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Register a new userOn the road to percent accuracy: nonlinear reaction of the matter power spectrum to dark energy and modified gravity
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Matteo Cataneo
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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.
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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.
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.
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 study the effects of dark energy (DE) anisotropic stress on features of the matter power spectrum (PS). We employ the Parametrized Post-Friedmannian (PPF) formalism to emulate an effective DE, and model its anisotropic stress properties through a two-parameter equation that governs its overall amplitude ($g_0$) and transition scale ($c_g$). For the background cosmology, we consider different equations of state to model DE including a constant $w_0$ parameter, and models that provide thawing (CPL) and freezing (nCPL) behaviors. We first constrain these parameters by using the Pantheon, BAO, $H_0$ and CMB Planck data. Then, we analyze the role played by these parameters in the linear PS. In order for the anisotropic stress not to provoke deviations larger than $10%$ and $5%$ with respect to the $Lambda$CDM PS at $k sim 0.01 ,h/text{Mpc}$, the parameters have to be in the range $-0.30< g_0 < 0.32$, $0 leq c_g^2 < 0.01$ and $-0.15 < g_0 < 0.16$, $0 leq c_g^2 < 0.01$, respectively. Additionally, we compute the leading nonlinear corrections to the PS using standard perturbation theory in real and redshift space, showing that the differences with respect to the $Lambda$CDM are enhanced, especially for the quadrupole and hexadecapole RSD multipoles.
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