Dynamic Zoom Simulations of structure formation beyond standard cosmology

(Abridged) A thorough interpretation of the current and upcoming generation of cosmological observations requires unprecedented large-scale, high-resolution simulations spanning multiple cosmological models and parameters. The realization of these computationally demanding simulations poses a crucial technical challenge. We present beyond - $\Lambda$CDM implementations of the Dynamic Zoom Simulations (DZS) method, a performance-enhancing technique tailored for large-scale simulations that produce lightcone-like outputs. This approach dynamically decreases the resolution of a simulation in the regions that are not in causal connection with the observer, saving computational resources without directly affecting the physical properties within the lightcone. We implemented the DZS algorithm in two state-of-the-art codes supporting non-standard cosmologies, namely modified $f(R)$ gravity in Arepo and dark sector interactions in Gadget4. We analyzed result accuracy and performance gains across resolution, simulation volume and model by comparing runs performed with and without the DZS algorithm. Our DZS reproduce the lightcone halo mass function, sky-projected massmaps, and matter and weak lensing convergence power spectra with an accuracy of $\simeq$ 0.1% or higher in most cases. In terms of performance, DZS runs in our test simulations can save up to $\sim$ 50% runtime compared to the non-DZS counterparts. A scaling to larger simulated volumes suggests that performance gains could improve by an additional $\sim$ 20% at the resolution levels of current state-of-the-art simulations. The validation of the DZS algorithm in non-standard models demonstrates that this technique can enable cost effective, large-scale ($\gtrsim$ 1 cGpc/h) simulations with state-of-the-art resolution, providing the computational framework needed to constrain and help the interpretation of forthcoming data.