arXiv subjects

Aurel Schneider

Publications and source records attributed to Aurel Schneider.

At least 37 records · Page 2Linked to original sources

arXiv2023

Constraining dark matter decays with cosmic microwave background and weak lensing shear observations

From observations at low and high redshifts, it is well known that the bulk of dark matter (DM) has to be stable or at least very long-lived. However, the possibility that a small fraction of DM is unstable or that all DM decays with a half-life time ($τ$) significantly longer than the age of the Universe is not ruled out. One-body decaying dark matter (DDM) consists of a minimal extension to the $Λ$CDM model. It causes a modification of the cosmic growth history as well as a suppression of the small-scale clustering signal, providing interesting consequences regarding the $S_8$ tension, which is the observed difference in the clustering amplitude between weak-lensing (WL) and cosmic microwave background (CMB) observations. In this paper, we investigate models in which a fraction or all DM decays into radiation, focusing on the long-lived regime, that is, $τ\gtrsim H_0^{-1}$ ( $H_0^{-1}$ being the Hubble time). We used WL data from the Kilo-Degree Survey (KiDS) and CMB data from Planck. First, we confirm that this DDM model cannot alleviate the $S_8$ difference. We then show that the most constraining power for DM decay does not come from the nonlinear WL data, but from CMB via the integrated Sachs-Wolfe effect. From the CMB data alone, we obtain constraints of $τ\geq 288$~Gyr if all DM is assumed to be unstable, and we show that a maximum fraction of $f=0.07$ is allowed to decay assuming the half-life time to be comparable to (or shorter than) one Hubble time. The constraints from the KiDS-1000 WL data are significantly weaker, $τ\geq 60$~Gyr and $f<0.34$. Combining the CMB and WL data does not yield tighter constraints than the CMB alone, except for short half-life times, for which the maximum allowed fraction becomes $f=0.03$. All limits are provided at the 95% confidence level.

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arXiv2023

Cosmological forecast of the 21-cm power spectrum using the halo model of reionization

The 21-cm power spectrum of reionization is a promising probe for cosmology and fundamental physics. Exploiting this new observable, however, requires fast predictors capable of efficiently scanning the very large parameter space of cosmological and astrophysical uncertainties. In this paper, we introduce the halo model of reionization (HMreio), a new analytical tool that combines the halo model of the cosmic dawn with the excursion-set bubble model for reionization, assuming an empirical correction factor to deal with overlapping ionization bubbles. First, HMreio is validated against results from the well-known semi-numerical code 21cmFAST, showing a good overall agreement for wave-modes of $k\lesssim 1$ h/Mpc. Based on this result, we perform a Monte-Carlo Markov-Chain (MCMC) forecast analysis assuming mock data from 1000-hour observations with the low-frequency part of the Square Kilometre Array (SKA) observatory. We simultaneously vary the six standard cosmological parameters together with seven astrophysical nuisance parameters quantifying the abundance and spectral properties of sources. Depending on the assumed theory error, we find very competitive constraints on cosmological parameters. In particular, it will be possible to conclusively test current cosmological tensions related to the Hubble parameter ($H_0$-tension) and the matter clustering amplitude ($S_8$-tension). Furthermore, the sum of the neutrino masses can be strongly constrained, making it possible to determine the neutrino mass hierarchy at the $\sim 90$ percent confidence level. However, these goals can only be achieved if the current modelling uncertainties are substantially reduced to below $\sim 3$ percent.

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arXiv2022

CosmoGridV1: a simulated $w$CDM theory prediction for map-level cosmological inference

We present CosmoGridV1: a large set of lightcone simulations for map-level cosmological inference with probes of large scale structure. It is designed for cosmological parameter measurement based on Stage-III photometric surveys with non-Gaussian statistics and machine learning. CosmoGridV1 spans the $w$CDM model by varying $Ω_m$, $σ_8$, $w_0$, $H_0$, $n_s$, $Ω_b$, and assumes three degenerate neutrinos with $\sum m_ν$ = 0.06 eV. This space is covered by 2500 grid points on a Sobol sequence. At each grid point, we run 7 simulations with PkdGrav3 and store 69 particle maps at nside=2048 up to $z$=3.5, as well as halo catalog snapshots. The fiducial cosmology has 200 independent simulations, along with their stencil derivatives. An important part of CosmoGridV1 is the benchmark set of 28 simulations, which include larger boxes, higher particle counts, and higher redshift resolution of shells. They allow for testing if new types of analyses are sensitive to choices made in CosmoGridV1. We add baryon feedback effects on the map level, using shell-based baryon correction model. The shells are used to create maps of weak gravitational lensing, intrinsic alignment, and galaxy clustering, using the UFalcon code. The main part of CosmoGridV1 are the raw particle count shells that can be used to create full-sky maps for a given $n(z)$. We also release projected maps for a Stage-III forecast, as well as maps used previously in KiDS-1000 deep learning constraints with CosmoGridV1. The data is available at www.cosmogrid.ai.

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arXiv2022

Suppressing variance in 21-cm signal simulations during reionization

Current best limits on the 21-cm signal during reionization are provided at large scales ($\gtrsim$100 Mpc). To model these scales, enormous simulation volumes are required which are computationally expensive. We find that the primary source of uncertainty at these large scales is sample variance, which decides the minimum size of simulations required to analyse current and upcoming observations. In large-scale structure simulations, the method of `fixing' the initial conditions (ICs) to exactly follow the initial power spectrum and `pairing' two simulations with exactly out-of-phase ICs has been shown to significantly reduce sample variance. Here we apply this `fixing and pairing' (F\&P) approach to reionization simulations whose clustering signal originates from both density fluctuations and reionization bubbles. Using a semi-numerical code, we show that with the traditional method, simulation boxes of $L\simeq 500$ (300) Mpc are required to model the large-scale clustering signal at $k$=0.1 Mpc$^{-1}$ with a precision of 5 (10) per cent. Using F\&P, the simulation boxes can be reduced by a factor of 2 to obtain the same precision level. We conclude that the computing costs can be reduced by at least a factor of 4 when using the F\&P approach.

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arXiv2022

Constraining baryonic feedback and cosmology with weak-lensing, X-ray, and kinematic Sunyaev-Zeldovich observations

Modern weak-lensing observations are becoming increasingly sensitive to baryonic feedback processes which are still poorly understood. So far, this challenge has been faced either by imposing scale-cuts in the data or by modelling baryonic effects with simple, one-parameter models. In this paper, we rely on a more general, seven-parameter prescription of baryonic feedback effects, which is primarily motivated by observations and has been shown to agree with a plethora of hydrodynamical simulations. By combining weak-lensing data from the Kilo-Degree Survey (KiDS-1000) with observations of gas around galaxy clusters, we are able to constrain baryonic parameters and learn more about feedback and cosmology. In particular, we use cluster gas fractions from X-ray data and gas profiles from kinematic Sunyaev-Zeldovich (kSZ) observations to provide evidence for baryonic feedback that is stronger than predicted by most hydrodynamical simulations. In terms of the matter power spectrum, we report a beyond-percent effect at wave-modes above $k\sim 0.1-0.45$ h/Mpc and a maximum suppression of $12-33$ percent at $k\sim7$ h/Mpc (68 percent confidence level). Regarding the combined parameter $Σ_8=σ_8(Ω_m/0.3)^{0.58}$, we find the known tension with the Planck satellite data to be reduced from 3.8 to 2.9 $σ$ once baryonic effects are fully included in the analysis pipeline. The tension is further decreased to 2.6 $σ$ when the weak-lensing data is combined with X-ray and kSZ observations. We conclude that, while baryonic feedback effects become more important in modern weak-lensing surveys, they are unlikely to act as the main culprit for the observed $Σ_8$-tension.

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arXiv2022

A Full $w$CDM Analysis of KiDS-1000 Weak Lensing Maps using Deep Learning

We present a full forward-modeled $w$CDM analysis of the KiDS-1000 weak lensing maps using graph-convolutional neural networks (GCNN). Utilizing the $\texttt{CosmoGrid}$, a novel massive simulation suite spanning six different cosmological parameters, we generate almost one million tomographic mock surveys on the sphere. Due to the large data set size and survey area, we perform a spherical analysis while limiting our map resolution to $\texttt{HEALPix}$ $n_\mathrm{side}=512$. We marginalize over systematics such as photometric redshift errors, multiplicative calibration and additive shear bias. Furthermore, we use a map-level implementation of the non-linear intrinsic alignment model along with a novel treatment of baryonic feedback to incorporate additional astrophysical nuisance parameters. We also perform a spherical power spectrum analysis for comparison. The constraints of the cosmological parameters are generated using a likelihood free inference method called Gaussian Process Approximate Bayesian Computation (GPABC). Finally, we check that our pipeline is robust against choices of the simulation parameters. We find constraints on the degeneracy parameter of $S_8 \equiv σ_8\sqrt{Ω_M/0.3} = 0.78^{+0.06}_{-0.06}$ for our power spectrum analysis and $S_8 = 0.79^{+0.05}_{-0.05}$ for our GCNN analysis, improving the former by 16%. This is consistent with earlier analyses of the 2-point function, albeit slightly higher. Baryonic corrections generally broaden the constraints on the degeneracy parameter by about 10%. These results offer great prospects for full machine learning based analyses of on-going and future weak lensing surveys.

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arXiv2022

Imprints of fermionic and bosonic mixed dark matter on the 21-cm signal at cosmic dawn

The 21-cm signal from the epoch of cosmic dawn prior to reionization consists of a promising observable to gain new insights into the dark matter (DM) sector. In this paper, we investigate its potential to constrain mixed (cold + non-cold) dark matter scenarios that are characterised by the non-cold DM fraction ($f_{\rm nCDM}$) and particle mass ($m_{\rm nCDM}$). As non-cold DM species, we investigate both a fermionic (sterile neutrino) and a bosonic (ultra-light axion) particle. We show how these scenarios affect the global signal and the power spectrum using a halo-model implementation of the 21-cm signal at cosmic dawn. Next to this study, we perform an inference-based forecast study based on realistic mock power spectra from the Square Kilometre Array (SKA) telescope. Assuming inefficient, yet non-zero star-formation in minihaloes (i.e. haloes with mass below $10^8$ M$_{\odot}$), we obtain stringent constraints on both $m_{\rm nCDM}$ and $f_{\rm nCDM}$ that go well beyond current limits. Regarding the special case of $f_{\rm nCDM}\sim 1$, for example, we find a constraint of $m_{\rm nCDM}>15$ keV (thermal mass) for fermionic DM and $m_{\rm nCDM}>2\times10^{-20}$ eV for bosonic DM. For the opposite case of dominating cold DM, we find that at most one percent of the total DM abundance can be made of a hot fermionic or bosonic relic. All constraints are provided at the 95 percent confidence level.

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arXiv2021

Emulation of baryonic effects on the matter power spectrum and constraints from galaxy cluster data

Baryonic feedback effects consist of a major systematic for upcoming weak-lensing and galaxy-clustering surveys. In this paper, we present an emulator for the baryonic suppression of the matter power spectrum. The emulator is based on the baryonification model, containing seven free parameters that are connected to the gas profiles and stellar abundances in haloes. We show that with the baryonic emulator, we can not only recover the power spectra of hydro-dynamical simulations at sub-percent precision but also establish a connection between the baryonic suppression of the power spectrum and the gas and stellar fractions in haloes. This connection allows us to predict the expected deviation from a dark-matter-only power spectrum using measured X-ray gas fractions of galaxy groups and clusters. With these measurements, we constrain the suppression to exceed the percent-level at k = 0.1-0.4 h/Mpc and to reach a maximum of 20-28 percent at around k = 7 h/Mpc (68 percent confidence level). As a further step, we also perform a detailed parameter study and we present a minimum set of four baryonic parameters that are required to recover the scale and redshift dependence observed in hydro-dynamical simulations. The baryonic emulator can be found at https://github.com/sambit-giri/BCemu.

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arXiv2021

Parameter inference with non-linear galaxy clustering: accounting for theoretical uncertainties

We implement EuclidEmulator (version 1), an emulator for the non-linear correction of the matter power spectrum, into the MCMC forecasting code MontePython. We compare the performance of Halofit, HMCode, and EuclidEmulator1, both at the level of power spectrum prediction and at the level of posterior probability distributions of the cosmological parameters, for different cosmological models and different galaxy power spectrum wave number cut-offs. We confirm that the choice of the power spectrum predictor has a non-negligible effect on the computed sensitivities when doing cosmological parameter forecasting, even for a conservative wave number cut-off of $0.2\,h\,{\rm Mpc}^{-1}$. We find that EuclidEmulator1 is on average up to $17\%$ more sensitive to the cosmological parameters than the other two codes, with the most significant improvements being for the Hubble parameter of up to $42\%$ and the equation of state of dark energy of up to $26\%$, depending on the case. In addition, we point out that the choice of the power spectrum predictor contributes to the risk of computing a significantly biased mean cosmology when doing parameter estimations. For the four tested scenarios we find biases, averaged over the cosmological parameters, of between 0.5 and 2$σ$ (from below $1σ$ up to $6σ$ for individual parameters). This paper provides a proof of concept that this risk can be mitigated by taking a well-tailored theoretical uncertainty into account as this allows to reduce the bias by a factor of 2 to 5, depending on the case under consideration, while keeping posterior credibility contours small: the standard deviations are amplified by a factor of $\leq1.4$ in all cases.

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arXiv2021

Decaying Dark Matter: Simulations and Weak-Lensing Forecast

Despite evidence for the existence of dark matter (DM) from very high and low redshifts, a moderate amount of DM particle decay remains a valid possibility. This includes both models with very long-lived yet unstable particles or mixed scenarios where only a small fraction of dark matter is allowed to decay. In this paper, we investigate how DM particles decaying into radiation affect non-linear structure formation. We look at the power spectrum and its redshift evolution, varying both the decay lifetime ($τ$) and the fraction of decaying-to-total dark matter ($f$), and we propose a fitting function that reaches sub-percent precision below $k\sim10$ h/Mpc. Based on this fit, we perform a forecast analysis for a Euclid-like weak lensing (WL) survey, including both massive neutrino and baryonic feedback parameters. We find that with WL observations alone, it is possible to rule out decay lifetimes smaller than $τ=75$ Gyr (at 95 percent CL) for the case that all DM is unstable. This constraint improves to $τ=182$ Gyr if the WL data is combined with CMB priors from the Planck satellite and to $τ=275$ Gyr if we further assume baryonic feedback to be fully constrained by upcoming Sunyaev-Zeldovich or X-ray data. The latter shows a factor of 3.2 improvement compared to constraints from CMB data alone. Regarding the scenario of a strongly decaying sub-component of dark matter with $τ\sim 30$ Gyr or lower, it will be possible to rule out a decaying-to-total fraction of $f>0.49$, $f>0.21$, and $f>0.13$ (at the 95 percent CL) for the same three scenarios. We conclude that the upcoming stage-IV WL surveys will allow us to significantly improve current constraints on the stability of the dark matter sector.

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arXiv2021

Dark acoustic oscillations: Imprints on the matter power spectrum and the halo mass function

Many non-minimal dark matter scenarios lead to oscillatory features in the matter power spectrum induced by interactions either within the dark sector or with particles from the standard model. Observing such dark acoustic oscillations would therefore be a major step towards understanding dark matter. We investigate what happens to oscillatory features during the process of nonlinear structure formation. We show that at the level of the power spectrum, oscillations are smoothed out by nonlinear mode coupling, gradually disappearing towards lower redshifts. In the halo mass function, however, the same oscillations remain visible until the present epoch. As a consequence, dark acoustic oscillations could be detectable in observations that are either based on the halo mass function or on the high-redshift power spectrum. We investigate the effect of such oscillations on different observables, namely, the cluster mass function, the stellar-to-halo mass relation, and the Lyman-$α$ flux power spectrum. We find that dark acoustic oscillations remain visible in all of these observables, but they are very extended and of low amplitude, making it challenging to detect them as distinct features in the data.

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arXiv2021

A halo model approach for the 21-cm power spectrum at cosmic dawn

Prior to the epoch of reionisation, the 21-cm signal of the cosmic dawn is dominated by the Lyman-$α$ coupling and gas temperature fluctuations caused by the first sources of radiation. While early efforts to model this epoch relied on analytical techniques, the community quickly transitioned to more expensive semi-numerical models. Here, we re-assess the viability of simpler approaches that allow for rapid explorations of the vast astrophysical parameter space. We propose a new analytical method to calculate the 21-cm power spectrum based on the framework of the halo model. Both the Lyman-$α$ coupling and temperature fluctuations are described by overlapping radiation flux profiles that include spectral red-shifting and source attenuation due to look-back (light-cone) effects. The 21-cm halo model is compared to the semi-numerical code 21cmFAST exhibiting generally good agreement, i.e., the power spectra differ by less than a factor of three over a large range of $k$-modes and redshifts. We show that the remaining differences between the two methods are comparable to the expected variations from modelling uncertainties associated with the abundance, bias, and accretion rates of haloes. While these current uncertainties must be reduced in the future, our work suggests that inference at acceptable accuracy will become feasible with very efficient halo models of the cosmic dawn.

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arXiv2020

Baryonic effects for weak lensing. Part I. Power spectrum and covariance matrix

Baryonic feedback effects lead to a suppression of the weak lensing angular power spectrum on small scales. The poorly constrained shape and amplitude of this suppression is an important source of uncertainties for upcoming cosmological weak lensing surveys such as Euclid or LSST. In this first paper in a series of two, we use simulations to build a Euclid-like tomographic mock data-set for the cosmic shear power spectrum and the corresponding covariance matrix, which are both corrected for baryonic effects following the baryonification method of Schneider et al. (2019). In addition, we develop an emulator to obtain fast predictions of the baryonic power suppression, allowing us to perform a likelihood inference analysis for a standard $Λ$CDM cosmology with both cosmological and astrophysical parameters. Our main findings are the following: (i) ignoring baryonic effects leads to a greater than 5$σ$ bias on the cosmological parameters $Ω_m$ and $σ_8$; (ii) restricting the analysis to the largest scales, that are mostly unaffected by baryons, makes the bias disappear, but results in a blow-up of the $Ω_m$-$σ_8$ contour area by more than a factor of 10; (iii) ignoring baryonic effects on the covariance matrix does not significantly affect cosmological parameter estimates; (iv) while the baryonic suppression is mildly cosmology dependent, this effect does not noticeably modify the posterior contours. Overall, we conclude that including baryonic uncertainties in terms of nuisance parameters results in unbiased and surprisingly tight constraints on cosmology.

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arXiv2020

Baryonic effects for weak lensing. Part II. Combination with X-ray data and extended cosmologies

An accurate modelling of baryonic feedback effects is required to exploit the full potential of future weak-lensing surveys such as Euclid or LSST. In this second paper in a series of two, we combine Euclid-like mock data of the cosmic shear power spectrum with an eROSITA X-ray mock of the cluster gas fraction to run a combined likelihood analysis including both cosmological and baryonic parameters. Following the first paper of this series, the baryonic effects (based on the baryonic correction model of Schneider et al. 2019) are included in both the tomographic power spectrum and the covariance matrix. However, this time we assume the more realistic case of a $Λ$CDM cosmology with massive neutrinos, and we consider several extensions of the currently favoured cosmological model. For the standard $Λ$CDM case, we show that including X-ray data reduces the uncertainties on the sum of the neutrino mass by $\sim30$ percent, while there is only a mild improvement on other parameters such as $Ω_m$ and $σ_8$. As extensions of $Λ$CDM, we consider the cases of a dynamical dark energy model (wCDM), a $f(R)$ gravity model (fRCDM), and a mixed dark matter model ($Λ$MDM) with both a cold and a warm/hot dark matter component. We find that combining weak lensing with X-ray data only leads to a mild improvement of the constraints on the additional parameters of wCDM, while the improvement is more substantial for both fRCDM and $Λ$MDM. Ignoring baryonic effects in the analysis pipeline leads to significant false-detections of either phantom dark energy or a light subdominant dark matter component. Overall we conclude that for all cosmologies considered, a general parametrisation of baryonic effects is both necessary and sufficient to obtain tight constraints on cosmological parameters.

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arXiv2019

Effects of baryons on weak lensing peak statistics

Upcoming weak-lensing surveys have the potential to become leading cosmological probes provided all systematic effects are under control. Recently, the ejection of gas due to feedback energy from active galactic nuclei (AGN) has been identified as major source of uncertainty, challenging the success of future weak-lensing probes in terms of cosmology. In this paper we investigate the effects of baryons on the number of weak-lensing peaks in the convergence field. Our analysis is based on full-sky convergence maps constructed via light-cones from $N$-body simulations, and we rely on the baryonic correction model of Schneider et al. (2019) to model the baryonic effects on the density field. As a result we find that the baryonic effects strongly depend on the Gaussian smoothing applied to the convergence map. For a DES-like survey setup, a smoothing of $θ_k\gtrsim8$ arcmin is sufficient to keep the baryon signal below the expected statistical error. Smaller smoothing scales lead to a significant suppression of high peaks (with signal-to-noise above 2), while lower peaks are not affected. The situation is more severe for a Euclid-like setup, where a smoothing of $θ_k\gtrsim16$ arcmin is required to keep the baryonic suppression signal below the statistical error. Smaller smoothing scales require a full modelling of baryonic effects since both low and high peaks are strongly affected by baryonic feedback.

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arXiv2019

Cosmological constraints with deep learning from KiDS-450 weak lensing maps

Convolutional Neural Networks (CNN) have recently been demonstrated on synthetic data to improve upon the precision of cosmological inference. In particular they have the potential to yield more precise cosmological constraints from weak lensing mass maps than the two-point functions. We present the cosmological results with a CNN from the KiDS-450 tomographic weak lensing dataset, constraining the total matter density $Ω_m$, the fluctuation amplitude $σ_8$, and the intrinsic alignment amplitude $A_{\rm{IA}}$. We use a grid of N-body simulations to generate a training set of tomographic weak lensing maps. We test the robustness of the expected constraints to various effects, such as baryonic feedback, simulation accuracy, different value of $H_0$, or the lightcone projection technique. We train a set of ResNet-based CNNs with varying depths to analyze sets of tomographic KiDS mass maps divided into 20 flat regions, with applied Gaussian smoothing of $σ=2.34$ arcmin. The uncertainties on shear calibration and $n(z)$ error are marginalized in the likelihood pipeline. Following a blinding scheme, we derive constraints of $S_8 = σ_8 (Ω_m/0.3)^{0.5} = 0.777^{+0.038}_{-0.036}$ with our CNN analysis, with $A_{\rm{IA}}=1.398^{+0.779}_{-0.724}$. We compare this result to the power spectrum analysis on the same maps and likelihood pipeline and find an improvement of about $30\%$ for the CNN. We discuss how our results offer excellent prospects for the use of deep learning in future cosmological data analysis.

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arXiv2019

Modelling baryonic feedback for survey cosmology

Observational cosmology in the next decade will rely on probes of the distribution of matter in the redshift range between $0<z<3$ to elucidate the nature of dark matter and dark energy. In this redshift range, galaxy formation is known to have a significant impact on observables such as two-point correlations of galaxy shapes and positions, altering their amplitude and scale dependence beyond the expected statistical uncertainty of upcoming experiments at separations under 10 Mpc. Successful extraction of information in such a regime thus requires, at the very least, unbiased models for the impact of galaxy formation on the matter distribution, and can benefit from complementary observational priors. This work reviews the current state of the art in the modelling of baryons for cosmology, from numerical methods to approximate analytical prescriptions, and makes recommendations for studies in the next decade, including a discussion of potential probe combinations that can help constrain the role of baryons in cosmological studies. We focus, in particular, on the modelling of the matter power spectrum, $P(k,z)$, as a function of scale and redshift, and of the observables derived from this quantity. This work is the result of a workshop held at the University of Oxford in November of 2018.

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arXiv2019

Quantifying baryon effects on the matter power spectrum and the weak lensing shear correlation

Feedback processes from baryons are expected to strongly affect weak-lensing observables of current and future cosmological surveys. In this paper we present a new parametrisation of halo profiles based on gas, stellar, and dark matter density components. This parametrisation is used to modify outputs of gravity-only $N$-body simulations (following the prescription of Schneider and Teyssier [1]) in order to mimic baryonic effects on the matter density field. The resulting baryonic correction model relies on a few well motivated physical parameters and is able to reproduce the redshift zero clustering signal of hydrodynamical simulations at two percent accuracy below $k\sim10$ h/Mpc. A detailed study of the baryon suppression effects on the matter power spectrum and the weak lensing shear correlation reveals that the signal is dominated by two parameters describing the slope of the gas profile in haloes and the maximum radius of gas ejection. We show that these parameters can be constrained with the observed gas fraction of galaxy groups and clusters from X-ray data. Based on these observations we predict a beyond percent effect on the power spectrum above $k=0.2-1.0$ h/Mpc with a maximum suppression of 15-25 percent around $k\sim 10$ h/Mpc. As a result, the weak lensing angular shear power spectrum is suppressed by 15-25 percent at scales beyond $\ell\sim 100-600$ and the shear correlations $ξ_{+}$ and $ξ_{-}$ are affected at the 10-25 percent level below 5 and 50 arc-minutes, respectively. The relatively large uncertainties of these predictions are a result of the poorly known hydrostatic mass bias of current X-ray observations as well as the generic difficulty to observe the low density gas outside of haloes.

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