Accurate predictions for the non-linear matter power spectrum are needed to confront theory with observations in current and near future weak lensing and galaxy clustering surveys. We propose a computationally cheap method to create an emulator for modified gravity models by utilizing existing emulators for $Λ$CDM. Using a suite of $N$-body simulations we construct a fitting function for the enhancement of both the linear and non-linear matter power spectrum in the commonly studied Hu-Sawicki $f(R)$ gravity model valid for wave-numbers $k \lesssim 5-10\, h\text{Mpc}^{-1}$ and redshifts $z \lesssim 3$. We show that the cosmology dependence of this enhancement is relatively weak so that our fit, using simulations coming from only one cosmology, can be used to get accurate predictions for other cosmological parameters. We also show that the cosmology dependence can, if needed, be included by using linear theory, approximate $N$-body simulations (such as COLA) and semi-analytical tools like the halo model. Our final fit can easily be combined with any emulator or semi-analytical models for the non-linear $Λ$CDM power spectrum to accurately, and quickly, produce a non-linear power spectrum for this particular modified gravity model. The method we use can be applied to fairly cheaply construct an emulator for other modified gravity models. As an application of our fitting formula we use it to compute Fisher-forecasts for how well galaxy clustering and weak lensing in a Euclid-like survey will be at constraining modifications of gravity.
We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the Cosmic Microwave Background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein-Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including $Λ$CDM, $w$CDM, $Λ$CDM+$N_\mathrm{eff}$, and $Λ$CDM…
Interpreting observations of the Lyman-$α$ forest flux power spectrum requires interpolation between a small number of expensive simulations. We present a Gaussian process emulator modelling the 1D flux power spectrum as a function of the amplitude and slope of the small-scale linear matter power spectrum, and the state of the intergalactic medium at the epoch of interest ($2 < z < 4$). This parameterisation enables the prediction of the flux power spectrum in extended cosmological models that are not explicitly included in the training set, eliminating the need to construct bespoke emulators …
We introduce an emulator approach to predict the non-linear matter power spectrum for broad classes of beyond-$Λ$CDM cosmologies, using only a suite of $Λ$CDM $N$-body simulations. By including a range of suitably modified initial conditions in the simulations, and rescaling the resulting emulator predictions with analytical `halo model reactions', accurate non-linear matter power spectra for general extensions to the standard $Λ$CDM model can be calculated. We optimise the emulator design by substituting the simulation suite with non-linear predictions from the standard {\sc halofit} tool. We…
Modeling nonlinear scales for dynamical dark energy cosmologies with COLA
CBPF - Brazilian Center for Research in Physics（巴西物理研究中心）；Instituto de Física Teórica da Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）；Department of Physics & Astronomy, Stony Brook University（石溪大学物理与天文学系）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学陈省身理论物理研究所）
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…
Testing a subset of viable cosmological models beyond General Relativity (GR), with implications for cosmic acceleration and the Dark Energy associated with it, is within the reach of Rubin Observatory Legacy Survey of Space and Time (LSST) and a part of its endeavor. Deviations from GR-w(z)CDM models can manifest in the growth rate of structure and lensing, as well as in screening effects on non-linear scales. We explore the constraining power of small-scale deviations predicted by the f(R) Hu-Sawicki Modified Gravity (MG) candidate, by emulating this model with COLA (COmoving Lagrangian Acce…
An accurate theoretical template of the redshift-space galaxy power spectrum, if applicable out to nonlinear scales, enables us to extract more stringent and robust constraints on cosmological parameters from the measured galaxy clustering. In this work, we develop a simulation-based template, so-called emulator, for the redshift-space power spectrum of dark matter halos. Using the redshift-space halo power spectra measured from the Dark Quest $N$-body simulation suite that covers 101 flat-geometry $w$CDM cosmologies around the Planck $Λ$CDM model, we feed these data into a feed-forward neural…
$\texttt{SPINE}$: Symbolic Models to Predict the Evolution of the $Λ$CDM Nonlinear Power Spectrum
University of Hull（赫尔大学）；E. A. Milne Centre for Astrophysics, University of Hull（赫尔大学 E. A. 米尔内天体物理中心）；Centre of Excellence for Data Science, AI, & Modelling (DAIM), University of Hull（赫尔大学数据科学、人工智能与建模卓越中心）；Max-Planck-Institut für extraterrestrische Physik（马克斯·普朗克地外物理研究所）；Universitäts-Sternwarte München（慕尼黑大学天文台）；Newcastle University（纽卡斯尔大学）
该研究提出SPINE和SPINEX两个分析模拟器，基于符号回归技术，可在0.01-2 h Mpc⁻¹波数范围内高精度预测ΛCDM非线性功率谱，精度优于5%，为宇宙学功率谱建模提供高效可解释的替代方案。
CMBolic: Symbolic emulators for the Cosmic Microwave Background. I. Lensing
CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）；Astrophysics, University of Oxford（牛津大学天体物理学系）；Institute of Cosmology & Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）
We study the clustering properties of dark matter halos in real- and redshift-space in cosmologies with massless and massive neutrinos through a large set of state-of-the-art N-body simulations. We provide quick and easy-to-use prescriptions for the halo bias on linear and mildly non-linear scales, both in real and redshift space, which are valid also for massive neutrinos cosmologies. Finally we present a halo bias emulator,$\textbf{BE-HaPPY}$, calibrated on the N-body simulations, which is fast enough to be used in the standard Markov Chain Monte Carlo approach to cosmological inference. For…
The spatial curvature ($Ω_K$) 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" $Λ$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 ($δ_{\rm b}$) in a local volume in the "flat" $Λ$CDM model, via the specific mapping between the background cosmological parameters and redshifts in the non…
Standard full-shape clustering analyses in Fourier space rely on a fixed power spectrum template, defined at the fiducial cosmology used to convert redshifts into distances, and compress the cosmological information into the Alcock-Paczynski parameters and the linear growth rate of structure. In this paper, we propose an analysis method that operates directly in the cosmology parameter space and varies the power spectrum template accordingly at each tested point. Predictions for the power spectrum multipoles from the TNS model are computed at different cosmologies in the framework of $Λ\rm{CDM…
Concordance $Λ$CDM universe is the simplest model that is consistent with a large variety of cosmological observations till date. But few recent observations indicate inconsistencies in $Λ$CDM model. In this paper, we consider the combination of recent SnIa+Bao+Cmb+Growth+$H(z)$+$H_{0}$ measurements to revisit the constraints on the dark energy evolution using the widely studied CPL parametrisation for the dark energy equation of state. Although the reconstructed behaviour for the dark energy equation of state confirms the inconsistency of $Λ$CDM at $95\%$ confidence level, the reconstructed $…
Nonlinear Information from DESI Luminous Red Galaxies: An Emulator-Based Analysis of Pre- and Post-Reconstruction Power Spectra
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli宇宙起源与演化研究集成机构（WPI））；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Department of Astrophysics and Atmospheric Sciences, Faculty of Science, Kyoto Sangyo University（京都产业大学理学部天体物理学与大气科学系）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息研究中心）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo（东京大学前沿研究机构 UTIAS 宇宙物理数学 Kavli研究所（WPI））
Ten-dimensional neural network emulator for the nonlinear matter power spectrum
Department of Physics & Astronomy, University of California, Riverside（加州大学河滨分校物理与天文系）；Department of Physics, University of Michigan（密歇根大学物理系）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Field Level Neural Network Emulator for Cosmological N-body Simulations
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Stony Brook University（石溪大学）；Flatiron Institute（熨斗研究所）；Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；Princeton University（普林斯顿大学）；Simons Foundation（西蒙斯基金会）
Taking advantage of the unprecedented statistical power of upcoming cosmic shear surveys will require exquisite knowledge of the matter power spectrum over a wide range of scales. Analytical methods can achieve such precision only up to quasi-linear scales. For smaller non-linear scales we must resort to $N$-body and hydrodynamical simulations, which despite recent technological advances and improved algorithms remain computationally expensive. Over the past decade machine learning and the advent of emulators have propelled our ability to hit the target accuracy with impressive computing effic…
We investigate the $H_0$ tension in a range of extended model frameworks beyond the standard $Λ$CDM without the data from cosmic microwave background (CMB). Specifically, we adopt the data from baryon acoustic oscillation, big bang nucleosynthesis and type Ia supernovae as indirect measurements of $H_0$ to study the tension. We show that the estimated value of $H_0$ from indirect measurements is overall lower than that from direct local ones regardless of the data sets and a range of extended models to be analyzed, which indicates that, although the significance of the tension varies depending…
Using Subaru Hyper Suprime-Cam (HSC) year 1 data, we perform the first $k$-cut cosmic shear analysis constraining both $Λ$CDM and $f(R)$ Hu-Sawicki modified gravity. To generate the $f(R)$ cosmic shear theory vector, we use the matter power spectrum emulator trained on COLA (COmoving Lagrangian Acceleration) simulations. The $k$-cut method is used to significantly down-weight sensitivity to small scale ($k > 1 \ h {\rm Mpc }^{-1}$) modes in the matter power spectrum where the emulator is less accurate, while simultaneously ensuring our results are robust to baryonic feedback model uncertainty.…
We present high-fidelity cosmology results from a blinded joint analysis of galaxy-galaxy weak lensing ($Δ\!Σ$) and projected galaxy clustering ($w_{\rm p}$) measured from the Hyper Suprime-Cam Year-1 (HSC-Y1) data and spectroscopic Sloan Digital Sky Survey (SDSS) galaxy catalogs in the redshift range $0.15<z<0.7$. We define luminosity-limited samples of SDSS galaxies to serve as the tracers of $w_{\rm p}$ in three spectroscopic redshift bins, and as the lens samples for $Δ\!Σ$. For the $Δ\!Σ$ measurements, we select a single sample of 4 million source galaxies over 140 deg$^2$ from HSC-Y1 wit…
One of the main science goals of the Large Synoptic Survey Telescope (LSST) is to uncover the nature of cosmic acceleration. In the base analysis, possible deviations from the Lambda-Cold-Dark-Matter ($Λ$CDM) background evolution will be probed by fitting a $w(z)$CDM model, which allows for a redshift-dependent dark energy equation of state with $w(z)$, within general relativity (GR). A rich array of other phenomena can arise due to deviations from the standard $Λ$CDM+GR model though, including modifications to the growth rate of structure and lensing, and novel screening effects on non-linear…
Gaussian-Process Emulation of the Redshift-Space Halo Power Spectrum Monopole in Cosmologies with Massive Neutrinos
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿科学研究院）；Chinese Academy of Sciences South America Center for Astronomy (CASSACA), National Astronomical Observatories, Chinese Academy of Sciences（中国科学院南美天文中心）
Dark Quest II: A Wide-Coverage Neural Network Emulator of the Nonlinear Matter Power Spectrum Across Extended Cosmologies
Graduate School of Social Data Science, Hitotsubashi University（立命馆大学社会科学数据科学研究生院）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学重力物理与量子信息中心，山梨大学理论物理研究所）；Department of Astrophysics and Atmospheric Sciences, Faculty of Science, Kyoto Sangyo University（京都 Sangyo 大学科学系天文学与大气科学系）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo（物理学与数学宇宙研究所（WPI），东京大学先进研究所（UTIAS），东京大学）；RIKEN Center for Advanced Intelligence Project（理化学研究院先进智能项目中心）
The cosmological principle states that the Universe is statistically homogeneous and isotropic at large distance scales. There currently exist many observations which indicate a departure from this principle. It has been shown that many of these observations can be explained by invoking superhorizon cosmological perturbations and may be consistent with the Big Bang paradigm. Remarkably, these modes simultaneously explain the observed Hubble tension, i.e., the discrepancy between the direct and indirect measurements of the Hubble parameter. We propose several tests of the cosmological principle…
Beyond $Λ$CDM: fundamental constants as cosmological observables
INAF-OATs, Trieste Observatory（意大利天体物理研究所-的里雅斯特天文台）；Institute for Fundamental Physics of the Universe (IFPU)（宇宙基础物理研究所）；Department of Physics, Beijing Normal University（北京师范大学物理学院）
MG-NECOLA: A Field-Level Emulator for $f(R)$ Gravity and Massive Neutrino Cosmologies
Universidad del Valle（谷大学）；Michigan Technological University（密歇根理工大学）；Università di Bologna（博洛尼亚大学）；INAF, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚天文与空间科学观测站）
We discuss structure formation in models with a spectator field in small-field inflation which accommodate a secondary period of inflation. In such models, subgalactic scale primordial fluctuations can be much suppressed in comparison to the usual power-law $Λ$CDM model while the large scale fluctuations remain consistent with current observations. We discuss how a secondary inflationary epoch may give rise to observable features in the small scale power spectrum and hence be tested by the structures in the Local Universe.
We study the background cosmological dynamics with a three component source content: a radiation fluid, a barotropic fluid to mimic the matter sector and a single scalar field which can act as dark energy giving rise to the late-time accelerated phase. Using the well-known dimensionless variables, we cast the dynamical equations into an autonomous system of ordinary differential equations (ASODE), which are studied by computing the fixed points and the conditions for their stability. The matter fluid and the scalar field are taken to be uncoupled at first and later, we consider a coupling betw…
In the context of forthcoming galaxy surveys, to ensure unbiased constraints on cosmology and gravity when using non-linear structure information, percent-level accuracy is required when modelling the power spectrum. This calls for frameworks that can accurately capture the relevant physical effects, while allowing for deviations from $Λ$CDM. Massive neutrino and baryonic physics are two of the most relevant such effects. We present an integration of the halo model reaction frameworks for massive neutrinos and beyond-$Λ$CDM cosmologies. The integrated halo model reaction, combined with a pseud…
Taking the neutrino oscillation data into consideration, a dimensionless parameter $Δ= (m_3-m_1)/(m_3+m_1)$ is adopted to parameterize the three neutrino mass eigenstates and the normal (positive $Δ$) or inverted (negative $Δ$) mass hierarchies in three typical cosmological models. Using the currently available cosmic observational data, several Markov Chain Monte Carlo chains are obtained with uniform priors on the free parameters at first. Applying importance sampling the results are compared with three new priors, i.e., logarithmic prior on $|Δ|$, linear and logarithmic priors on $Σm_ν$. It…
To effectively exploit large-scale structure surveys, we depend on accurate and reliable predictions of non-linear cosmological structure formation. Tools for efficient and comprehensive computational modelling are therefore essential to perform cosmological parameter inference analyses. We present the public software package ReACT, demonstrating its capability for the fast and accurate calculation of non-linear power spectra from non-standard physics. We showcase ReACT through a series of analyses on the DGP and $f(R)$ gravity models, adopting LSST-like cosmic shear power spectra. Accurate no…
We study observational constraints on a specific dark energy model in the framework of Gleyzes-Langlois-Piazza-Vernizzi theories, which extends the Galileon ghost condensate (GGC) to the domain of beyond Horndeski theories. In this model, we show that the Planck cosmic microwave background (CMB) data, combined with datasets of baryon acoustic oscillations, supernovae type Ia, and redshift-space distortions, give the tight upper bound $|α_{\rm H}^{(0)}| \le {\cal O}(10^{-6})$ on today's beyond-Horndeski (BH) parameter $α_{\rm H}$. This is mostly attributed to the shift of CMB acoustic peaks ind…
Biased tracers, Hybrid Effective Field Theory and Modified Gravity
CBPF - Brazilian Center for Research in Physics（巴西物理研究中心）；Institute for Computational Cosmology, Department of Physics, Durham University（杜伦大学）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学）
We present the results obtained from the full-shape cosmology analysis of the redshift-space power spectra for 4 galaxy samples of the SDSS-III BOSS DR12 galaxy catalog over $0.2 < z < 0.75$. For the theoretical template, we use an emulator that was built from an ensemble set of $N$-body simulations, which enables fast and accurate computation of the redshift-space power spectrum of halos. Combining with the halo occupation distribution to model the halo-galaxy connection, we can compute the redshift-space power spectrum of BOSS-like galaxies in the flat $Λ$CDM cosmology. In our cosmology infe…
We derive constraints on a coupled quintessence model with pure momentum exchange from the public $\sim$1000 deg$^2$ cosmic shear measurements from the Kilo-Degree Survey and the $\it{Planck}$ 2018 Cosmic Microwave Background data. We compare this model with $Λ$CDM and find similar $χ^2$ and log-evidence values. We accelerate parameter estimation by sourcing cosmological power spectra from the neural network emulator COSMOPOWER. We highlight the necessity of such emulator-based approaches to reduce the computational runtime of future similar analyses, particularly from Stage IV surveys. As an …
Tightening Cosmological Constraints Within and Beyond $Λ$CDM Using Gamma-Ray Bursts Calibrated with Type Ia Supernovae
INAF - Osservatorio Astronomico di Capodimonte（意大利国家天体物理研究所卡波迪蒙特天文台）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天文与天体物理研究院）；Department of Astronomy, Beijing Normal University（北京师范大学天文系）；INAF - Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；Università di Camerino（卡梅里诺大学）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Istituto Nazionale di Fisica Nucleare, Sezione di Perugia（意大利国家核物理研究所佩鲁贾分部）；SUNY Polytechnic（纽约州立理工大学）；Al-Farabi Kazakh National University（阿里-法拉比哈萨克国立大学）；ICRANet（国际相对论天体物理中心网络）
