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We introduce an emulator approach to predict the non-linear matter powerspectrum for broad classes of beyond-$\Lambda$CDM cosmologies, using only asuite of $\Lambda$CDM $N$-body simulations. By including a range of suitablymodified initial conditions in the simulations, and rescaling the resultingemulator predictions with analytical `halo model reactions', accuratenon-linear matter power spectra for general extensions to the standard$\Lambda$CDM model can be calculated. We optimise the emulator design bysubstituting the simulation suite with non-linear predictions from the standard{\sc halofit} tool. We review the performance of the emulator for artificiallygenerated departures from the standard cosmology as well as for theoreticallymotivated models, such as $f (R)$ gravity and massive neutrinos. For themajority of cosmologies we have tested, the emulator can reproduce the matterpower spectrum with errors $\lesssim 1\%$ deep into the highly non-linearregime. This work demonstrates that with a well-designed suite of $\Lambda$CDMsimulations, extensions to the standard cosmological model can be tested in thenon-linear regime without any reliance on expensive beyond-$\Lambda$CDMsimulations.

On the road to percent accuracy II: calibration of the non-linear matter power spectrum for arbitrary cosmologies