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, $\texttt{GEVOLUTION}$ and $\texttt{SCREENING}$, to calculate Doppler lensing convergence in cosmic voids of different sizes and halos of different masses. Our analysis reveals scale-dependent performance: $\texttt{SCREENING}$ 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), $\texttt{SCREENING}$ 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: $\texttt{GEVOLUTION}$ is recommended for precision studies critical to $Λ$CDM or modified gravity tests, while $\texttt{SCREENING}$ offers a computationally efficient alternative for relativistic treatments with large catalogs of voids and halos, assisting future astrophysical surveys.