Modeling Nearest Neighbor distributions of biased tracers using Hybrid Effective Field Theory
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 lowredshift HEFT component fields and bias parameter values. These are the same ingredients needed to predict the twopoint clustering. For a specific sample of halos, we show that both the twopoint clustering \textit{and} the $k{\rm NN}$${\rm CDF}$s can be wellfit on quasilinear scales ($\gtrsim 20 h^{1}{\rm Mpc}$) by the secondorder HEFT formalism with the \textit{same values} of the bias parameters, implying that joint modeling of the two is possible. Finally, using a Fisher matrix analysis, we show that including $k{\rm NN}$${\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 twopoint 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 smallscale cosmological clustering.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.10287
 Bibcode:
 2021arXiv210710287B
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 To be submitted to MNRAS