Emulating the nonlinear effects of modified gravity on the matter power spectrum for reconstruction

Including nonlinear information from modified gravity (MG) brings more constraining power to the model-independent reconstruction of MG functions. However, the calculation of the nonlinear matter power spectrum with MGCAMB+ReACT is expensive in repeated likelihood evaluations, which limits the exploration of the high-dimensional parameter space. In this work, we construct a neural-network emulator for the nonlinear correction R MG(k,z)=P MG NL(k,z)/P MG L(k,z), which is trained with CosmoPower on approximately 9 times10 5 samples and validated with representative spectra, an independent validation set, and MCMC tests with synthetic data. For CDM and moderate MG nonlinear corrections, the emulated power spectra agree with the reference predictions to within 1.5% over the full scale range considered. For the extreme nonlinear case, the same accuracy is retained for k<0.8, Mpc-1. Over the independent validation set, the mean residual is close to zero, with the 2 sigma scatter below 1% for k<0.5, Mpc-1 and about 2% on smaller scales. The synthetic data MCMC analyses recover the input CDM cosmology and the GR limits of the reconstructed MG functions within the posterior uncertainties, showing the accuracy and reliability of the emulator for Stage-IV-like surveys. We also demonstrate three applications: using R MG to distinguish models with nearly degenerate linear power spectra, using the emulator for theory predictions for current photometric-survey 3 times2 pt likelihoods, and forecasting DESI+CSST constraints with principal component analysis.