Search

We present a pedagogical review of the halo model, a flexible framework that can describe the distribution of matter and its tracers on non-linear scales for both conventional and exotic cosmological models. We start with the premise that the complex structure of the cosmic web can be described by the sum of its individual components: dark matter, gas, and galaxies, all distributed within spherical haloes with a range of masses. The halo properties are specified through a series of simulation-calibrated ingredients including the halo mass function, non-linear halo bias and a dark matter density profile that can additionally account for the impact of baryon feedback. By incorporating a model of the galaxy halo occupation distribution, the properties of central and satellite galaxies, their non-linear bias and intrinsic alignment can be predicted. Through analytical calculations of spherical collapse in exotic cosmologies, the halo model also provides predictions for non-linear clustering in beyond-$\Lambda$CDM models. The halo model has been widely used to model observations of a variety of large-scale structure probes, most notably as the primary technique to model the underlying non-linear matter power spectrum. By documenting these varied and often distinct use cases, we seek to further coherent halo model analyses of future multi-tracer observables. This review is accompanied by the release of pyhalomodel: https://github.com/alexander-mead/pyhalomodel , flexible software to conduct a wide range of halo-model calculations., Comment: Comments from the community are gratefully received for version 1

The discrepancy between the weak lensing (WL) and the {\it Planck} measurements of $S_8$ has been a subject of several studies. These studies tend to show that a suppression of the amplitude of the mass power spectrum $P(k)$ at high $k$ could resolve it. The WL signal at small-scale is sensitive to various effects, such as baryonic effects and intrinsic alignment. The accuracy of $P(k)$ depends on the modelling precision of these effects. A common approach for calculating $P(k)$ relies on a halo model. Amongst the various components necessary for the construction of $P(k)$, the halo mass function (HMF) is an important one. Traditionally, the HMF has been assumed to follow a fixed model. Recent literature shows that baryonic physics, amongst several other factors, could affect the HMF. In this study, we investigate the impact of allowing the HMF to vary. This provides a way of testing the validity of the halo model-HMF calibration using data. We find that the {\it Planck} cosmology is not compatible with the vanilla HMF for both the DES-y3 and the KiDS-1000 data. When the cosmology and the HMF parameters are allowed to vary, the {\it Planck} cosmology is no longer in tension. The modified HMF predicts a matter power spectrum with a $\sim 25\%$ power loss at $k\sim 1~{\rm h/Mpc}$, in agreement with the recent studies. We show that Stage IV surveys will be able to measure the HMF parameters with a few percent accuracy., Comment: 16 pages (including appendixes), 10 figures, 3 tables, main results in Figs. 5&6

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

We present constraints on the flat $\Lambda$CDM cosmological model through a joint analysis of galaxy abundance, galaxy clustering and galaxy-galaxy lensing observables with the Kilo-Degree Survey. Our theoretical model combines a flexible conditional stellar mass function, to describe the galaxy-halo connection, with a cosmological N-body simulation-calibrated halo model to describe the non-linear matter field. Our magnitude-limited bright galaxy sample combines 9-band optical-to-near-infrared photometry with an extensive and complete spectroscopic training sample to provide accurate redshift and stellar mass estimates. Our faint galaxy sample provides a background of accurately calibrated lensing measurements. We constrain the structure growth parameter $S_8=\sigma_8\sqrt{\Omega_{\mathrm{m}}/0.3}=0.773^{+0.028}_{-0.030}$, and the matter density parameter $\Omega_{\mathrm{m}}=0.290^{+0.021}_{-0.017}$. The galaxy-halo connection model adopted in the work is shown to be in agreement with previous studies. Our constraints on cosmological parameters are comparable to, and consistent with, joint $3\times2{\mathrm{pt}}$ clustering-lensing analyses that additionally include a cosmic shear observable. This analysis therefore brings attention to the significant constraining power in the often-excluded non-linear scales for galaxy clustering and galaxy-galaxy lensing observables. By adopting a theoretical model that accounts for non-linear halo bias, halo exclusion, scale-dependent galaxy bias and the impact of baryon feedback, this work demonstrates the potential and a way forward to include non-linear scales in cosmological analyses. Varying the width of the satellite galaxy distribution with an additional parameter yields a strong preference for sub-Poissonian variance, improving the goodness of fit by 0.18 in reduced $\chi^{2}$ value compared to a fixed Poisson distribution., Comment: 25 pages, 16 figures, accepted for publication in A&A, v3 with updated figure from Corrigendum (https://www.aanda.org/articles/aa/full_html/2024/08/aa50702e-24/aa50702e-24.html, https://doi.org/10.1051/0004-6361/202450702e)

We determine the error introduced in a joint halo model analysis of galaxy-galaxy lensing and galaxy clustering observables when adopting the standard approximation of linear halo bias. Considering the Kilo-Degree Survey, we forecast that ignoring the non-linear halo bias would result in up to 5$\sigma$ offsets in the recovered cosmological parameters describing structure growth, $S_8$, and the matter density parameter, $\Omega_{\mathrm{m}}$. We include the scales $10^{-1.3}

We conduct a pseudo-$C_\ell$ analysis of the tomographic cross-correlation between 1000 deg$^2$ of weak lensing data from the Kilo-Degree Survey (KiDS-1000) and the thermal Sunyaev-Zeldovich (tSZ) effect measured by Planck and the Atacama Cosmology Telescope (ACT). Using HMx, a halo-model-based approach that consistently models the gas, star, and dark matter components, we are able to derive constraints on both cosmology and baryon feedback for the first time from these data, marginalising over redshift uncertainties, intrinsic alignment of galaxies, and contamination by the cosmic infrared background (CIB). We find our results to be insensitive to the CIB, while intrinsic alignment provides a small but significant contribution to the lensing--tSZ cross-correlation. The cosmological constraints are consistent with those of other low-redshift probes and prefer strong baryon feedback. The inferred amplitude of the lensing--tSZ cross-correlation signal, which scales as $\sigma_8(\Omega_\mathrm{m}/0.3)^{0.2}$, is low by $\sim 2\,\sigma$ compared to the primary cosmic microwave background constraints by Planck. The lensing--tSZ measurements are then combined with pseudo-$C_\ell$ measurements of KiDS-1000 cosmic shear into a novel joint analysis, accounting for the full cross-covariance between the probes, providing tight cosmological constraints by breaking parameter degeneracies inherent to both probes. The joint analysis gives an improvement of 40% on the constraint of $S_8=\sigma_8\sqrt{\Omega_\mathrm{m}/0.3}$ over cosmic shear alone, while providing constraints on baryon feedback consistent with hydrodynamical simulations, demonstrating the potential of such joint analyses with baryonic tracers such as the tSZ effect. We discuss remaining modelling challenges that need to be addressed if these baryonic probes are to be included in future precision-cosmology analyses., Comment: 21 pages, 16 figures. Accepted in A&A. Comments welcome. Code, data vectors, and covariances are available at https://github.com/tilmantroester/KiDS-1000xtSZ

We constrain the redshift dependence of gas pressure bias $\left\langle b_{y} P_{\mathrm{e}}\right\rangle$ (bias-weighted average electron pressure), which characterises the thermodynamics of intergalactic gas, through a combination of cross-correlations between galaxy positions and the thermal Sunyaev-Zeldovich (tSZ) effect, as well as galaxy positions and the gravitational lensing of the cosmic microwave background (CMB). The galaxy sample is from the fourth data release of the Kilo-Degree Survey (KiDS). The tSZ $y$ map and the CMB lensing map are from the {\textit{Planck}} 2015 and 2018 data releases, respectively. The measurements are performed in five redshift bins with $z\lesssim1$. With these measurements, combining galaxy-tSZ and galaxy-CMB lensing cross-correlations allows us to break the degeneracy between galaxy bias and gas pressure bias, and hence constrain them simultaneously. In all redshift bins, the best-fit values of $\bpe$ are at a level of $\sim 0.3\, \mathrm{meV/cm^3}$ and increase slightly with redshift. The galaxy bias is consistent with unity in all the redshift bins. Our results are not sensitive to the non-linear details of the cross-correlation, which are smoothed out by the {\textit{Planck}} beam. Our measurements are in agreement with previous measurements as well as with theoretical predictions. We also show that our conclusions are not changed when CMB lensing is replaced by galaxy lensing, which shows the consistency of the two lensing signals despite their radically different redshift ranges. This study demonstrates the feasibility of using CMB lensing to calibrate the galaxy distribution such that the galaxy distribution can be used as a mass proxy without relying on the precise knowledge of the matter distribution., Comment: 20 pages, 14 figures, 3 tables, accepted for publication on Astronomy & Astrophysics

We derive a simple prescription for including beyond-linear halo bias within the standard, analytical halo-model power spectrum calculation. This results in a corrective term that is added to the usual two-halo term. We measure this correction using data from $N$-body simulations and demonstrate that it can boost power in the two-halo term by a factor of $\sim2$ at scales $k\sim0.7\,h Mpc^{-1}$, with the exact magnitude of the boost determined by the specific pair of fields in the two-point function. How this translates to the full power spectrum depends on the relative strength of the one-halo term, which can mask the importance of this correction to a greater or lesser degree, again depending on the fields. Generally we find that our correction is more important for signals that arise from lower-mass haloes. When comparing our calculation to simulated data we find that the under-prediction of power in the transition region between the two- and one-halo terms, which typically plagues halo-model calculations, is almost completely eliminated when including the full non-linear halo bias. We show improved results for the auto and cross spectra of galaxies, haloes and matter. In the specific case of matter-matter or matter-halo power we note that a large fraction of the improvement comes from the non-linear biasing between low- and high-mass haloes. We envisage our model being useful in the analytical modelling of cross correlation signals. Our non-linear bias halo-model code is available at https://github.com/alexander-mead/BNL, Comment: 14 pages; 6 figures; 3 appendices; v2 - matches MNRAS accepted version

We present constraints on extensions to the flat $\Lambda$CDM cosmological model by varying the spatial curvature $\Omega_K$, the sum of the neutrino masses $\sum m_\nu$, the dark energy equation of state parameter $w$, and the Hu-Sawicki $f(R)$ gravity $f_{R0}$ parameter. With the combined $3\times2$pt measurements of cosmic shear from the Kilo-Degree Survey (KiDS-1000), galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), and galaxy-galaxy lensing from the overlap between KiDS-1000, BOSS, and the spectroscopic 2-degree Field Lensing Survey (2dFLenS), we find results that are fully consistent with a flat $\Lambda$CDM model with $\Omega_K=0.011^{+0.054}_{-0.057}$, $\sum m_\nu<1.76$ eV (95% CL), and $w=-0.99^{+0.11}_{-0.13}$. The $f_{R0}$ parameter is unconstrained in our fully non-linear $f(R)$ cosmic shear analysis. Considering three different model selection criteria, we find no clear preference for either the fiducial flat $\Lambda$CDM model or any of the considered extensions. Besides extensions to the flat $\Lambda$CDM parameter space, we also explore restrictions to common subsets of the flat $\Lambda$CDM parameter space by fixing the amplitude of the primordial power spectrum to the Planck best-fit value, as well as adding external data from supernovae and lensing of the CMB. Neither the beyond-$\Lambda$CDM models nor the imposed restrictions explored in this analysis are able to resolve the $\sim 3\sigma$ tension in $S_8$ between the $3\times2$pt constraints and Planck, with the exception of $w$CDM, where the $S_8$ tension is resolved. The tension in the $w$CDM case persists, however, when considering the joint $S_8$-$w$ parameter space. The joint flat $\Lambda$CDM CMB lensing and $3\times2$pt analysis is found to yield tight constraints on $\Omega_{\rm m}=0.307^{+0.008}_{-0.013}$, $\sigma_8=0.769^{+0.022}_{-0.010}$, and $S_8=0.779^{+0.013}_{-0.013}$., Comment: 15 pages, 9 figures, 3 tables, accepted in A&A. This paper concludes the KiDS-1000 series of papers: Heymans, Tr\"oster et al. (arXiv:2007.15632), Asgari et al. (arXiv:2007.15633), Hildebrandt et al. (arXiv:2007.15635), Joachimi et al. (arXiv:2007.01844), and Giblin et al. (arXiv:2007.01845). Data products, likelihoods, and posteriors can be found http://kids.strw.leidenuniv.nl/DR4/lensing.php

Some beyond $\Lambda$CDM cosmological models have dark-sector energy densities that suffer phase transitions. Fluctuations entering the horizon during such a transition can receive enhancements that ultimately show up as a distinctive bump in the power spectrum relative to a model with no phase transition. In this work, we study the non-linear evolution of such signatures in the matter power spectrum and correlation function using N-body simulations, perturbation theory and HMcode - a halo-model based method. We focus on modelling the response, computed as the ratio of statistics between a model containing a bump and one without it, rather than in the statistics themselves. Instead of working with a specific theoretical model, we inject a parametric family of Gaussian bumps into otherwise standard $\Lambda$CDM spectra. We find that even when the primordial bump is located at linear scales, non-linearities tend to produce a second bump at smaller scales. This effect is understood within the halo model due to a more efficient halo formation. In redshift space these nonlinear signatures are partially erased because of the damping along the line-of-sight direction produced by non-coherent motions of particles at small scales. In configuration space, the bump modulates the correlation function reflecting as oscillations in the response, as it is clear in linear Eulerian theory; however, they become damped because large scale coherent flows have some tendency to occupy regions more depleted of particles. This mechanism is explained within Lagrangian Perturbation Theory and well captured by our simulations., Comment: 15 pages, 8 figures

We present an updated version of the HMcode augmented halo model that can be used to make accurate predictions of the non-linear matter power spectrum over a wide range of cosmologies. Major improvements include modelling of BAO damping in the power spectrum and an updated treatment of massive neutrinos. We fit our model to simulated power spectra and show that we can match the results with an RMS error of 2.5 per cent across a range of cosmologies, scales $k < 10\,h\mathrm{Mpc}^{-1}$, and redshifts $z<2$. The error rarely exceeds 5 per cent and never exceeds 16 per cent. The worst-case errors occur at $z\simeq2$, or for cosmologies with unusual dark-energy equations of state. This represents a significant improvement over previous versions of HMcode, and over other popular fitting functions, particularly for massive-neutrino cosmologies with high neutrino mass. We also present a simple halo model that can be used to model the impact of baryonic feedback on the power spectrum. This six-parameter physical model includes gas expulsion by AGN feedback and encapsulates star formation. By comparing this model to data from hydrodynamical simulations we demonstrate that the power spectrum response to feedback is matched at the $<1$ per cent level for $z<1$ and $k<20\,h\mathrm{Mpc}^{-1}$. We also present a single-parameter variant of this model, parametrized in terms of feedback strength, which is only slightly less accurate. We make code available for our non-linear and baryon models at https://github.com/alexander-mead/HMcode and it is also available within CAMB and soon within CLASS., Comment: 17 pages, 5 figures, 4 appendices; v2 - matches accepted version, new appendix with comparisons between HMcode and 6 different emulators

We study the new mechanism of the axion production suggested recently in [1,2]. This mechanism is based on the so-called Axion Quark Nugget (AQN) dark matter model, which was originally invented to explain the similarity of the dark and visible cosmological matter densities. We perform numerical simulations to evaluate the axion flux on the Earth's surface. We examine annual and daily modulations, which have been studied previously and are known to occur for any type of dark matter. We also discuss a novel type of short time enhancements which are unique to the AQN model: the statistical fluctuations and burst-like amplification, both of which can drastically amplify the axion signal, up to a factor $\sim10^2-10^3$ for a very short period of time. The present work studies the AQN-induced axions within the mass window $10^{-6}{\rm\,eV}\lesssim m_a\lesssim10^{-3}\rm\,eV$ with typical velocities $\langle v_a\rangle\sim0.6c$. We also comment on the broadband detection strategy to search for such relativistic axions by studying the daily and annual time modulations as well as random burst-like amplifications., Comment: Accepted in Physical Review D, 23 pages, 13 figures. arXiv admin note: text overlap with arXiv:1905.00022

Observational cosmology in the next decade will rely on probes of the distribution of matter in the redshift range between $0

We advocate for the idea that there is a fundamentally new mechanism for axion production on Earth, as recently suggested in Fischer et al. (2018) and Liang & Zhitnitsky (2018). We specifically focus on production of axions within Earth, with low velocities such that they will be trapped in the gravitational field. Our computations are based on the so-called Axion Quark Nugget (AQN) dark matter model, which was originally invented to explain the similarity of the dark and visible cosmological matter densities. This occurs in the model irrespective of the axion mass $m_\mathrm{a}$ or initial misalignment angle $\theta_0$. Annihilation of antimatter AQNs with visible matter inevitably produce axions when AQNs hit Earth. The emission rate of axions with velocities below escape velocity is very tiny compared to the overall emission, however these axions will be accumulated over the 4.5 billion year life time of the Earth, which greatly enhances the discovery potential. We perform numerical simulations with a realistically modeled incoming AQN velocity and mass distribution, and explore how AQNs interact as they travel through the interior of the Earth. We use this to estimate the axion flux on the surface of the Earth, the velocity-spectral features of trapped axions, the typical annihilation pattern of AQN, and the density profile of the axion halo around the Earth. Knowledge of these properties is necessary to make predictions for the observability of trapped axions using CAST, ADMX, MADMAX, CULTASK, ORPHEUS, ARIADNE, CASPEr, ABRACADABRA, QUAX, DM Radio., Comment: 22 pages, 8 figures, accepted by Physical Review D

We construct the mean thermal Sunyaev-Zel'dovich (tSZ) Comptonization y profile around Luminous Red Galaxies (LRGs) in the redshift range 0.16 < z < 0.47 from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) using the Planck y map. The mean central tSZ signal for the full sample is y ~ 1.8 * 10^(-7) and we detect tSZ emission out to ~30 arcmin, which is well beyond the 10 arcmin angular resolution of the y map and well beyond the virial radii of the LRGs. We compare the measured profile with predictions from the cosmo-OWLS suite of cosmological hydrodynamical simulations. This comparison agrees well for models that include feedback from active galactic nuclei (AGN), but not with hydrodynamic models without this energetic feedback mechanism. This suggests that an additional heating mechanism is required over SNe feedback and star formation to explain the y data profile. We also compare our results with predictions based on the halo model with a universal pressure profile (UPP) giving the y signal. The predicted profile is consistent with the data, but only if we account for the clustering of haloes via a two-halo term and if halo masses are estimated using the mean stellar-to-halo mass (SHM) relation of Coupon et al. (2015) or Wang et al.(2016) estimated from gravitational lensing measurements. We also discuss the importance of scatter in the SHM relation on the model predictions., Comment: 12 pages, 6 figures, accepted by MNRAS

The Core Cosmology Library (CCL) provides routines to compute basic cosmological observables to a high degree of accuracy, which have been verified with an extensive suite of validation tests. Predictions are provided for many cosmological quantities, including distances, angular power spectra, correlation functions, halo bias and the halo mass function through state-of-the-art modeling prescriptions available in the literature. Fiducial specifications for the expected galaxy distributions for the Large Synoptic Survey Telescope (LSST) are also included, together with the capability of computing redshift distributions for a user-defined photometric redshift model. A rigorous validation procedure, based on comparisons between CCL and independent software packages, allows us to establish a well-defined numerical accuracy for each predicted quantity. As a result, predictions for correlation functions of galaxy clustering, galaxy-galaxy lensing and cosmic shear are demonstrated to be within a fraction of the expected statistical uncertainty of the observables for the models and in the range of scales of interest to LSST. CCL is an open source software package written in C, with a python interface and publicly available at https://github.com/LSSTDESC/CCL., Comment: 38 pages, 18 figures, matches ApJS accepted version

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., Comment: 18+6 pages, 15 figures. Matches MNRAS accepted version. Few typos corrected

We search the Planck data for a thermal Sunyaev-Zel'dovich (tSZ) signal due to gas filaments between pairs of Luminous Red Galaxies (LRG's) taken from the Sloan Digital Sky Survey Data Release 12 (SDSS/DR12). We identify $\sim$260,000 LRG pairs in the DR12 catalog that lie within 6-10 $h^{-1} \mathrm{Mpc}$ of each other in tangential direction and within 6 $h^{-1} \mathrm{Mpc}$ in radial direction. We stack pairs by rotating and scaling the angular positions of each LRG so they lie on a common reference frame, then we subtract a circularly symmetric halo from each member of the pair to search for a residual signal between the pair members. We find a statistically significant (5.3$\sigma$) signal between LRG pairs in the stacked data with a magnitude $\Delta y = (1.31 \pm 0.25) \times 10^{-8}$. The uncertainty is estimated from two Monte Carlo null tests which also establish the reliability of our analysis. Assuming a simple, isothermal, cylindrical filament model of electron over-density with a radial density profile proportional to $r_c/r$ (as determined from simulations), where $r$ is the perpendicular distance from the cylinder axis and $r_c$ is the core radius of the density profile, we constrain the product of over-density and filament temperature to be $\delta_c \times (T_{\rm e}/10^7 \, {\rm K}) \times (r_c/0.5h^{-1} \, {\rm Mpc}) = 2.7 \pm 0.5$. To our knowledge, this is the first detection of filamentary gas at over-densities typical of cosmological large-scale structure. We compare our result to the BAHAMAS suite of cosmological hydrodynamic simulations (McCarthy et al. 2017) and find a slightly lower, but marginally consistent Comptonization excess, $\Delta y = (0.84 \pm 0.24) \times 10^{-8}$., Comment: 10 pages, 9 figures, accepted for publication in MNRAS (v4 and v5 to include funding acknowledgements. No other changes.)

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher-order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35%. We apply the transform to toy 21cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise, and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function., Comment: 15 pages, 10 figures. Minor changes to match version published in MNRAS

We perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg$^2$ of imaging data by the Kilo Degree Survey (KiDS) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of $N$-body simulations. We methodically analyze different combinations of the observables, finding that galaxy-galaxy lensing measurements are particularly useful in improving the constraint on the intrinsic alignment amplitude (by 30%, positive at $3.5\sigma$ in the fiducial data analysis), while the multipole power spectra are useful in tightening the constraints along the lensing degeneracy direction (e.g. factor of two stronger matter density constraint in the fiducial analysis). The fully combined constraint on $S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3} = 0.742 \pm 0.035$, which is an improvement by 20% compared to KiDS alone, corresponds to a $2.6\sigma$ discordance with Planck, and is not significantly affected by fitting to a more conservative set of scales. Given the tightening of the parameter space, we are unable to resolve the discordance with an extended cosmology that is simultaneously favored in a model selection sense, including the sum of neutrino masses, curvature, evolving dark energy, and modified gravity. The complementarity of our observables allows for constraints on modified gravity degrees of freedom that are not simultaneously bounded with either probe alone, and up to a factor of three improvement in the $S_8$ constraint in the extended cosmology compared to KiDS alone., Comment: 31 pages, 20 figures, results unchanged, version accepted for publication by MNRAS. Abstract abridged. Our measurements and fitting pipeline are public at https://github.com/sjoudaki/CosmoLSS

We test extensions to the standard cosmological model with weak gravitational lensing tomography using 450 deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). In these extended cosmologies, which include massive neutrinos, nonzero curvature, evolving dark energy, modified gravity, and running of the scalar spectral index, we also examine the discordance between KiDS and cosmic microwave background measurements from Planck. The discordance between the two datasets is largely unaffected by a more conservative treatment of the lensing systematics and the removal of angular scales most sensitive to nonlinear physics. The only extended cosmology that simultaneously alleviates the discordance with Planck and is at least moderately favored by the data includes evolving dark energy with a time-dependent equation of state (in the form of the $w_0-w_a$ parameterization). In this model, the respective $S_8 = \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ constraints agree at the $1\sigma$ level, and there is `substantial concordance' between the KiDS and Planck datasets when accounting for the full parameter space. Moreover, the Planck constraint on the Hubble constant is wider than in LCDM and in agreement with the Riess et al. (2016) direct measurement of $H_0$. The dark energy model is moderately favored as compared to LCDM when combining the KiDS and Planck measurements, and remains moderately favored after including an informative prior on the Hubble constant. In both of these scenarios, marginalized constraints in the $w_0-w_a$ plane are discrepant with a cosmological constant at the $3\sigma$ level. Moreover, KiDS constrains the sum of neutrino masses to 4.0 eV (95% CL), finds no preference for time or scale dependent modifications to the metric potentials, and is consistent with flatness and no running of the spectral index. The analysis code is public at https://github.com/sjoudaki/kids450, Comment: 22 pages, 16 figures, results unchanged, version accepted for publication by MNRAS

I examine differences in non-linear structure formation between cosmological models that share a $z=0$ linear power spectrum in both shape and amplitude, but that differ via their growth history. $N$-body simulations of these models display an approximately identical large-scale-structure skeleton, but reveal deeply non-linear differences in the demographics and properties of haloes. I investigate to what extent the spherical-collapse model can help in understanding these differences, in both real and redshift space. I discuss how this is difficult to do if one attempts to identify haloes directly, because in that case one is subject to the vagaries of halo finding algorithms. However, I demonstrate that the halo model of structure formation provides an accurate non-linear response in the power spectrum, but only if results from spherical collapse that include formation hysteresis are properly incorporated. I comment on how this fact can be used to provide per cent level accurate matter power spectrum predictions for dark energy models for $k\leq5\,h\mathrm{Mpc}^{-1}$ by using the halo model as a correction to accurate $\Lambda$CDM simulations. In the appendix I provide some fitting functions for the linear-collapse threshold ($\delta_\mathrm{c}$) and virialized overdensity ($\Delta_\mathrm{v}$) that are valid for a wide range of dark energy models. I also make my spherical-collapse code available at https://github.com/alexander-mead/collapse, Comment: 10 pages, 5 figures, accepted to MNRAS; v2 - small changes to align with published version, revised fitting function that can be more easily implemented

We present an accurate non-linear matter power spectrum prediction scheme for a variety of extensions to the standard cosmological paradigm, which uses the tuned halo model previously developed in Mead (2015b). We consider dark energy models that are both minimally and non-minimally coupled, massive neutrinos and modified gravitational forces with chameleon and Vainshtein screening mechanisms. In all cases we compare halo-model power spectra to measurements from high-resolution simulations. We show that the tuned halo model method can predict the non-linear matter power spectrum measured from simulations of parameterised $w(a)$ dark energy models at the few per cent level for $k<10\,h\mathrm{Mpc}^{-1}$, and we present theoretically motivated extensions to cover non-minimally coupled scalar fields, massive neutrinos and Vainshtein screened modified gravity models that result in few per cent accurate power spectra for $k<10\,h\mathrm{Mpc}^{-1}$. For chameleon screened models we achieve only 10 per cent accuracy for the same range of scales. Finally, we use our halo model to investigate degeneracies between different extensions to the standard cosmological model, finding that the impact of baryonic feedback on the non-linear matter power spectrum can be considered independently of modified gravity or massive neutrino extensions. In contrast, considering the impact of modified gravity and massive neutrinos independently results in biased estimates of power at the level of 5 per cent at scales $k>0.5\,h\mathrm{Mpc}^{-1}$. An updated version of our publicly available HMcode can be found at https://github.com/alexander-mead/HMcode, Comment: 18 pages, 9 figures, published in MNRAS, v2 - closely matches published version, no major changes

We investigate the impact of astrophysical systematics on cosmic shear cosmological parameter constraints from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), and the concordance with cosmic microwave background measurements by Planck. We present updated CFHTLenS cosmic shear tomography measurements extended to degree scales using a covariance calibrated by a new suite of N-body simulations. We analyze these measurements with a new model fitting pipeline, accounting for key systematic uncertainties arising from intrinsic galaxy alignments, baryonic effects in the nonlinear matter power spectrum, and photometric redshift uncertainties. We examine the impact of the systematic degrees of freedom on the cosmological parameter constraints, both independently and jointly. When the systematic uncertainties are considered independently, the intrinsic alignment amplitude is the only degree of freedom that is substantially preferred by the data. When the systematic uncertainties are considered jointly, there is no consistently strong preference in favor of the more complex models. We quantify the level of concordance between the CFHTLenS and Planck datasets by employing two distinct data concordance tests, grounded in Bayesian evidence and information theory. We find that the two data concordance tests largely agree with one another, and that the level of concordance between the CFHTLenS and Planck datasets is sensitive to the exact details of the systematic uncertainties included in our analysis, ranging from decisive discordance to substantial concordance as the treatment of the systematic uncertainties becomes more conservative. The least conservative scenario is the one most favored by the cosmic shear data, but it is also the one that shows the greatest degree of discordance with Planck. The data and analysis code are public at https://github.com/sjoudaki/cfhtlens_revisited, Comment: 21 pages, 12 figures, results unchanged, version accepted for publication by MNRAS

We present an optimized variant of the halo model, designed to produce accurate matter power spectra well into the non-linear regime for a wide range of cosmological models. To do this, we introduce physically motivated free parameters into the halo-model formalism and fit these to data from high-resolution $N$-body simulations. For a variety of $\Lambda$CDM and $w$CDM models the halo-model power is accurate to $\simeq 5$ per cent for $k\leq 10h\,\mathrm{Mpc}$ and $z\leq 2$. An advantage of our new halo model is that it can be adapted to account for the effects of baryonic feedback on the power spectrum. We demonstrate this by fitting the halo model to power spectra from the OWLS hydrodynamical simulation suite via parameters that govern halo internal structure. We are able to fit all feedback models investigated at the 5 per cent level using only two free parameters, and we place limits on the range of these halo parameters for feedback models investigated by the OWLS simulations. Accurate predictions to high-$k$ are vital for weak lensing surveys, and these halo parameters could be considered nuisance parameters to marginalize over in future analyses to mitigate uncertainty regarding the details of feedback. Finally, we investigate how lensing observables predicted by our model compare to those from simulations and from HALOFIT for a range of $k$-cuts and feedback models and quantify the angular scales at which these effects become important. Code to calculate power spectra from the model presented in this paper can be found at https://github.com/alexander-mead/hmcode, Comment: 17 pages, 10 figures, published in MNRAS, v2 - minor text additions, closely matched published version, v3 - corrected equation (B10) in the appendix

Viable modifications of gravity that may produce cosmic acceleration need to be screened in high-density regions such as the Solar System, where general relativity is well tested. Screening mechanisms also prevent strong anomalies in the large-scale structure and limit the constraints that can be inferred on these gravity models from cosmology. We find that by suppressing the contribution of the screened high-density regions in the matter power spectrum, allowing a greater contribution of unscreened low densities, modified gravity models can be more readily discriminated from the concordance cosmology. Moreover, by variation of density thresholds, degeneracies with other effects may be dealt with more adequately. Specializing to chameleon gravity as a worked example for screening in modified gravity, employing N-body simulations of f(R) models and the halo model of chameleon theories, we demonstrate the effectiveness of this method. We find that a percent-level measurement of the clipped power at k < 0.3 h/Mpc can yield constraints on chameleon models that are more stringent than what is inferred from Solar System tests or distance indicators in unscreened dwarf galaxies. Finally, we verify that our method is also applicable to the Vainshtein mechanism., Comment: 5 pages, 2 figures; v2 matches published version, including application to Vainshtein mechanism

We develop and test an algorithm to rescale a simulated dark-matter particle distribution or halo catalogue from a standard gravity model to that of a modified gravity model. This method is based on that of Angulo & White but with some additional ingredients to account for (i) scale-dependent growth of linear density perturbations and (ii) screening mechanisms that are generic features of viable modified gravity models. We attempt to keep the method as general as possible, so that it may plausibly be applied to a wide range of modified theories, although tests against simulations are restricted to a subclass of $f(R)$ models at this stage. We show that rescaling allows the power spectrum of matter to be reproduced at the $\sim 3$ per cent level in both real and redshift space up to $k=0.1h\,\mathrm{Mpc}^{-1}$ if we change the box size and alter the particle displacement field; this limit can be extended to $k=1h\,\mathrm{Mpc}^{-1}$ if we additionally alter halo internal structure. We simultaneously develop an algorithm that can be applied directly to a halo catalogue, in which case the halo mass function and clustering can be reproduced at the $\sim 5$ per cent level. Finally we investigate the clustering of halo particle distributions, generated from rescaled halo catalogues, and find that a similar accuracy can be reached., Comment: 19 pages, 13 figures, accepted for publication in MNRAS, v3 - closely matches published version

Recently, the Kepler Space Telescope has detected several planets in orbit around a close binary star system. These so-called circumbinary planets will experience non-trivial spatial and temporal distributions of radiative flux on their surfaces, with features not seen in their single-star orbiting counterparts. Earthlike circumbinary planets inhabited by photosynthetic organisms will be forced to adapt to these unusual flux patterns. We map the flux received by putative Earthlike planets (as a function of surface latitude/longitude and time) orbiting the binary star systems Kepler-16 and Kepler-47, two star systems which already boast circumbinary exoplanet detections. The longitudinal and latitudinal distribution of flux is sensitive to the centre of mass motion of the binary, and the relative orbital phases of the binary and planet. Total eclipses of the secondary by the primary, as well as partial eclipses of the primary by the secondary add an extra forcing term to the system. We also find that the patterns of darkness on the surface are equally unique. Beyond the planet's polar circles, the surface spends a significantly longer time in darkness than latitudes around the equator, due to the stars' motions delaying the first sunrise of spring (or hastening the last sunset of autumn). In the case of Kepler-47, we also find a weak longitudinal dependence for darkness, but this effect tends to average out if considered over many orbits. In the light of these flux and darkness patterns, we consider and discuss the prospects and challenges for photosynthetic organisms, using terrestrial analogues as a guide., Comment: 26 pages, 43 figures, accepted for publication in the International Journal of Astrobiology

We discuss the extension to redshift space of a rescaling algorithm, designed to alter the effective cosmology of a pre-existing simulated particle distribution or catalogue of dark matter haloes. The rescaling approach was initially developed by Angulo & White and was adapted and applied to halo catalogues in real space in our previous work. This algorithm requires no information other than the initial and target cosmological parameters, and it contains no tuned parameters. It is shown here that the rescaling method also works well in redshift space, and that the rescaled simulations can reproduce the growth rate of cosmological density fluctuations appropriate for the target cosmology. Even when rescaling a grossly non-standard model with Lambda=0 and zero baryons, the redshift-space power spectrum of standard LCDM can be reproduced to about 5% error for k<0.2h Mpc^-1. The ratio of quadrupole-to-monopole power spectra remains correct to the same tolerance up to k=1h Mpc^-1, provided that the input halo catalogue contains measured internal velocity dispersions., Comment: 14 pages, 6 figures, accepted for publication in MNRAS

We present and test a method for modifying the catalogue of dark matter haloes produced from a given cosmological simulation, so that it resembles the result of a simulation with an entirely different set of parameters. This extends the method of Angulo & White (2010), which rescales the full particle distribution from a simulation. Working directly with the halo catalogue offers an advantage in speed, and also allows modifications of the internal structure of the haloes to account for nonlinear differences between cosmologies. Our method can be used directly on a halo catalogue in a self contained manner without any additional information about the overall density field: although the large-scale displacement field is required by the method, this can be inferred from the halo catalogue alone. We show proof of concept of our method by rescaling a matter-only simulation with no baryon acoustic oscillation (BAO) features to a more standard LCDM model containing a cosmological constant and a BAO signal. In conjunction with the halo occupation approach, this method provides a basis for the rapid generation of mock galaxy samples spanning a wide range of cosmological parameters., Comment: 17 pages, 10 figures, accepted for publication in MNRAS