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Register a new userOn the road to percent accuracy IV: ReACT -- computing the non-linear power spectrum beyond $Lambda$CDM
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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 cosmological parameter inference analyses. We present the public software package ReACT, demonstrating its capability for the fast and accurate calculation of non-linear power spectra from non-standard physics. We showcase ReACT through a series of analyses on the DGP and $f(R)$ gravity models, adopting LSST-like cosmic shear power spectra. Accurate non-linear modelling with ReACT has the potential to more than double LSSTs constraining power on the $f(R)$ parameter, in contrast to an analysis that is limited to the quasi-linear regime. We find that ReACT is sufficiently robust for the inference of consistent constraints on theories beyond $Lambda$CDM for current and ongoing surveys. With further improvement, particularly in terms of the accuracy of the non-linear $Lambda$CDM power spectrum, ReACT can, in principle, meet the accuracy requirements for future surveys such as Euclid and LSST.
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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.
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 the matter power spectrum caused by new physics beyond the concordance cosmology. Using standard fitting functions for the halo abundance and the halo mass-concentration relation, the total matter power spectrum in the presence of massive neutrinos is predicted to percent-level accuracy, out to $k=10 , h , {rm Mpc}^{-1}$. We find that refining the prescriptions for the halo properties using $N$-body simulations improves the recovered accuracy to better than 1%. This paper serves as another demonstration for how the halo model reaction framework, in combination with a single suite of standard $Lambda$CDM simulations, can recover percent-level accurate predictions for beyond-$Lambda$CDM matter power spectra, well into the non-linear regime.
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 conditions in the simulations, and rescaling the resulting emulator predictions with analytical `halo model reactions, accurate non-linear matter power spectra for general extensions to the standard $Lambda$CDM model can be calculated. We optimise the emulator design by substituting the simulation suite with non-linear predictions from the standard {sc halofit} tool. We review the performance of the emulator for artificially generated departures from the standard cosmology as well as for theoretically motivated models, such as $f (R)$ gravity and massive neutrinos. For the majority of cosmologies we have tested, the emulator can reproduce the matter power spectrum with errors $lesssim 1%$ deep into the highly non-linear regime. This work demonstrates that with a well-designed suite of $Lambda$CDM simulations, extensions to the standard cosmological model can be tested in the non-linear regime without any reliance on expensive beyond-$Lambda$CDM simulations.
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 $Lambda$CDM matter power spectrum to the physics of an extended cosmological parameter space. By comparing our predictions to $N$-body simulations we demonstrate that with no-free parameters we can recover the nonlinear matter power spectrum for a wide range of different $w_0$-$w_a$ dark energy models to better than 1% accuracy out to $k approx 1 , h , {rm Mpc}^{-1}$. We obtain a similar performance for both DGP and $f(R)$ gravity, with the nonlinear matter power spectrum predicted to better than 3% accuracy over the same range of scales. When including direct measurements of the halo mass function from the simulations, this accuracy improves to 1%. With a single suite of standard $Lambda$CDM $N$-body simulations, our methodology provides a direct route to constrain a wide range of non-standard extensions to the concordance cosmology in the high signal-to-noise nonlinear regime.
Cosmological constraints are usually derived under the assumption of a $6$ parameters $Lambda$-CDM theoretical framework or simple one-parameter extensions. In this paper we present, for the first time, cosmological constraints in a significantly extended scenario, varying up to $12$ cosmological parameters simultaneously, including the sum of neutrino masses, the neutrino effective number, the dark energy equation of state, the gravitational waves background and the running of the spectral index of primordial perturbations. Using the latest Planck 2015 data release (with polarization) we found no significant indication for extensions to the standard $Lambda$-CDM scenario, with the notable exception of the angular power spectrum lensing amplitude, $A_{rm lens}$ that is larger than the expected value at more than two standard deviations even when combining the Planck data with BAO and supernovae type Ia external datasets. In our extended cosmological framework, we find that a combined Planck+BAO analysis constrains the value of the r.m.s. density fluctuation parameter to $sigma_8=0.781_{-0.063}^{+0.065}$ at $95 %$ c.l., helping to relieve the possible tensions with the CFHTlenS cosmic shear survey. We also find a lower value for the reionization optical depth $tau=0.058_{-0.043}^{+0.040}$ at $95$ % c.l. respect to the one derived under the assumption of $Lambda$-CDM. The scalar spectral index $n_S$ is now compatible with a Harrison-Zeldovich spectrum to within $2.5$ standard deviations. Combining the Planck dataset with the HST prior on the Hubble constant provides a value for the equation of state $w < -1$ at more than two standard deviations while the neutrino effective number is fully compatible with the expectations of the standard three neutrino framework.
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