The impact of our peculiar motion on primordial non-Gaussianity measurements using the LIGER4GAL framework

TL;DR

This work quantifies how relativistic redshift-space distortions, especially the observer’s peculiar velocity imprint (FOTO), bias primordial non-Gaussianity measurements from large-scale structure. It introduces LIGER4GAL, an updated tracer-based mock-generation framework that applies linear-order relativistic RSDs at the tracer level while preserving nonlinear clustering accuracy, enabling realistic DESI-like LRG mocks from the high-resolution HMDPL simulation. Through extensive validation against theory and lower-resolution versions, the study demonstrates that neglecting FOTO can systematically bias f_nl, with biases exceeding 1σ in a substantial fraction of realizations when including large-scale modes down to k_min = 0.0015 h/Mpc. The results underscore the necessity of incorporating relativistic RSDs in EFT-based full-shape and PNG analyses for Stage-IV surveys and provide a practical, public toolkit for generating DESI-like mocks. Overall, LIGER4GAL enables more accurate, survey-tailored analyses of the large-scale structure and PNG constraints in the presence of relativistic effects.

Abstract

Current and forthcoming galaxy surveys will map the observable Universe with unprecedented depth, sky coverage, and precision. These maps are affected by relativistic redshift-space distortions (RSDs), which become increasingly relevant on ultra-large scales. Accurate modelling of these relativistic RSDs is essential to avoid systematic biases in key cosmological measurements, such as primordial non-Gaussianity (PNG). To address this, we introduce an updated implementation of the LIGER method, LIGER4GAL, which incorporates all linear-order relativistic RSDs directly at the tracer level of high-resolution N-body simulations. We demonstrate that LIGER4GAL improves upon previous iterations of the LIGER method by reproducing the expected non-linear clustering while maintaining accuracy for relativistic RSDs on large scales. We use the updated code to generate a DESI-like sample of luminous red galaxies from the Huge MultiDark Planck simulation. By measuring the power spectrum multipoles of this sample with and without the imprint of relativistic RSDs, we assess the impact of relativistic effects on measurements of the local PNG signal ($f_\mathrm{nl}$). We find that the omission of the''finger-of-the-observer'' (sourced by the peculiar velocity of the observer) effect in the power spectrum modelling can bias measurements of $f_{\rm nl}$ by more than $1$ ($0.25$) $ σ_{f_{\rm nl}}$ in 40% (80%) of the possible realizations of the universe if scales down to $k_\mathrm{min} = 0.0015\,h/\mathrm{Mpc}$ are included.

Figures (7)

• Figure 1: Left: Field approach schematic of LIGER4DM. Right: LIGER4GAL approach implemented in this work.
• Figure 2: Schematic summarising how the haloes (Section \ref{['liger4gal']}) and then galaxies (Section \ref{['galaxy_sample']}) are shifted to build the light cones. We first apply the shift $\Delta \boldsymbol{x}_h$ (shown with a green arrow, see Eq. \ref{['eq:shift_lig']}) to the halo positions, including both local and integrated terms. Then, we perform the peculiar velocity correction $\Delta \boldsymbol{x}_\mathrm{g,v}$ (red arrows) described by Eq.(\ref{['v_shift_gal']}) to each galaxy. In an analogue way, we produce a global magnification term $\mathcal{M}_\mathrm{h,s}$ for each halo (see Eq. \ref{['eq:Mag_lig']}), that is applied to each galaxy inhabiting it after correcting for the individual galaxy peculiar velocities with Eq.(\ref{['v_mag_gal']}).
• Figure 3: Mollweide projection in ecliptic coordinates of the DESI Year-5 like sample we generated , used to construct the LRG-DESI and BCLRG-DESI catalogues. The blue cross marks the direction of the observer’s velocity adopted in this work 2020, while the opposite direction is indicated by the red square. The galactic plane is shown as a dashed black line.
• Figure 4: Halo and LRG galaxies survey functions. With a grey dotted line we show the radial density and the linear and evolution biases of the full sky halo sample H, while with a black continuous line and a red-dashed line we show the same quantities along with the magnification bias, for the LRG-like samples in the full-sky (FS) and DESI setting respectively. The radial densities of the two LRG samples differ due to the application of the incompleteness factor of Eq. \ref{['HOD_Zheng_cen']} only to the latter. As mentioned in Sect. \ref{['validation']}, the halo magnification bias is null, thus not shown.
• Figure 5: Upper : We show the halo angular power spectra of the H-FS catalogues (black dashed lines) and of the low-resolution BCH-FS catalogues, where mean of the mocks is shown with a red dashed line and the R.M.S. with a pink-shaded region). Spectra are shown for the $z \in [0.5,0.6]$ bin, with $\mathcal{R}$ and $\mathcal{O}$ mocks in the left and right panels. CAMB linear (grey dotted lines) and halofit (grey dash-dotted) predictions are overplotted. Lower : Residuals relative to the CAMB non-linear prediction.