Non-linear Matter Power Spectrum Research Articles

FREmu: Power Spectrum Emulator for f(R) Gravity

To investigate gravity in the nonlinear regime of cosmic structure using measurements from stage IV surveys, it is imperative to accurately compute large-scale structure observables, such as nonlinear matter power spectra, for gravity models that extend beyond general relativity. However, the theoretical predictions of nonlinear observables are typically derived from N-body simulations, which demand substantial computational resources. In this study, we introduce a novel public emulator, termed FREmu, designed to provide rapid and precise forecasts of nonlinear power spectra specifically for the Hu–Sawicki f(R) gravity model across scales 0.0089h Mpc−1 < k < 0.5h Mpc−1 and redshifts 0 < z < 3. FREmu leverages principal component analysis and artificial neural networks to establish a mapping from parameters to power spectra, utilizing training data derived from the Quijote-MG simulation suite. With a parameter space encompassing seven dimensions, including Ω m , Ω b , h, n s , σ 8, M ν , and fR0 , the emulator achieves an accuracy exceeding 95% for the majority of cases, thus proving to be highly efficient for constraining parameters.

Dark scattering: accelerated constraints from KiDS-1000 with ReACT and CosmoPower

ABSTRACT We present constraints on the dark scattering model through cosmic shear measurements from the Kilo Degree Survey (KiDS-1000), using an accelerated pipeline with novel emulators produced with CosmoPower. Our main emulator, for the dark scattering non-linear matter power spectrum, is trained on predictions from the halo model reaction framework, previously validated against simulations. Additionally, we include the effects of baryonic feedback from HMCode2016, whose contribution is also emulated. We analyse the complete set of statistics of KiDS-1000, namely band powers, COSEBIs, and correlation functions, for dark scattering in two distinct cases. In the first case, taking into account only KiDS cosmic shear data, we constrain the amplitude of the dark energy–dark matter interaction to be $\vert A_{\rm ds} \vert \lesssim 20$$\rm b\,GeV^{-1}$ at 68 per cent C.L. Furthermore, we add information from the cosmic microwave background (CMB) from Planck, along with baryon acoustic oscillations (BAO) from 6dFGS, SDSS, and BOSS, approximating a combined weak lensing+CMB+BAO analysis. From this combination, we constrain $A_{\rm ds} = 10.6^{+4.5}_{-7.3}$$\rm b\,GeV^{-1}$ at 68 per cent C.L. We confirm that with this estimated value of $A_{\rm ds}$ the interacting model considered in this work offers a promising alternative to solve the $S_8$ tension.

SYREN-HALOFIT: A fast, interpretable, high-precision formula for the ΛCDM nonlinear matter power spectrum

Context. Rapid and accurate evaluation of the nonlinear matter power spectrum, P(k), as a function of cosmological parameters and redshift is of fundamental importance in cosmology. Analytic approximations provide an interpretable solution, yet current approximations are neither fast nor accurate relative to numerical emulators. Aims. We aim to accelerate symbolic approximations to P(k) by removing the requirement to perform integrals, instead using short symbolic expressions to compute all variables of interest. We also wish to make such expressions more accurate by re-optimising the parameters of these models (using a larger number of cosmologies and focussing on cosmological parameters of more interest for present-day studies) and providing correction terms. Methods. We use symbolic regression to obtain simple analytic approximations to the nonlinear scale, kσ, the effective spectral index, neff, and the curvature, C, which are required for the HALOFIT model. We then re-optimise the coefficients of HALOFIT to fit a wide range of cosmologies and redshifts. We then again exploit symbolic regression to explore the space of analytic expressions to fit the residuals between P(k) and the optimised predictions of HALOFIT. Our results are designed to match the predictions of EUCLIDEMULATOR2, but we validate our methods against N-body simulations. Results. We find symbolic expressions for kσ, neff and C which have root mean squared fractional errors of 0.8%, 0.2% and 0.3%, respectively, for redshifts below 3 and a wide range of cosmologies. We provide re-optimised HALOFIT parameters, which reduce the root mean squared fractional error (compared to EUCLIDEMULATOR2) from 3% to below 2% for wavenumbers k = 9 × 10−3 − 9 h Mpc−1. We introduce SYREN-HALOFIT (symbolic-regression-enhanced HALOFIT), an extension to HALOFIT containing a short symbolic correction which improves this error to 1%. Our method is 2350 and 3170 times faster than current HALOFIT and HMCODE implementations, respectively, and 2680 and 64 times faster than EUCLIDEMULATOR2 (which requires running CLASS) and the BACCO emulator. We obtain comparable accuracy to EUCLIDEMULATOR2 and the BACCO emulator when tested on N-body simulations. Conclusions. Our work greatly increases the speed and accuracy of symbolic approximations to P(k), making them significantly faster than their numerical counterparts without loss of accuracy.

Sesame: A power spectrum emulator pipeline for beyond-ΛCDM models

The mysterious nature of the dark sector of the Λ-cold-dark-matter (ΛCDM) model is one of the main motivators behind the study of alternative cosmological models. A central quantity of interest for these models is the matter power spectrum, which quantifies structure formation on various scales and can be cross-validated through theory, simulations, and observations. Here, we present a tool that can be used to create emulators for the non-linear matter power spectrum, and similar global clustering statistics, for models beyond ΛCDM with very little computation effort and without the need for supercomputers. We use fast approximate N-body simulations to emulate the boost, B(k, z) = Pbeyond − ΛCDM(k, z)/PΛCDM(k, z), and then rely on existing high-quality emulators made for ΛCDM to isolate Pbeyond − ΛCDM(k, z). Since both the ΛCDM and beyond-ΛCDM models are simulated in our approach, some of the lack of power on small scales due to the low force-resolution in the simulations is factored out, allowing us to extend the emulator to k ∼ 3 − 5 h Mpc−1 and still maintain good accuracy. In addition, errors from the simulation and emulation process can easily be estimated and factored into the covariance when using the emulator on data. As an example of using the pipeline, we create an emulator for the well-studied f(R) model with massive neutrinos, using approximately 3000 CPU hours of computation time. Provided with the paper is a fully functioning pipeline that generates parameter samples, runs a Boltzmann solver to produce initial conditions, runs the simulations, and then gathers all the data and runs it through a machine learning module to develop the emulator. This tool, named Sesame, can be used by anyone to generate a power spectrum emulator for the cosmological model of their choice.

Structure formation in various dynamical dark energy scenarios

This research investigates the impact of the nature of Dark Energy (DE) on structure formation, focusing on the matter power spectrum and the Integrated Sachs–Wolfe effect (ISW). By analyzing the matter power spectrum at redshifts z=0 and z=5, as well as the ISW effect on the scale of ℓ=10−100, the study provides valuable insights into the influence of DE equations of state (EoS) on structure formation. The findings reveal that dynamical DE models exhibit a stronger matter power spectrum compared to constant DE models, with the JBP model demonstrating the highest amplitude and the CPL model the weakest. Additionally, the study delves into the ISW effect, highlighting the time evolution of the ISW source term F(a) and its derivative dF(a)/da, and demonstrating that models with constant DE EoS exhibit a stronger amplitude of F(a) overall, while dynamical models such as CPL exhibit the highest amplitude among the dynamical models, whereas JBP has the lowest. The study also explores the ISW auto-correlation power spectrum and the ISW cross-correlation power spectrum, revealing that dynamical DE models dominate over those with constant DE EoS across various surveys. Moreover, it emphasizes the potential of studying the non-linear matter power spectrum and incorporating datasets from the small scales to further elucidate the dynamical nature of dark energy. This comprehensive analysis underscores the significance of both the matter power spectrum and the ISW signal in discerning the nature of dark energy, paving the way for future research to explore the matter power spectrum at higher redshifts and in the non-linear regime, providing deeper insights into the dynamical nature of dark energy.

DEMNUni: cross-correlating the nonlinear ISWRS effect with CMB-lensing and galaxies in the presence of massive neutrinos

We present an analytical modelling of the angular cross-correlations between the Integrated Sachs Wolfe-Rees Sciama (ISWRS) effect and large-scale structure tracers in the presence of massive neutrinos. Our method has been validated against large N-body simulations with a massive neutrino particle component, namely the DEMNUni suite. We investigate the impact of different neutrino masses on the cross-correlations between the ISWRS effect and both the galaxy clustering and the lensing of the Cosmic Microwave Background (CMB). We also test the ability of current nonlinear matter power spectrum modellings to reproduce neutrino effects in such cross-correlations. We show that the multipole position of a characteristic sign inversion in the cross-spectra, due to nonlinear effects, is strongly related to the total neutrino mass Mν and depends almost linearly on it. While these nonlinear cross-correlation signals may not be able alone to constrain the neutrino mass, our approach paves the way to the detection of such cross-spectra on small scales for their exploitation in combination with main probes from future galaxy surveys and CMB experiments.

Cosmological gravity on all scales. Part III. Non-linear matter power spectrum in phenomenological modified gravity

Model-independent tests of gravity with cosmology are important when testing extensions to the standard cosmological model. To maximise the impact of these tests one requires predictions for the matter power spectrum on non-linear scales. In this work we validate the ReACT approach to the non-linear matter power spectrum against a suite of phenomenological modified gravity N-body simulations with a time-varying gravitational constant, covering a wider range of parameter space than previously examined. This vanilla application of ReACT has limited range and precision due to the different concentration-mass relation c(M) that occurs when gravity is modified. We extend this approach with a fitting function for a modified concentration-mass relation, allowing for accurate (1%) computation of the matter power spectrum up k = 2 h Mpc-1 across a substantial range of parameter space. This fitting function allows precision model-independent tests of modified gravity to be carried out using the data from upcoming large scale structure surveys.

Hybrid bias and displacement emulators for field-level modelling of galaxy clustering in real and redshift space

ABSTRACT Recently, hybrid bias expansions have emerged as a powerful approach to modelling the way in which galaxies are distributed in the Universe. Similarly, field-level emulators have recently become possible, thanks to advances in machine learning and N-body simulations. In this paper, we explore whether both techniques can be combined to provide a field-level model for the clustering of galaxies in real and redshift space. Specifically, here we will demonstrate that field-level emulators are able to accurately predict all the operators of a second-order hybrid bias expansion. The precision achieved in real and redshift space is similar to that obtained for the non-linear matter power spectrum. This translates to roughly 1–2 per cent precision for the power spectrum of a BOSS (Baryon Oscillation Spectroscopic Survey) and a Euclid-like galaxy sample up to $k\sim 0.6\ h\, {\rm Mpc}^{-1}$. Remarkably, this combined approach also delivers precise predictions for field-level galaxy statistics. Despite all these promising results, we detect several areas where further improvements are required. Therefore, this work serves as a road map for the developments required for a more complete exploitation of upcoming large-scale structure surveys.

A weak lensing perspective on non-linear structure formation with fuzzy dark matter

ABSTRACT We investigate non-linear structure formation in the context of the fuzzy dark matter (FDM) model and compare it to the cold dark matter (CDM) model from a weak lensing perspective. Employing Eulerian perturbation theory (PT) up to fourth order, we calculate the tree-level matter trispectra and the one-loop matter spectra and bispectra from consistently chosen initial conditions. Furthermore, we conduct N-body simulations with CDM and FDM initial conditions to predict the non-linear matter power spectra. Subsequently, we derive the respective lensing spectra, bispectra, and trispectra for CDM and FDM within the framework of a Euclid-like weak lensing survey. In our analysis, we compute attainable cumulative signal-to-noise ratios and estimate χ2-functionals, aimed at distinguishing FDM from CDM at particle masses of m = 10−21 eV, m = 10−22 eV, and m = 10−23 eV. Our results indicate that PT predictions are insufficient for distinguishing between the CDM and FDM models within the context of our simulated weak lensing survey for the considered particle masses. Assuming that N-body simulations overestimate late-time small-scale power in the FDM model, future weak lensing surveys may provide the means to discriminate between FDM and CDM up to a mass of m = 10−23 eV. However, for stronger constraints on the FDM mass, observations of the local high-z universe may be more suitable.

DES Y3 cosmic shear down to small scales: Constraints on cosmology and baryons

We present the first analysis of cosmic shear measured in DES Y3 that employs the entire range of angular scales in the data. To achieve this, we built upon recent advances in the theoretical modelling of weak lensing provided by a combination of N-body simulations, physical models of baryonic processes, and neural networks. Specifically, we used BACCOemu to model the linear and non-linear matter power spectrum including baryonic physics, allowing us to robustly exploit scales smaller than those used by the DES Collaboration. We show that the additional data produce cosmological parameters that are tighter but consistent with those obtained from larger scales, while also constraining the distribution of baryons. In particular, we measured the mass scale at which haloes have lost half of their gas, log Mc = 14.38−0.56+0.60 log(h−1 M⊙), and a parameter that quantifies the weighted amplitudes of the present-day matter inhomogeneities, S8 = 0.799−0.015+0.023. Our constraint on S8 is statistically compatible with that inferred from the Planck satellite data at the 0.9σ level. We find instead a 1.4σ shift in comparison to that from the official DES Y3 cosmic shear, because of different choices in the modelling of intrinsic alignment, non-linearities, baryons, and lensing shear ratios. We conclude that small scales in cosmic shear data contain valuable astrophysical and cosmological information and thus should be included in standard analyses.

Revisiting Vainshtein screening for fast N-body simulations

We revisit a method to incorporate the Vainshtein screening mechanism in N-body simulations proposed by R. Scoccimarro in [1]. We further extend this method to cover a subset of Horndeski theories that evade the bound on the speed of gravitational waves set by the binary neutron star merger GW170817. The procedure consists of the computation of an effective gravitational coupling that is time and scale dependent, G eff (k,z), where the scale dependence will incorporate the screening of the fifth-force. This is a fast procedure that when contrasted to the alternative of solving the full equation of motion for the scalar field inside N-body codes, reduces considerably the computational time and complexity required to run simulations. To test the validity of this approach in the non-linear regime, we have implemented it in a COmoving Lagrangian Approximation (COLA) N-body code, and ran simulations for two gravity models that have full N-body simulation outputs available in the literature, nDGP and Cubic Galileon. We validate the combination of the COLA method with this implementation of the Vainshtein mechanism with full N-body simulations for predicting the boost function: the ratio between the modified gravity non-linear matter power spectrum and its General Relativity counterpart. This quantity is of great importance for building emulators in beyond-ΛCDM models, and we find that the method described in this work has an agreement of below 2% for scales down to k ≈ 3h/Mpc with respect to full N-body simulations.

SP(k) – a hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum

ABSTRACT Upcoming large-scale structure surveys will measure the matter power spectrum to approximately per cent level accuracy with the aim of searching for evidence for new physics beyond the standard model of cosmology. In order to avoid biasing our conclusions, the theoretical predictions need to be at least as accurate as the measurements for a given choice of cosmological parameters. However, recent theoretical work has shown that complex physical processes associated with galaxy formation (particularly energetic feedback processes associated with stars and especially supermassive black holes) can alter the predictions by many times larger than the required accuracy. Here we present SP(k), a model for the effects of baryon physics on the non-linear matter power spectrum based on a new large suite of hydrodynamical simulations. Specifically, the ANTILLES suite consists of 400 simulations spanning a very wide range of the ‘feedback landscape’ and show that the effects of baryons on the matter power spectrum can be understood at approaching the per cent level in terms of the mean baryon fraction of haloes, at scales of up to $k \, {\lesssim } \, 10\, h$ Mpc−1 and redshifts up to z = 3. For the range of scales and redshifts that will be probed by forthcoming cosmic shear measurements, most of the effects are driven by galaxy group mass haloes (M ∼ 1013–14 M⊙). We present a simple python implementation of our model, available at https://github.com/jemme07/pyspk, which can be used to incorporate baryon effects in standard gravity-only predictions, allowing for marginalization over baryon physics within cosmological pipelines.

Hi-COLA: fast, approximate simulations of structure formation in Horndeski gravity

We introduce Hi-COLA, a code designed to run fast, approximate N-body simulations of non-linear structure formation in reduced Horndeski gravity. Given an input Lagrangian, Hi-COLA dynamically constructs the appropriate field equations and consistently solves for the cosmological background, linear growth, and screened fifth force of that theory. Hence Hi-COLA is a general, adaptable, and useful tool that allows the mildly non-linear regime of many Horndeski theories to be investigated for the first time, at low computational cost. In this work, we first describe the screening approximations and simulation setup of Hi-COLA for theories with Vainshtein screening. We validate the code against traditional N-body simulations for cubic Galileon gravity, finding 2.5% agreement up to k max = 1.2 h/Mpc. To demonstrate the flexibility of Hi-COLA, we additionally run the first simulations of an extended shift-symmetric gravity theory. We use the consistency and modularity of Hi-COLA to dissect how the modified background, linear growth, and screened fifth force all contribute to departures from ΛCDM in the non-linear matter power spectrum. Hi-COLA can be found at https://github.com/Hi-COLACode/Hi-COLA.

Fast and accurate predictions of the non-linear matter power spectrum for general models of Dark Energy and Modified Gravity

ABSTRACT We embed linear and non-linear parametrizations of beyond standard cosmological physics in the halo model reaction framework, providing a model-independent prescription for the non-linear matter power spectrum. As an application, we focus on Horndeski theories, using the Effective Field Theory of Dark Energy (EFTofDE) to parametrize linear and quasi-non-linear perturbations. In the non-linear regime, we investigate both a non-linear parametrized post-Friedmann (nPPF) approach as well as a physically motivated and approximate phenomenological model based on the error function (Erf). We compare the parametrized approaches’ predictions of the non-linear matter power spectrum to the exact solutions, as well as state-of-the-art emulators, in an evolving dark energy scenario and two well-studied modified gravity models, finding sub-per cent agreement in the reaction using the Erf model at z ≤ 1 and k ≤ 5 h Mpc−1. This suggests only an additional three free constants, above the background and linear theory parameters, are sufficient to model non-linear, non-standard cosmology in the matter power spectrum at scales down to k ≤ 3h Mpc−1 within $2{{\ \rm per\ cent}}$ accuracy. We implement the parametrizations into ver.2.0 of the ReACT code: ACTio et ReACTio.

Constraining the baryonic feedback with cosmic shear using the DES Year-3 small-scale measurements

ABSTRACT We use the small scales of the Dark Energy Survey (DES) Year-3 cosmic shear measurements, which are excluded from the DES Year-3 cosmological analysis, to constrain the baryonic feedback. To model the baryonic feedback, we adopt a baryonic correction model and use the numerical package baccoemu to accelerate the evaluation of the baryonic non-linear matter power spectrum. We design our analysis pipeline to focus on the constraints of the baryonic suppression effects, utilizing the implication given by a principal component analysis on the Fisher forecasts. Our constraint on the baryonic effects can then be used to better model and ameliorate the effects of baryons in producing cosmological constraints from the next-generation large-scale structure surveys. We detect the baryonic suppression on the cosmic shear measurements with a ∼2σ significance. The characteristic halo mass for which half of the gas is ejected by baryonic feedback is constrained to be $M_c \gt 10^{13.2} \, h^{-1} \, \mathrm{M}_{\odot }$ (95 per cent C.L.). The best-fitting baryonic suppression is $\sim 5{{\ \rm per\ cent}}$ at $k=1.0 \, {\rm Mpc}\ h^{-1}$ and $\sim 15{{\ \rm per\ cent}}$ at $k=5.0 \, {\rm Mpc} \ h^{-1}$. Our findings are robust with respect to the assumptions about the cosmological parameters, specifics of the baryonic model, and intrinsic alignments.

DEMNUni: comparing nonlinear power spectra prescriptions in the presence of massive neutrinos and dynamical dark energy

We provide an accurate comparison, against large cosmological N-body simulations, of different prescriptions for modelling nonlinear matter power spectra in the presence of massive neutrinos and dynamical dark energy. We test the current most widely used approaches: fitting functions (HALOFIT and HMcode), the halo-model reaction (ReACT) and emulators (baccoemu and EuclidEmulator2). Focussing on redshifts z ≤ 2 and scales k ≲ 1 h/Mpc (where the simulation mass resolution provides ∼ 1% accuracy), we find that HMcode and ReACT considerably improve over the HALOFIT prescriptions of Smith and Takahashi (both combined with the Bird correction), with an overall agreement of 2% for all the cosmological scenarios considered. Concerning emulators, we find that, especially at low redshifts, EuclidEmulator2 remarkably agrees with the simulated spectra at ≲ 1% level in scenarios with dynamical dark energy and massless neutrinos, reaching a maximum difference of ∼ 2% at z = 2. baccoemu has a similar behaviour as EuclidEmulator2, except for a couple of dark energy models. In cosmologies with massive neutrinos, at z = 0 all the nonlinear prescriptions improve their agreement with respect to the massless neutrino case, except for the Bird and TakaBird models which, however, are not tailored to w 0–wa models. At z > 0 we do not find a similar improvement when including massive neutrinos, probably due to the lower impact of neutrino free-streaming at higher redshifts; rather at z = 2 EuclidEmulator2 exceeds 2% agreement for some dark energy equation of state. When considering ratios between the matter power spectrum computed in a given cosmological model and its ΛCDM counterpart, all the tested prescriptions agree with simulated data, at sub-percent or percent level, depending on z. Finally, we also test how nonlinear prescriptions compare against simulations when computing cosmic shear and angular galaxy clustering spectra. For the former, we find a 2–3% agreement for HMcode, baccoemu, EuclidEmulator2 and ReACT; for the latter, due to the minimum stellar mass of the simulated galaxies, shot noise highly affects the signal and makes the discrepancies as high as 5%.

Separate universe approach to evaluate nonlinear matter power spectrum for nonflat ΛCDM model

The spatial curvature ($\Omega_K$) of the Universe is one of the most fundamental quantities that could give a link to the early universe physics. In this paper we develop an approximate method to compute the nonlinear matter power spectrum, $P(k)$, for "non-flat" $\Lambda$CDM models using the separate universe (SU) ansatz which states that the effect of the curvature on structure formation is equivalent to that of long-wavelength density fluctuation ($\delta_{\rm b}$) in a local volume in the "flat" $\Lambda$CDM model, via the specific mapping between the background cosmological parameters and redshifts in the non-flat and flat models. By utilizing the fact that the normalized response of $P(k)$ to $\delta_{\rm b}$ (equivalently $\Omega_K$), which describes how the non-zero $\Omega_K$ alters $P(k)$ as a function of $k$, is well approximated by the response to the Hubble parameter $h$ within the flat model, our method allows one to generalize the prediction of $P(k)$ for flat cosmologies via fitting formulae or emulators to that for non-flat cosmologies. We use $N$-body simulations for the non-flat $\Lambda$CDM models with $|\Omega_K|\leq 0.1$ to show that our method can predict $P(k)$ for non-flat models up to $k \simeq 6\,h{\rm Mpc}^{-1}$ in the redshift range $z\simeq [0,1.5]$, to the fractional accuracy within $\sim 1$% that roughly corresponds to requirements for weak lensing cosmology with upcoming surveys. We find that the emulators, those built for flat cosmologies such as EuclidEmulator, can predict the non-flat $P(k)$ with least degradation.

Enabling matter power spectrum emulation in beyond-ΛCDM cosmologies with COLA

We compare and validate COLA (COmoving Lagrangian Acceleration) simulations against existing emulators in the literature, namely Bacco and Euclid Emulator 2. Our analysis focuses on the non-linear response function, i.e., the ratio between the non-linear dark matter power spectrum in a given cosmology with respect to a pre-defined reference cosmology, which is chosen to be the Euclid Emulator 2 reference cosmology in this paper. We vary three cosmological parameters, the total matter density, the amplitude of the primordial scalar perturbations and the spectral index.By comparing the COLA non-linear response function with those computed from each emulator in the redshift range 0 ≤ z ≤ 3, we find that the COLA method is in excellent agreement with the two emulators for scales up to k ∼ 1 h/Mpc as long as the deviations of the matter power spectrum from the reference cosmology are not too large.We validate the implementation of massive neutrinos in our COLA simulations by varying the sum of neutrino masses to three different values, 0.0 eV, 0.058 eV and 0.15 eV.We show that all three non-linear prescriptions used in this work agree at the 1% level at k ≤ 1 h/Mpc. We then introduce the Effective Field Theory of Dark Energy in our COLA simulations using the N-body gauge method. We consider two different modified gravity models in which the growth of structure is enhanced or suppressed at small scales, and show that the response function with respect to the change of modified gravity parameters depends weakly on cosmological parameters in these models.

Numerical implementation of the Cubic Galileon model in pinocchio

ABSTRACT We present a perturbative treatment of non-linear galaxy clustering in the context of the cubic Galileon modified gravity model, in terms of second-order Lagrangian Perturbation theory and an extension of ellipsoidal collapse that includes Vainshtein screening. We numerically implement such prescriptions in the approximate pinocchio code, and use it to generate realizations of the matter density field and halo catalogues with different prescriptions for ellipsoidal collapse. We investigate the impact of three different approximations in the computation of collapse times on the halo mass function, halo bias, and matter power spectrum. In the halo mass function, both the modified gravity effect and the screening effect are significant in the high-mass end, similar to what is found for other MG models. We perform a comparison with N-body simulations to assess the validity of our approach, and show that we can reproduce the same trend observed in simulations for all quantities considered. With a simple modification to the grouping algorithm of pinocchio to take into account the gravity modification, and without the need to re-calibrate the algorithm, we show that we can reproduce the linear halo bias and the mildly non-linear matter power spectrum of simulations with good accuracy, especially for the implementation with Vainshtein screening. We stress that, while approximate, our method is orders of magnitude faster than a full N-body simulation, making it an optimal tool for the quick generation of large sets of halo catalogues for cosmological observables.

Response approach to the integrated shear 3-point correlation function: the impact of baryonic effects on small scales

ABSTRACT The integrated shear 3-point correlation function ζ± is a higher-order statistic of the cosmic shear field that describes the modulation of the 2-point correlation function ξ± by long-wavelength features in the field. Here, we introduce a new theoretical model to calculate ζ± that is accurate on small angular scales, and that allows to take baryonic feedback effects into account. Our model builds on the realization that the small-scale ζ± is dominated by the non-linear matter bispectrum in the squeezed limit, which can be evaluated accurately using the non-linear matter power spectrum and its first-order response functions to density and tidal field perturbations. We demonstrate the accuracy of our model by showing that it reproduces the small-scale ζ± measured in simulated cosmic shear maps. The impact of baryonic feedback enters effectively only through the corresponding impact on the non-linear matter power spectrum, thereby permitting to account for these astrophysical effects on ζ± similarly to how they are currently accounted for on ξ±. Using a simple idealized Fisher matrix forecast for a DES-like survey we find that, compared to ξ±, a combined $\xi _{\pm }\ \&amp;\ \zeta _{\pm }$ analysis can lead to improvements of order $20\!-\!40{{\ \rm per\ cent}}$ on the constraints of cosmological parameters such as σ8 or the dark energy equation of state parameter w0. We find similar levels of improvement on the constraints of the baryonic feedback parameters, which strengthens the prospects for cosmic shear data to obtain tight constraints not only on cosmology but also on astrophysical feedback models. These encouraging results motivate future works on the integrated shear 3-point correlation function towards applications to real survey data.