Effective Theories of Redshift-Space Galaxy Peculiar Velocities

TL;DR

The paper develops an EFT framework for predicting redshift-space peculiar velocity statistics in both Lagrangian and Eulerian formalisms, computing 2-point pairwise velocity moments up to the second order at 1-loop and validating the approach against nonlinear N-body simulations. A velocity-aware IR resummation scheme is introduced to accurately model BAO features in velocity statistics, distinct from galaxy clustering. The authors demonstrate that the combined EFT treatment of velocity and density observables yields percent-level recovery of the growth rate and BAO signatures, and they release velocisaurus to enable fast EFT predictions. These advances pave the way for robust cosmological constraints from upcoming peculiar velocity surveys and kinetic Sunyaev-Zeldovich measurements.

Abstract

We present predictions for redshift-space peculiar velocity statistics in the Lagrangian and Eulerian formulations of the effective field theory (EFT) of large-scale structure. We compute 2-point pairwise velocity statistics up to the second moment at next-to-leading (1-loop) order, showing that they can be modeled together with redshift-space galaxy densities with a consistent set of EFT coefficients. We show that peculiar velocity statistics have a distinct dependence on long-wavelength bulk flows that necessitates a variation on the usual infrared (IR) resummation procedure used to model baryon acoustic oscillations (BAO) in galaxy clustering. This can be implemented recursively in powers of the velocity in both the Lagrangian and Eulerian frameworks. We validate our analytic calculations against fully nonlinear N-body simulations, demonstrating that they can be used to recover the growth rate at better than percent level precision, well beyond the statistical requirements of upcoming peculiar velocity surveys and measurements of the kinetic Sunyaev-Zeldovich (kSZ) effect. As part of this work, we release $\href{https://github.com/sfschen/velocisaurus}{\texttt{velocisaurus}}$, a fast $\texttt{Python}$ code for computing EFT predictions of peculiar velocity statistics.

Figures (8)

• Figure 1: BAO in the $z = 0$ pairwise velocity spectrum in the Zeldovich approximation for a tracer with linear Lagrangian bias $b_\delta = 0.5$, evaluated at an angle $\mu = 1$ parallel to the line of sight. (Left) Comparison of the exact Zeldovich predction (black dashed) to the prediction of various resummation schemes. Both linear theory and the C21 resummation scheme deviate from Zeldovich at fairly large scales while the new resummation scheme is in good agreement. (Right) The same comparison with PT predictions at 1-loop order. The C21 resummation is notably improved though still in worse agreement than the new scheme.
• Figure 2: Same as Figure \ref{['fig:vk_ir_resum']} but for the pairwise velocity dispersion spectrum ${{{\sigma^2_s(k)}}}$. Notably, the 1-loop prediction in the C21 scheme now sigificantly overpredicts the BAO amplitude even at $k < 0.1\ h$ Mpc$^{-1}$ while the new scheme is in excellent agreement with the full Zeldovich calculation at both linear and 1-loop order.
• Figure 3: Predictions for the BAO contributions to $v_s$ and $\sigma^2_s$ in the Zeldovich universe using LPT. Here, the derivative formula is exact, such that the black-dashed and the orange lines are identical. On the other hand, the C21 scheme (blue) shows significant differences in its prediction for $\sigma^2_s$, though it succeeds in predicting $v_s$ almost exactly. Predictions for resummed LPT with only modes longer than $k_{\rm IR} = 0.125 h$ Mpc$^{-1}$ resummed in the derivative scheme is shown in green, showing good quantitative agreement on perturbative scales while differing towards smaller scales where the UV modes effects become more important.
• Figure 4: Fits to multipoles $\ell$ of the first three redshift-space pairwise velocity moments for our two halo samples at fixed cosmology. Both EPT (solid) and LPT (dashed) are in very good agreement with the N-body measurements, with a better range of fit to smaller scales at the higher redshift, though we note that the EPT and LPT seem to better predict $\sigma_2^{s,2}$ and $v_{s,3}$, respectively. For comparison, dotted lines show un-resummed SPT predictions without EFT corrections. The bottom panels shows residuals relative to error bars $\sigma$ for the mean of the $25$ boxes, each with volume $(2 h^{-1} \text{Gpc})^3$ box; the shaded gray band marks the $1\sigma$ region of the measurements. We note that discreteness effects in several spectra, particular in the higher multipoles, are significantly larger than the nominal statistical errors.
• Figure 5: Predictions for the BAO feauture in redshift-space peculiar velocity spectra for our two fiducial halo samples, computed by subtracting the contributions due to $P_{\rm lin}^{\rm nw}$ and, where needed, a broadband polynomial (dotted) forced to zero at large scales to account for differences from fitting the broadband power. Both the Eulerian and Lagrangian theories are in excellent agreement with the data even when the BAO signal is completely out of phase with linear theory (dashed).