Tracing Cosmological Signature with Doppler Lensing: Insights from Cosmological Simulations

Doppler lensing, a relativistic effect resulting from the peculiar velocities of galaxies along the line of sight, provides insight into the large-scale structure of the Universe. Relativistic simulations are essential for modeling Doppler lensing because they incorporate gravity and motion in spacetime. We compare two relativistic $N$-body simulation frameworks, $\mathtt{\text{GEVOLUTION}}$ and $\mathtt{\text{SCREENING}}$, to calculate Doppler lensing convergence in cosmic voids of different sizes and halos of different masses. Our analysis reveals scale-dependent performance: $\mathtt{\text{SCREENING}}$ shows larger differences in small voids (radius range: 15–25 Mpc/h) with a mean absolute relative difference of 38.5%, due to linearized dynamics failing in nonlinear regimes. Medium voids (25–35 Mpc/h) show better agreement (9.5% mean difference). For large voids (35–45 Mpc/h), $\mathtt{\text{SCREENING}}$ exhibits intermediate differences (16.9% mean difference) with central instabilities. Moreover, our Doppler convergence analysis with massive halos (${10}^{11.5}$–${10}^{14}{h}^{-1}{\mathrm{M}}_{\odot }$) demonstrates excellent consistency (1.6–3.6% mean difference). These findings provide clear guidance for simulation choice: $\mathtt{\text{GEVOLUTION}}$ is recommended for precision studies critical to $\mathrm{\Lambda }$CDM or modified gravity tests, while $\mathtt{\text{SCREENING}}$ offers a computationally efficient alternative for relativistic treatments with large catalogs of voids and halos, assisting future astrophysical surveys.