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We compare and validate COLA (COmoving Lagrangian Acceleration) simulationsagainst existing emulators in the literature, namely Bacco and Euclid Emulator2. Our analysis focuses on the non-linear response function, i.e., the ratiobetween the non-linear dark matter power spectrum in a given cosmology withrespect to a pre-defined reference cosmology, which is chosen to be the EuclidEmulator 2 reference cosmology in this paper. We vary three cosmologicalparameters, the total matter density, the amplitude of the primordial scalarperturbations and the spectral index. By comparing the COLA non-linear responsefunction with those computed from each emulator in the redshift range $0 \leq z\leq 3$, we find that the COLA method is in excellent agreement with the twoemulators for scales up to $k \sim 1 \ h$/Mpc as long as the deviations of thematter power spectrum from the reference cosmology are not too large. Wevalidate the implementation of massive neutrinos in our COLA simulations byvarying the sum of neutrino masses to three different values, $0.0$ eV, $0.058$eV and $0.15$ eV. We show that all three non-linear prescriptions used in thiswork agree at the $1\%$ level at $k \leq 1 \ h$/Mpc. We then introduce theEffective Field Theory of Dark Energy in our COLA simulations using the$N$-body gauge method. We consider two different modified gravity models inwhich the growth of structure is enhanced or suppressed at small scales, andshow that the response function with respect to the change of modified gravityparameters depends weakly on cosmological parameters in these models.

Enabling matter power spectrum emulation in beyond-$\Lambda$CDM cosmologies with COLA