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In order to probe modifications of gravity at cosmological scales, one needsaccurate theoretical predictions. N-body simulations are required to explorethe non-linear regime of structure formation but are very time consuming. Inthis work, we release a new public emulator, dubbed e-MANTIS, that performs anaccurate and fast interpolation between the predictions of $f(R)$ modifiedgravity cosmological simulations, run with ECOSMOG. We sample a wide 3Dparameter space given by the current background scalar field value$10^{-7}<\left|f_{R_0}\right|<10^{-4}$, matter density$0.24<\Omega_\mathrm{m}<0.39$, and primordial power spectrum normalisation$0.6<\sigma_8<1.0$, with 110 points sampled from a Latin Hypercube. For eachmodel we perform pairs of $f(R)$CDM and $\Lambda$CDM simulations covering aneffective volume of $\left(560 \, h^{-1}\mathrm{Mpc}\right)^3$ with a massresolution of $\sim 2 \times 10^{10} h^{-1} M_\odot$. We build an emulator forthe matter power spectrum boost $B(k)=P_{f(R)}(k)/P_{\Lambda\mathrm{CDM}}(k)$using a Gaussian Process Regression method. The boost is mostly independent of$h$, $n_{s}$, and $\Omega_{b}$, which reduces the dimensionality of therelevant cosmological parameter space. Additionally, it is more robust againststatistical and systematic errors than the raw power spectrum, thus stronglyreducing our computational needs. According to our dedicated study of numericalsystematics, the resulting emulator has an estimated maximum error of $3\%$across the whole cosmological parameter space, for scales $0.03 \h\mathrm{Mpc}^{-1} < k < 7 \ h\mathrm{Mpc}^{-1}$, and redshifts $0 < z < 2$,while in most cases the accuracy is better than $1\%$. Such an emulator couldbe used to constrain $f(R)$ gravity with weak lensing analyses

The e-MANTIS emulator: fast predictions of the non-linear matter power spectrum in $f(R)$CDM cosmology