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In the context of forthcoming galaxy surveys, to ensure unbiased constraints on cosmology and gravity when using non-linear structure information, percent-level accuracy is required when modelling the power spectrum. This calls for frameworks that can accurately capture the relevant physical effects, while allowing for deviations from $Lambda$CDM. Massive neutrino and baryonic physics are two of the most relevant such effects. We present an integration of the halo model reaction frameworks for massive neutrinos and beyond-$Lambda$CDM cosmologies. The integrated halo model reaction, combined with a pseudo power spectrum modelled by HMCode2020 is then compared against $N$-body simulations that include both massive neutrinos and an $f(R)$ modification to gravity. We find that the framework is 5% accurate down to at least $kapprox 3 , h/{rm Mpc}$ for a modification to gravity of $|f_{rm R0}|leq 10^{-5}$ and for the total neutrino mass $M_ u equiv sum m_ u leq 0.15$ eV. We also find that the framework is 4(1)% consistent with the Bacco (EuclidEmulator2) emulator for $ u w$CDM cosmologies down to at least $k approx 3 , h$/Mpc. Finally, we compare against hydrodynamical simulations employing HMCode2020s baryonic feedback modelling on top of the halo model reaction. For $ u Lambda$CDM cosmologies we find 2% accuracy for $M_ u leq 0.48$eV down to at least $kapprox 5h$/Mpc. Similar accuracy is found when comparing to $ u w$CDM hydrodynamical simulations with $M_ u = 0.06$eV. This offers the first non-linear and theoretically general means of accurately including massive neutrinos for beyond-$Lambda$CDM cosmologies, and further suggests that baryonic effects can be reliably modelled independently of massive neutrino and dark energy physics. These extensions have been integrated into the publicly available ReACT code.
To effectively exploit large-scale structure surveys, we depend on accurate and reliable predictions of non-linear cosmological structure formation. Tools for efficient and comprehensive computational modelling are therefore essential to perform cosm
We analytically model the non-linear effects induced by massive neutrinos on the total matter power spectrum using the halo model reaction framework of Cataneo et al. 2019. In this approach the halo model is used to determine the relative change to t
We introduce an emulator approach to predict the non-linear matter power spectrum for broad classes of beyond-$Lambda$CDM cosmologies, using only a suite of $Lambda$CDM $N$-body simulations. By including a range of suitably modified initial condition
We present a general method to compute the nonlinear matter power spectrum for dark energy and modified gravity scenarios with percent-level accuracy. By adopting the halo model and nonlinear perturbation theory, we predict the reaction of a $Lambda$
Numerical simulations of massive neutrino cosmologies consistently find a spoon-like feature in the non-linear matter power spectrum ratios of cosmological models that differ only in the neutrino mass fraction f_N. Typically, the ratio approaches uni