Fast generation of weak lensing maps in modified gravity with COLA

Accurate predictions of weak lensing observables are essential for understanding the large-scale structure of the Universe and probing the nature of gravity. In this work, we present a lightcone implementation to generate maps of the weak lensing convergence field using the COmoving Lagrangian Acceleration (COLA) method. The lightcone is constructed in spherical shells from the source to the observer following an onion representation of the Universe. We validate the COLA-generated convergence maps in General Relativity by comparing five statistics to those of maps obtained with publically available high-resolution $N$-body simulations: the power spectrum, bispectrum, probability distribution function, peak counts and Minkowski functionals. The convergence power spectrum is accurate to within $5\%$ up to $\ell\sim500$ and to within $10\%$ up to $\ell\sim750$, confirming the accuracy of this method on both linear and non-linear scales. For the probability distribution function, peak counts and Minkowski functionals, we determine the map pixel resolution required for COLA to capture the statistical features of the $N$-body convergence maps. Our validation tests provide a baseline for the convergence map specifications at which we can trust COLA for each statistic considered. Using these map specifications, we extend our analyses to two representative theories of Modified Gravity, and demonstrate their imprints on the five convergence statistics considered. This work represents a step towards precise weak lensing predictions under both General Relativity and Modified Gravity with reduced computational cost, providing a robust framework to explore the nature of gravity using field-level inference.