Matter Power Spectrum Research Articles

Fast full N-body simulations of generic modified gravity: derivative coupling models

We present mg-glam, a code developed for the very fast production of full N-body cosmological simulations in modified gravity (MG) models. We describe the implementation, numerical tests and first results of a large suite of cosmological simulations for two broad classes of MG models with derivative coupling terms — the Vainshtein- and Kmouflage-type models — which respectively features the Vainshtein and Kmouflage screening mechanism. Derived from the parallel particle-mesh code glam, mg-glam incorporates an efficient multigrid relaxation technique to solve the characteristic nonlinear partial differential equations of these models. For Kmouflage, we have proposed a new algorithm for the relaxation solver, and run the first simulations of the model to understand its cosmological behaviour. In a companion paper, we describe versions of this code developed for conformally-coupled MG models, including several variants of f(R) gravity, the symmetron model and coupled quintessence. Altogether, mg-glam has so far implemented the prototypes for most MG models of interest, and is broad and versatile. The code is highly optimised, with a tremendous (over two orders of magnitude) speedup when comparing its running time with earlier N-body codes, while still giving accurate predictions of the matter power spectrum and dark matter halo abundance. mg-glam is ideal for the generation of large numbers of MG simulations that can be used in the construction of mock galaxy catalogues and accurate emulators for ongoing and future galaxy surveys.

An Analytic Model for the Subgalactic Matter Power Spectrum in Fuzzy Dark Matter Halos

Abstract Fuzzy dark matter (FDM), a scalar particle coupled to the gravitational field without self-interaction, whose mass range is m ∼ 10−24–10−20 eV, is one of the promising alternative dark matter candidates to cold dark matter. The quantum interference pattern, which is a unique structure of FDM, can be seen in halos in cosmological FDM simulations. In this paper, we first provide an analytic model of the subgalactic matter power spectrum originating from quantum clumps in FDM halos, in which the density distribution of the FDM is expressed by a superposition of quantum clumps whose size corresponds to the de Broglie wavelength of the FDM. These clumps are assumed to be distributed randomly, such that the ensemble average density follows a halo profile such as the Navarro–Frenk–White profile. We then compare the convergence power spectrum projected along the line of sight around the Einstein radius, which is converted from the subgalactic matter power spectrum, to that measured in the strong lens system SDSS J0252 + 0039. While we find that the current observation provides no useful constraint on the FDM mass, we show that future deep, high spatial resolution observations of strong lens systems can tightly constrain FDM with a mass around 10−22 eV.

Constraining ultralight axions with galaxy surveys

Ultralight axions and other bosons are dark matter candidates present in many high energy physics theories beyond the Standard Model. In particular, the string axiverse postulates the existence of up to \U0001d4aa(100) light scalar bosons constituting the dark sector. We test the validity of the effective field theory of large-scale structure approach to mixed ultralight axion dark matter by making our own mock galaxy catalogs and find an anisotropic ultralight axion signature in the galaxy quadrupole. We use the Fourier-space galaxy clustering statistics from the Baryon Oscillation Spectroscopic Survey (BOSS) and obtain upper bounds for the axion relic density Ω_a h2<0.004 for axions of mass 10-31 eV≤ m_a≤ 10-26 eV at 95% confidence. We also improve existing constraints by a factor of over 4.5 and 2.1 for axion masses of 10-25 eV and 10-32 eV compared to CMB alone. To improve the convergence speed of our analysis, we develop an augmented interpolation scheme allowing a fast computation of the axion contribution to the linear matter power spectrum. This method leads to a 70% reduction of the computational cost for the full Monte Carlo Markov chains analysis.

Accelerating Large-Scale-Structure data analyses by emulating Boltzmann solvers and Lagrangian Perturbation Theory

The linear matter power spectrum is an essential ingredient in all theoretical models for interpreting large-scale-structure observables. Although Boltzmann codes such as CLASS or CAMB are very efficient at computing the linear spectrum, the analysis of data usually requires 104-106 evaluations, which means this task can be the most computationally expensive aspect of data analysis. Here, we address this problem by building a neural network emulator that provides the linear theory (total and cold) matter power spectrum in about one millisecond with ≈0.2%(0.5%) accuracy over redshifts z ≤ 3 (z ≤ 9), and scales10-4 ≤ k [h Mpc-1] &lt; 50. We train this emulator with more than 200,000 measurements, spanning a broad cosmological parameter space that includes massive neutrinos and dynamical dark energy. We show that the parameter range and accuracy of our emulator is enough to get unbiased cosmological constraints in the analysis of a Euclid-like weak lensing survey. Complementing this emulator, we train 15 other emulators for the cross-spectra of various linear fields in Eulerian space, as predicted by 2nd-order Lagrangian Perturbation theory, which can be used to accelerate perturbative bias descriptions of galaxy clustering. Our emulators are specially designed to be used in combination with emulators for the nonlinear matter power spectrum and for baryonic effects, all of which are publicly available at http://www.dipc.org/bacco.

Linear cosmological constraints on two-body decaying dark matter scenarios and the S8 tension

The '$S_8$ tension' is a longstanding discrepancy between the cosmic microwave background (CMB) and weak gravitational lensing determination of the amplitude of matter fluctuations, parametrized as $S_8\equiv\sigma_8(\Omega_m/0.3)^{0.5}$, where $\sigma_8$ is the root mean square of matter fluctuations on a 8 $h^{-1}$Mpc scale, and $\Omega_m$ is the total matter abundance. It was recently shown that dark matter (DM) decaying into a massless (dark radiation) and a massive (warm DM) species, with a lifetime $\Gamma^{-1} \simeq 55~(\varepsilon/0.007)^{1.4}$ Gyrs -- where $\varepsilon$ represent the mass-energy fraction transferred to the massless component -- can ease the tension. Thanks to a fast and accurate fluid approximation scheme for the warm species, we perform a comprehensive study of this 2-body decaying DM scenario, discussing in detail its dynamics and its impact on the CMB and linear matter power spectra. We then investigate the implications for the '$S_8$ tension' against a number of changes in the analysis: different $S_8$ priors, marginalization over the lensing information in Planck data, trading Planck high$-\ell$ polarization data for those from the SPTpol and ACTPol surveys, and the inclusion of the recent results from the Xenon1T collaboration. We conclude that the preference for decaying DM, apparent only when the $S_8$ value determined from weak lensing data is added to the analysis, does not sensibly degrade the fit to any of the cosmological data-sets considered, and that the model could potentially explain the anomalous electron recoil excess reported by the Xenon1T collaboration. Furthermore, we explictly show that while current CMB data alone are not sensitive enough to distinguish between standard CDM and decaying DM, next-generation CMB observations (CMB-S4) can unambiguously detect its signature.

Mixed dark matter: matter power spectrum and halo mass function

We investigate and quantify the impact of mixed (cold and warm) dark matter models on large-scale structure observables. In this scenario, dark matter comes in two phases, a cold one (CDM) and a warm one (WDM): the presence of the latter causes a suppression in the matter power spectrum which is allowed by current constraints and may be detected in present-day and upcoming surveys. We run a large set of N-body simulations in order to build an efficient and accurate emulator to predict the aforementioned suppression with percent precision over a wide range of values for the WDM mass, Mwdm, and its fraction with respect to the totality of dark matter, fwdm. The suppression in the matter power spectrum is found to be independent of changes in the cosmological parameters at the 2% level for k≲ 10 h/Mpc and z≤ 3.5. In the same ranges, by applying a baryonification procedure on both ΛCDM and CWDM simulations to account for the effect of feedback, we find a similar level of agreement between the two scenarios. We examine the impact that such suppression has on weak lensing and angular galaxy clustering power spectra. Finally, we discuss the impact of mixed dark matter on the shape of the halo mass function and which analytical prescription yields the best agreement with simulations. We provide the reader with an application to galaxy cluster number counts.

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.

Cosmological simulations of number counts

In this paper we present for the first time the angular power spectra C ℓ(z,z') for number counts from relativisticN-body simulations. We use the relativistic N-body code gevolution with its exact integration of lightlike geodesics which include all relativistic scalar contributions to the number counts. We compare our non-perturbative numerical results with the results from class using the hmcode approximation for the non-linear matter power spectrum. We find that this simple description is excellent for both, the density and the convergence.On the other hand, the current implementation of redshift-space distortions in Boltzmann codes is not accurate.We also find that the largest contribution to the unequal-redshift power spectra is the cross-correlation of the density and the lensing contribution to the number counts, especially for redshift bins that are far apart. Correlatingthe number counts with the convergence map we find that the signal is dominated by the lensing-lensing term when the convergence field redshift is not higher than the number counts one, while it is dominated by the density-lensing term in the opposite case.In the present study, the issue of galaxy bias is deliberately left aside by considering only unbiased samples of matter particles from the simulations.

Contributions from primordial non-Gaussianity and general relativity to the galaxy power spectrum

We compute the real space galaxy power spectrum, including the leading order effects of General Relativity and primordial non-Gaussianity from the f NL and g NL parameters. Such contributions come from the one-loop matter power spectrum terms dominant at large scales, and from the factors of the non-linear bias parameter b NL (akin to the Newtonian b ϕ). We assess the detectability of these contributions in Stage-IV surveys. In particular, we note that specific values of the bias parameter may erase the primordial and relativistic contributions to the configuration space power spectrum.

Minimal theory of massive gravity in the light of CMB data and the S8 tension

We investigate the minimal theory of massive gravity (MTMG) in the light of different observational datasets that are in tension within the $\mathrm{\ensuremath{\Lambda}}$ cold dark matter cosmology. In particular, we analyze the MTMG model, for the first time, with the Planck--cosmic microwave background (CMB) data, and how these precise measurements affect the free parameters of the theory. The MTMG model can affect the CMB power spectrum at large angular scales and cause a suppression on the amplitude of the matter power spectrum. We find that on adding Planck-CMB data, the graviton has a small, positive, but nonzero mass at 68% confidence level, and from this perspective, we show that the tension between redshift space distortions measurements and Planck-CMB data in the parametric space ${S}_{8}\ensuremath{-}{\mathrm{\ensuremath{\Omega}}}_{m}$ can be resolved within the MTMG scenario. Through a robust and accurate analysis, we find that the ${H}_{0}$ tension between the CMB and the local distance ladder measurements still remains but can be reduced to $\ensuremath{\sim}3.5\ensuremath{\sigma}$ within the MTMG theory. The MTMG is very well consistent with the CMB observations, and undoubtedly, it can serve as a viable candidate among other modified gravity theories.

Cosmological boost factor for dark matter annihilation at redshifts of z=10−100 using the power spectrum approach

We compute the cosmological boost factor at high redshifts of $z=10$-$100$ by integrating the non-linear matter power spectrum measured from high-resolution cosmological $N$-body simulations. An accurate boost factor is required to estimate the energy injection from dark matter annihilation, which may affect the cosmological re-ionization process. We combined various box-size simulations (side lengths of $1 \, {\rm kpc}$-$10 \, {\rm Mpc}$) to cover a wide range of scales, i.e. $k=1$-$10^7 \, {\rm Mpc}^{-1}$. The boost factor is consistent with the linear theory prediction at $z \gtrsim 50$ but strongly enhanced at $z \lesssim 40$ as a result of non-linear matter clustering. Although dark matter free-streaming damping was imposed at $k_{\rm fs}=10^6 \, {\rm Mpc}^{-1}$ in the initial power spectrum, the damping disappears at later times of $z\lesssim40$ as a result of the power transfer from large to small scales. Because the simulations do not explore very small-scale clustering at $k>10^7 \, {\rm Mpc}^{-1}$, our result is a lower bound on the boost factor at $z \lesssim 40$. A simple fitting function of the boost factor is also presented.

Baryonic imprints on DM haloes: population statistics from dwarf galaxies to galaxy clusters

ABSTRACT In a purely cold dark matter (CDM) universe, the initial matter power spectrum and its subsequent gravitational growth contain no special mass- or time-scales, and so neither do the emergent population statistics of internal dark matter (DM) halo properties. Using 1.5 million haloes from three illustristng realizations of a ΛCDM universe, we show that galaxy formation physics drives non-monotonic features (‘wiggles’) into DM property statistics across six decades in halo mass, from dwarf galaxies to galaxy clusters. We characterize these features by extracting the halo mass-dependent statistics of five DM halo properties – velocity dispersion, NFW concentration, density- and velocity-space shapes, and formation time – using kernel-localized linear regression (Kllr). Comparing precise estimates of normalizations, slopes, and covariances between realizations with and without galaxy formation, we find systematic deviations across all mass-scales, with maximum deviations of 25 per cent at the Milky Way mass of $10^{12} \, {\rm M}_\odot$. The mass-dependence of the wiggles is set by the interplay between different cooling and feedback mechanisms, and we discuss its observational implications. The property covariances depend strongly on halo mass and physics treatment, but the correlations are mostly robust. Using multivariate Kllr and interpretable machine learning, we show the halo concentration and velocity-space shape are principal contributors, at different mass, to the velocity dispersion variance. Statistics of mass accretion rate and DM surface pressure energy are provided in an appendix. We publicly release halo property catalogues and kllr parameters for the TNG runs at 20 epochs up to z = 12.

Lifting weak lensing degeneracies with a field-based likelihood

ABSTRACT We present a field-based approach to the analysis of cosmic shear data to infer jointly cosmological parameters and the dark matter distribution. This forward modelling approach samples the cosmological parameters and the initial matter fluctuations, using a physical gravity model to link the primordial fluctuations to the non-linear matter distribution. Cosmological parameters are sampled and updated consistently through the forward model, varying (1) the initial matter power spectrum, (2) the geometry through the distance-redshift relationship, and (3) the growth of structure and light-cone effects. Our approach extracts more information from the data than methods based on two-point statistics. We find that this field-based approach lifts the strong degeneracy between the cosmological matter density, Ωm, and the fluctuation amplitude, σ8, providing tight constraints on these parameters from weak lensing data alone. In the simulated four-bin tomographic experiment we consider, the field-based likelihood yields marginal uncertainties on σ8 and Ωm that are, respectively, a factor of 3 and 5 smaller than those from a two-point power spectrum analysis applied to the same underlying data.

Analytical warm dark matter power spectrum on small scales

Using the Reduced Relativistic Gas (RRG) model, we analytically determinethe matter power spectrum for Warm Dark Matter (WDM) on small scales,k > 1 h/Mpc. The RRG is a simplified model for the ideal relativisticgas, but very accurate in the cosmological context. In another work,we have shown that, for typical allowed masses for dark matter particles,m>5 keV, the higher order multipoles, ℓ ≥ 2, in the Einstein-Boltzmannsystem of equations are negligible on scales k < 10 h/Mpc.Hence, we can follow the perturbations of WDM using the ideal fluidframework, with equation of state and sound speed of perturbationsgiven by the RRG model. We derive a Mészáros-like equation for WDMand solve it analytically in radiation, matter and dark energy dominatederas. Joining these solutions, we get an expression that determinesthe value of WDM perturbations as a function of redshift and wavenumber.Then we construct the matter power spectrum and transfer functionof WDM on small scales and compare it to some results coming fromLyman-α forest observations. Besides being a clear and pedagogicalanalytical development to understand the evolution of WDM perturbations,our power spectrum results are consistent with the observations consideredand the other determinations of the degree of warmness of dark matter particles.

CMB anisotropies and linear matter power spectrum in models with non-thermal neutrinos and primordial magnetic fields

Angular power spectra of temperature anisotropies and polarization of the cosmic microwave background (CMB) as well as the linear matter power spectra are calculated for models with three light neutrinos with non-thermal phase-space distributions in the presence of a primordial stochastic magnetic field. The non-thermal phase-space distribution function is assumed to be the sum of a Fermi-Dirac and a gaussian distribution. It is found that the known effective description of the non-thermal model in terms of a twin thermal model with extra relativistic degrees of freedom can also be extended to models including a stochastic magnetic field. Numerical solutions are obtained for a range of magnetic field parameters.

Multifidelity emulation for the matter power spectrum using Gaussian processes

ABSTRACT We present methods for emulating the matter power spectrum by combining information from cosmological N-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter space of a limited number of simulations. We present the first implementation in cosmology of multifidelity emulation, where many low-resolution simulations are combined with a few high-resolution simulations to achieve an increased emulation accuracy. The power spectrum’s dependence on cosmology is learned from the low-resolution simulations, which are in turn calibrated using high-resolution simulations. We show that our multifidelity emulator predicts high-fidelity (HF) counterparts to percent-level relative accuracy when using only three HF simulations and outperforms a single-fidelity emulator that uses 11 simulations, although we do not attempt to produce a converged emulator with high absolute accuracy. With a fixed number of HF training simulations, we show that our multifidelity emulator is ≃100 times better than a single-fidelity emulator at $k \le 2 \, h\textrm {Mpc}{^{-1}}$, and ≃20 times better at $3 \le k \lt 6.4 \, h\textrm {Mpc}{^{-1}}$. Multifidelity emulation is fast to train, using only a simple modification to standard Gaussian processes. Our proposed emulator shows a new way to predict non-linear scales by fusing simulations from different fidelities.

Dark sector to restore cosmological concordance

We develop a new phenomenological model that addresses current tensions between observations of the early and late Universe. Our scenario features: (i) a decaying dark energy fluid (DDE), which undergoes a transition at $z \sim 5,000$, to raise today's value of the Hubble parameter -- addressing the $H_0$ tension, and (ii) an ultra-light axion (ULA), which starts oscillating at $z\gtrsim 10^4$, to suppress the matter power spectrum -- addressing the $S_8$ tension. Our Markov Chain Monte Carlo analyses show that such a Dark Sector model fits a combination of Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations, and Large Scale Structure (LSS) data slightly better than the $\Lambda$CDM model, while importantly reducing both the $H_0$ and $S_8$ tensions with late universe probes ($\lesssim 3\sigma$). Combined with measurements from cosmic shear surveys, we find that the discrepancy on $S_8$ is reduced to the $1.4\sigma$ level, and the value of $H_0$ is further raised. Adding local supernovae measurements, we find that the $H_0$ and $S_8$ tensions are reduced to the $1.4\sigma$ and $1.2\sigma$ level respectively, with a significant improvement $\Delta\chi^2\simeq -18$ compared to the $\Lambda$CDM model. With this complete dataset, the DDE and ULA are detected at $\simeq 4\sigma$ and $\simeq2\sigma$, respectively. We discuss a possible particle physics realization of this model, with a dark confining gauge sector and its associated axion, although embedding the full details within microphysics remains an urgent open question. Our scenario will be decisively probed with future CMB and LSS surveys.

CARPool Covariance: Fast, unbiased covariance estimation for large-scale structure observables

Abstract The covariance matrix $\boldsymbol{\Sigma }$ of non-linear clustering statistics that are measured in current and upcoming surveys is of fundamental interest for comparing cosmological theory and data and a crucial ingredient for the likelihood approximations underlying widely used parameter inference and forecasting methods. The extreme number of simulations needed to estimate $\boldsymbol{\Sigma }$ to sufficient accuracy poses a severe challenge. Approximating $\boldsymbol{\Sigma }$ using inexpensive but biased surrogates introduces model error with respect to full simulations, especially in the non-linear regime of structure growth. To address this problem we develop a matrix generalization of Convergence Acceleration by Regression and Pooling (CARPool) to combine a small number of simulations with fast surrogates and obtain low-noise estimates of $\boldsymbol{\Sigma }$ that are unbiased by construction. Our numerical examples use CARPool to combine GADGET-III N-body simulations with fast surrogates computed using COmoving Lagrangian Acceleration (COLA). Even at the challenging redshift z = 0.5, we find variance reductions of at least $\mathcal {O}(10^1)$ and up to $\mathcal {O}(10^4)$ for the elements of the matter power spectrum covariance matrix on scales 8.9 × 10−3 &amp;lt; kmax &amp;lt; 1.0 hMpc−1. We demonstrate comparable performance for the covariance of the matter bispectrum, the matter correlation function and probability density function of the matter density field. We compare eigenvalues, likelihoods, and Fisher matrices computed using the CARPool covariance estimate with the standard sample covariance and generally find considerable improvement except in cases where $\boldsymbol{\Sigma }$ is severely ill-conditioned.

Constraining f(R) gravity with a k -cut cosmic shear analysis of the Hyper Suprime-Cam first-year data

Using Subaru Hyper Suprime-Cam (HSC) year 1 data, we perform the first $k$-cut cosmic shear analysis constraining both $\Lambda$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 have also developed a test to ensure that the effects of poorly modeled small scales are nulled as intended. For $\Lambda$CDM we find $S_8 = \sigma_8 (\Omega_m / 0.3) ^ {0.5} = 0.789 ^{+0.039}_{-0.022}$, while the constraints on the $f(R)$ modified gravity parameters are prior dominated. In the future, the $k$-cut method could be used to constrain a large number of theories of gravity where computational limitations make it infeasible to model the matter power spectrum down to extremely small scales.

New Relativistic Theory for Modified Newtonian Dynamics.

We propose a relativistic gravitational theory leading to modified Newtonian dynamics, a paradigm that explains the observed universal galactic acceleration scale and related phenomenology. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed cosmic microwave background and matter power spectra on linear cosmological scales. We show that its action expanded to second order is free of ghost instabilities and discuss its possible embedding in a more fundamental theory.