Model-agnostic basis functions for the 2-point correlation function of dark matter in linear theory
Aseem Paranjape (IUCAA), Ravi K. Sheth (UPenn/ICTP)
arXiv:2410.21374v1 Announce Type: new
Abstract: We consider approximating the linearly evolved 2-point correlation function (2pcf) of dark matter $xi_{rm lin}(r;boldsymbol{theta})$ in a cosmological model with parameters $boldsymbol{theta}$ as the linear combination $xi_{rm lin}(r;boldsymbol{theta})approxsum_i,b_i(r),w_i(boldsymbol{theta})$, 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 $xi_{rm lin}(r)$ 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 $boldsymbol{theta}$ above. The optimal NN trained on data in which only ${Omega_{rm m},h}$ are varied in a $textit{flat}$ $Lambda$CDM model produces a basis $mathcal{B}$ comprising $9$ functions capable of describing $xi_{rm lin}(r)$ to $sim0.6%$ accuracy in $textit{curved}$ $w$CDM models varying 7 parameters within $sim5%$ of their fiducial, flat $Lambda$CDM values. Scales such as the peak, linear point and zero-crossing of $xi_{rm lin}(r)$ 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 $xi_{rm lin}(r)$ in modified gravity models near our fiducial $Lambda$CDM model. Using our basis functions in model-agnostic BAO analyses can potentially lead to significant statistical gains.arXiv:2410.21374v1 Announce Type: new
Abstract: We consider approximating the linearly evolved 2-point correlation function (2pcf) of dark matter $xi_{rm lin}(r;boldsymbol{theta})$ in a cosmological model with parameters $boldsymbol{theta}$ as the linear combination $xi_{rm lin}(r;boldsymbol{theta})approxsum_i,b_i(r),w_i(boldsymbol{theta})$, 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 $xi_{rm lin}(r)$ 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 $boldsymbol{theta}$ above. The optimal NN trained on data in which only ${Omega_{rm m},h}$ are varied in a $textit{flat}$ $Lambda$CDM model produces a basis $mathcal{B}$ comprising $9$ functions capable of describing $xi_{rm lin}(r)$ to $sim0.6%$ accuracy in $textit{curved}$ $w$CDM models varying 7 parameters within $sim5%$ of their fiducial, flat $Lambda$CDM values. Scales such as the peak, linear point and zero-crossing of $xi_{rm lin}(r)$ 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 $xi_{rm lin}(r)$ in modified gravity models near our fiducial $Lambda$CDM model. Using our basis functions in model-agnostic BAO analyses can potentially lead to significant statistical gains.