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.
Categories: astro-ph.CO