%0 Generic %1 banerjee2021modeling %A Banerjee, Arka %A Kokron, Nickolas %A Abel, Tom %D 2021 %K library %T Modeling Nearest Neighbor distributions of biased tracers using Hybrid Effective Field Theory %U http://arxiv.org/abs/2107.10287 %X We investigate the application of Hybrid Effective Field Theory (HEFT) -- which combines a Lagrangian bias expansion with subsequent particle dynamics from $N$-body simulations -- to the modeling of $k$-Nearest Neighbor Cumulative Distribution Functions ($kNN$-$CDF$s) of biased tracers of the cosmological matter field. The $kNN$-$CDF$s are sensitive to all higher order connected $N$-point functions in the data, but are computationally cheap to compute. We develop the formalism to predict the $kNN$-$\rm CDF$s of discrete tracers of a continuous field from the statistics of the continuous field itself. Using this formalism, we demonstrate how $k\rm NN$-$CDF$ statistics of a set of biased tracers, such as halos or galaxies, of the cosmological matter field can be modeled given a set of low-redshift HEFT component fields and bias parameter values. These are the same ingredients needed to predict the two-point clustering. For a specific sample of halos, we show that both the two-point clustering and the $kNN$-$CDF$s can be well-fit on quasi-linear scales ($20 h^-1Mpc$) by the second-order HEFT formalism with the same values of the bias parameters, implying that joint modeling of the two is possible. Finally, using a Fisher matrix analysis, we show that including $kNN$-$CDF$ measurements over the range of allowed scales in the HEFT framework can improve the constraints on $\sigma_8$ by roughly a factor of $3$, compared to the case where only two-point measurements are considered. Combining the statistical power of $kNN$ measurements with the modeling power of HEFT, therefore, represents an exciting prospect for extracting greater information from small-scale cosmological clustering.

@misc{banerjee2021modeling, abstract = {We investigate the application of Hybrid Effective Field Theory (HEFT) -- which combines a Lagrangian bias expansion with subsequent particle dynamics from $N$-body simulations -- to the modeling of $k$-Nearest Neighbor Cumulative Distribution Functions ($k{\rm NN}$-${\rm CDF}$s) of biased tracers of the cosmological matter field. The $k{\rm NN}$-${\rm CDF}$s are sensitive to all higher order connected $N$-point functions in the data, but are computationally cheap to compute. We develop the formalism to predict the $k{\rm NN}$-${\rm CDF}$s of discrete tracers of a continuous field from the statistics of the continuous field itself. Using this formalism, we demonstrate how $k{\rm NN}$-${\rm CDF}$ statistics of a set of biased tracers, such as halos or galaxies, of the cosmological matter field can be modeled given a set of low-redshift HEFT component fields and bias parameter values. These are the same ingredients needed to predict the two-point clustering. For a specific sample of halos, we show that both the two-point clustering \textit{and} the $k{\rm NN}$-${\rm CDF}$s can be well-fit on quasi-linear scales ($\gtrsim 20 h^{-1}{\rm Mpc}$) by the second-order HEFT formalism with the \textit{same values} of the bias parameters, implying that joint modeling of the two is possible. Finally, using a Fisher matrix analysis, we show that including $k{\rm NN}$-${\rm CDF}$ measurements over the range of allowed scales in the HEFT framework can improve the constraints on $\sigma_8$ by roughly a factor of $3$, compared to the case where only two-point measurements are considered. Combining the statistical power of $k{\rm NN}$ measurements with the modeling power of HEFT, therefore, represents an exciting prospect for extracting greater information from small-scale cosmological clustering.}, added-at = {2021-07-23T12:01:21.000+0200}, author = {Banerjee, Arka and Kokron, Nickolas and Abel, Tom}, biburl = {https://www.bibsonomy.org/bibtex/2847402ee831ca2a87cd8ed72766d2358/gpkulkarni}, description = {Modeling Nearest Neighbor distributions of biased tracers using Hybrid Effective Field Theory}, interhash = {1b0529c862c4d2d8f490e492843558e8}, intrahash = {847402ee831ca2a87cd8ed72766d2358}, keywords = {library}, note = {cite arxiv:2107.10287Comment: To be submitted to MNRAS}, timestamp = {2021-07-23T12:01:21.000+0200}, title = {Modeling Nearest Neighbor distributions of biased tracers using Hybrid Effective Field Theory}, url = {http://arxiv.org/abs/2107.10287}, year = 2021 }