Numerical Simulations of the Dark Universe: State of the Art and the Next Decade

We present a review of the current state of the art of cosmological dark matter simulations, with particular emphasis on the implications for dark matter detection efforts and studies of dark energy. This review is intended both for particle physicists, who may find the cosmological simulation literature opaque or confusing, and for astro-physicists, who may not be familiar with the role of simulations for observational and experimental probes of dark matter and dark energy. Our work is complementary to the contribution by M. Baldi in this issue, which focuses on the treatment of dark energy and cosmic acceleration in dedicated N-body simulations. Truly massive dark matter-only simulations are being conducted on national supercomputing centers, employing from several billion to over half a trillion particles to simulate the formation and evolution of cosmologically representative volumes (cosmic scale) or to zoom in on individual halos (cluster and galactic scale). These simulations cost millions of core-hours, require tens to hundreds of terabytes of memory, and use up to petabytes of disk storage. The field is quite internationally diverse, with top simulations having been run in China, France, Germany, Korea, Spain, and the USA. Predictions from such simulations touch on almost every aspect of dark matter and dark energy studies, and we give a comprehensive overview of this connection. We also discuss the limitations of the cold and collisionless DM-only approach, and describe in some detail efforts to include different particle physics as well as baryonic physics in cosmological galaxy formation simulations, including a discussion of recent results highlighting how the distribution of dark matter in halos may be altered. We end with an outlook for the next decade, presenting our view of how the field can be expected to progress. (abridged)Comment: 54 pages, 4 figures, 3 tables; invited contribution to the special issue "The next decade in Dark Matter and Dark Energy" of the new Open Access journal "Physics of the Dark Universe". Replaced with accepted versio

How closely do baryons follow dark matter on large scales?

We investigate the large-scale clustering and gravitational interaction of baryons and dark matter (DM) over cosmic time using a set of collisionless N-body simulations. Both components, baryons and DM, are evolved from distinct primordial density and velocity power spectra as predicted by early-universe physics. We first demonstrate that such two-component simulations require an unconventional match between force and mass resolution (i.e. force softening on at least the mean particle separation scale). Otherwise, the growth on any scale is not correctly recovered because of a spurious coupling between the two species at the smallest scales. With these simulations, we then demonstrate how the primordial differences in the clustering of baryons and DM are progressively diminished over time. In particular, we explicitly show how the BAO signature is damped in the spatial distribution of baryons and imprinted in that of DM. This is a rapid process, yet it is still not fully completed at low redshifts. On large scales, the overall shape of the correlation function of baryons and DM differs by 2% at z = 9 and by 0.2% at z = 0. The differences in the amplitude of the BAO peak are approximately a factor of 5 larger: 10% at z = 9 and 1% at z = 0. These discrepancies are, however, smaller than effects expected to be introduced by galaxy formation physics in both the shape of the power spectrum and in the BAO peak, and are thus unlikely to be detected given the precision of the next generation of galaxy surveys. Hence, our results validate the standard practice of modelling the observed galaxy distribution using predictions for the total mass clustering in the Universe.Comment: 9 pages, 6 figures. Replaced with version published in MNRA

On the Statistics of Biased Tracers in the Effective Field Theory of Large Scale Structures

With the completion of the Planck mission, in order to continue to gather cosmological information it has become crucial to understand the Large Scale Structures (LSS) of the universe to percent accuracy. The Effective Field Theory of LSS (EFTofLSS) is a novel theoretical framework that aims to develop an analytic understanding of LSS at long distances, where inhomogeneities are small. We further develop the description of biased tracers in the EFTofLSS to account for the effect of baryonic physics and primordial non-Gaussianities, finding that new bias coefficients are required. Then, restricting to dark matter with Gaussian initial conditions, we describe the prediction of the EFTofLSS for the one-loop halo-halo and halo-matter two-point functions, and for the tree-level halo-halo-halo, matter-halo-halo and matter-matter-halo three-point functions. Several new bias coefficients are needed in the EFTofLSS, even though their contribution at a given order can be degenerate and the same parameters contribute to multiple observables. We develop a method to reduce the number of biases to an irreducible basis, and find that, at the order at which we work, seven bias parameters are enough to describe this extremely rich set of statistics. We then compare with the output of $N$-body simulations. For the lowest mass bin, we find percent level agreement up to $k\simeq 0.3\,h\,{\rm Mpc}^{-1}$ for the one-loop two-point functions, and up to $k\simeq 0.15\,h\,{\rm Mpc}^{-1}$ for the tree-level three-point functions, with the $k$-reach decreasing with higher mass bins. This is consistent with the theoretical estimates, and suggests that the cosmological information in LSS amenable to analytical control is much more than previously believed.Comment: 54 pages, 16 figures, v2: added references and explanations, corrected typo

The One-Loop Matter Bispectrum in the Effective Field Theory of Large Scale Structures

Given the importance of future large scale structure surveys for delivering new cosmological information, it is crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbative scheme to compute the clustering of dark matter in the weakly nonlinear regime in an expansion in $k/k_{\rm NL}$, where $k$ is the wavenumber of interest and $k_{\rm NL}$ is the wavenumber associated to the nonlinear scale. It has been recently shown that the EFTofLSS matches to $1\%$ level the dark matter power spectrum at redshift zero up to $k\simeq 0.3 h\,$Mpc$^{-1}$ and $k\simeq 0.6 h\,$Mpc$^{-1}$ at one and two loops respectively, using only one counterterm that is fit to data. Similar results have been obtained for the momentum power spectrum at one loop. This is a remarkable improvement with respect to former analytical techniques. Here we study the prediction for the equal-time dark matter bispectrum at one loop. We find that at this order it is sufficient to consider the same counterterm that was measured in the power spectrum. Without any remaining free parameter, and in a cosmology for which $k_{\rm NL}$ is smaller than in the previously considered cases ($\sigma_8=0.9$), we find that the prediction from the EFTofLSS agrees very well with $N$-body simulations up to $k\simeq 0.25 h\,$Mpc$^{-1}$, given the accuracy of the measurements, which is of order a few percent at the highest $k$'s of interest. While the fit is very good on average up to $k\simeq 0.25 h\,$Mpc$^{-1}$, the fit performs slightly worse on equilateral configurations, in agreement with expectations that for a given maximum $k$, equilateral triangles are the most nonlinear.Comment: 39 pages, 12 figures; v2: JCAP published version, improved numerical data, added explanation and clarification

Noiseless Gravitational Lensing Simulations

The microphysical properties of the DM particle can, in principle, be constrained by the properties and abundance of substructures in DM halos, as measured through strong gravitational lensing. Unfortunately, there is a lack of accurate theoretical predictions for the lensing signal of substructures, mainly because of the discreteness noise inherent to N-body simulations. Here we present Recursive-TCM, a method that is able to provide lensing predictions with an arbitrarily low discreteness noise, without any free parameters or smoothing scale. This solution is based on a novel way of interpreting the results of N-body simulations, where particles simply trace the evolution and distortion of Lagrangian phase-space volume elements. We discuss the advantages of this method over the widely used cloud-in-cells and adaptive-kernel smoothing density estimators. Applying the new method to a cluster-sized DM halo simulated in warm and cold DM scenarios, we show how the expected differences in their substructure population translate into differences in the convergence and magnification maps. We anticipate that our method will provide the high-precision theoretical predictions required to interpret and fully exploit strong gravitational lensing observations.Comment: 13 pages, 13 figures. Updated fig 12, references adde

Precision modelling of the matter power spectrum in a Planck-like Universe

We use a suite of high-resolution N-body simulations and state-of-the-art perturbation theory to improve the code halofit, which predicts the nonlinear matter power spectrum. We restrict attention to parameters in the vicinity of the Planck Collaboration’s best fit. On large-scales (k≲ 0.07 h Mpc−1), our model evaluates the 2-loop calculation from the Multi-point Propagator Theory of Bernardeau et al. (2012). On smaller scales (k≳ 0.7 h Mpc−1), we transition to a smoothing-spline-fit model, that characterises the differences between the Takahashi et al. (2012) recalibration of halofit2012 and our simulations. We use an additional suite of simulations to explore the response of the power spectrum to variations in the cosmological parameters. In particular, we examine: the time evolution of the dark energy equation of state (w0, wa); the matter density Ωm; the physical densities of CDM and baryons (ωc, ωb); and the primordial power spectrum amplitude As, spectral index ns, and its running α. We construct correction functions, which improve halofit’s dependence on cosmological parameters. Our newly calibrated model reproduces all of our data with ≲ 1% precision. Including various systematic errors, such as choice of N-body code, resolution, and through inspection of the scaled second order derivatives, we estimate the accuracy to be ≲ 3% over the hyper-cube: w0 ∈ { − 1.05, −0.95}, wa ∈ { − 0.4, 0.4}, Ωm, 0 ∈ {0.21, 0.4}, ωc ∈ {0.1, 0.13}, ωb ∈ {2.0, 2.4}, ns ∈ {0.85, 1.05}, As ∈ {1.72 × 10−9, 2.58 × 10−9}, α ∈ { − 0.2, 0.2} up to k = 9.0 h Mpc−1 and out to z = 3. Outside of this range the model reverts to halofit2012. We release all power spectra data with the C-code NGenHalofit at: https://[email protected]/ngenhalofitteam/ngenhalofitpublic.git