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Understanding non-linear structure formation is crucial for fully exploring the data generated by stage IV surveys, requiring accurate modelling of the power spectrum. This is challenging for deviations from Λ cold dark matter, but we must ensure that alternatives are well tested, to avoid false detections. We present an extension of the halo model reaction framework for interacting dark energy. We modify the halo model including the additional force present in the Dark Scattering model and implement it into ReACT. The reaction is combined with a pseudo-spectrum from EuclidEmulator2 and compared to N -body simulations. Using standard mass function and concentration-mass relation, we find predictions to be 1 per cent accurate at z  = 0 up to k  = 0.8  h  Mpc−1 for the largest interaction strength tested (ξ = 50 b GeV−1), improving to 2  h  Mpc−1 at z  = 1. For smaller interaction strength (10 b GeV−1), we find 1 per cent agreement at z  = 1 up to scales above 3.5  h  Mpc−1, being close to 1  h  Mpc−1 at z  = 0. Finally, we improve our predictions with the inclusion of baryonic feedback and massive neutrinos and study degeneracies between the effects of these contributions and those of the interaction. Limiting the scales to where our modelling is 1 per cent accurate, we find a degeneracy between the interaction and feedback, but not with massive neutrinos. We expect the degeneracy with feedback to be resolvable by including smaller scales. This work represents the first analytical tool for calculating the non-linear spectrum for interacting dark energy models. [ABSTRACT FROM AUTHOR]

In the context of forthcoming galaxy surveys, to ensure unbiased constraints on cosmology and gravity when using non-linear structure information, per cent-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 cold dark matter (ΛCDM). 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 ΛCDM 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 4 per cent accurate down to at least |$k\approx 3 \, h\, {\rm Mpc}^{-1}$| for a modification to gravity of | f R0| ≤ 10−5 and for the total neutrino mass M ν ≡ ∑ m ν ≤ 0.15 eV. We also find that the framework is 4 per cent consistent with EuclidEmulator2 as well as the Bacco emulator for most of the considered ν w CDM cosmologies down to at least |$k \approx 3 \, h$|  Mpc−1. Finally, we compare against hydrodynamical simulations employing HMCode2020 's baryonic feedback modelling on top of the halo model reaction. For νΛCDM cosmologies, we find 2 per cent accuracy for M ν ≤ 0.48 eV down to at least k ≈ 5 h  Mpc−1. Similar accuracy is found when comparing to ν w CDM hydrodynamical simulations with M ν = 0.06 eV. This offers the first non-linear, theoretically general means of accurately including massive neutrinos for beyond-ΛCDM cosmologies, and further suggests that baryonic, massive neutrino, and dark energy physics can be reliably modelled independently. [ABSTRACT FROM AUTHOR]