin}(r)$ to $\sim0.6\%$ accuracy in $\textit{curved}$ $w$CDM models varying 7 parameters within $\sim5\%$ of their fiducial, flat $Λ$CDM values. Scales such as the peak, linear point and zero-crossing of $ξ_{\rm lin}(r)$ are also recovered with very high accuracy. We compare our approach to other compression schemes in the literature, and speculate that $\mathcal{B}$ may also encompass $ξ_{\rm lin}(r)$ in modified gravity models near our fiducial $Λ$CDM model. Using our basis functions in model-agnostic BAO analyses can potentially lead to significant statistical gains.