Cosmological Simulations with Massive Neutrinos: Efficiency and Accuracy

A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter \zeta, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (\zeta = 1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance to include the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size and initial redshift). We find that, the nonlinear power spectra can differ by ~30% for 10% deviation from GR (|\zeta-1| = 0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.

We examine the influence of percent-level dark energy corrections to the nonlinear matter power spectrum on constraints of the dark energy equation of state from future weak lensing probes. We explicitly show that a poor approximation (off by $\ensuremath{\gtrsim}10%$) to the nonlinear corrections causes a $\ensuremath{\gtrsim}1\ensuremath{\sigma}$ bias on the determination of the dark energy equation of state. Future weak lensing surveys must therefore incorporate dark energy modifications to the nonlinear matter power spectrum accurate to the percent-level, to avoid introducing significant bias in their measurements. For the WMAP5 cosmology, the more accurate power spectrum is more sensitive to dark energy properties, resulting in a factor of 2 improvement in dark energy equation of state constraints. We explore the complementary constraints on dark energy from future weak lensing and supernova surveys. A space-based, Joint Dark Energy Mission-like survey measures the equation of state in five independent redshift bins to $\ensuremath{\sim}10%$, while this improves to $\ensuremath{\sim}5%$ for a wide-field ground-based survey like the Large Synoptic Survey Telescope. These constraints are contingent upon our ability to control weak lensing systematic uncertainties to the sub-percent level.

While cosmological simulations of galaxy formation have reached maturity and are able to reproduce many fundamental galaxy and halo properties, no consensus has yet been reached on the impact of ‘baryonic feedback’ on the non-linear matter power spectrum. This severely limits the precision of (and potentially biases) small-scale cosmological constraints obtained from weak lensing and galaxy surveys. Recent observational evidence indicates that ‘baryonic feedback’ may be more extreme than commonly assumed in current cosmological hydrodynamical simulations. In this paper, we therefore explore a range of empirical AGN feedback models, within the FABLE simulation suite, with different parameterizations as a function of cosmic time, host halo properties, and/or spatial location where feedback energy is thermalized. We demonstrate that an AGN radio-mode feedback acting in a larger population of black holes, with jets thermalizing at relatively large cluster-centric distances, as exemplified by our XFABLE model, is in good agreement with the latest weak lensing + kSZ constraints across all k-scales. Furthermore, XFABLE maintains good agreement with the galaxy stellar mass function, and gas fraction measurements, as well as consistency with key galaxy group and cluster properties, including scaling relations and ICM radial profiles, within current observational uncertainties. Our work highlights the pressing need to model black hole accretion and feedback physics with a greater level of realism, including relativistic, magnetized jets in full cosmological simulations. Finally, we discuss how a range of complementary observational probes in the near future will enable us to constrain AGN feedback models, and therefore reduce ‘baryonic feedback’ modelling uncertainty for the upcoming era of large cosmological surveys.

The Lagrangian perturbation theory provides a simple yet powerful way of computing the nonlinear matter power spectrum, and it has been applied to biased tracers such as halos and galaxies. The number conservation of matter particles allows a simple relation between the fluctuations at the initial and late times, which is essential in deriving the exact expression for the nonlinear matter power spectrum. Here, we investigate the significance of the number conservation in the Lagrangian perturbation theory for biased tracers. We use N-body simulations to test the significance of the number conservation, by tracing dark matter halo samples in time. For the mass-bin sample Δ log M h ( h − 1 M ⊙ ) = 0.5 at z ≃ 3, the theoretical predictions for the halos overestimate the power spectrum at z = 0 by a factor of 3, while the simulation results match the theoretical predictions if the number conservation of halos is imposed in the simulations throughout the evolution. Starting with a halo sample at z = 0 as another test, we trace back in time the particles that belong to the halos at z = 0 and use their center-of-mass positions as halo positions at z &gt; 0. The halo power spectra at z &gt; 0 from the simulations agree with the theoretical predictions of the Lagrangian perturbation theory. This numerical experiment proves that the number conservation is crucial in the Lagrangian perturbation theory predictions. We discuss the implications for various applications of the Lagrangian perturbation theory for biased tracers.

The integrated shear 3-point correlation function ζ± is a higher-order statistic of the cosmic shear field that describes the modulation of the 2-point correlation function ξ± by long-wavelength features in the field. Here, we introduce a new theoretical model to calculate ζ± that is accurate on small angular scales, and that allows to take baryonic feedback effects into account. Our model builds on the realization that the small-scale ζ± is dominated by the non-linear matter bispectrum in the squeezed limit, which can be evaluated accurately using the non-linear matter power spectrum and its first-order response functions to density and tidal field perturbations. We demonstrate the accuracy of our model by showing that it reproduces the small-scale ζ± measured in simulated cosmic shear maps. The impact of baryonic feedback enters effectively only through the corresponding impact on the non-linear matter power spectrum, thereby permitting to account for these astrophysical effects on ζ± similarly to how they are currently accounted for on ξ±. Using a simple idealized Fisher matrix forecast for a DES-like survey we find that, compared to ξ±, a combined $\xi _{\pm }\ \&amp;\ \zeta _{\pm }$ analysis can lead to improvements of order $20\!-\!40{{\ \rm per\ cent}}$ on the constraints of cosmological parameters such as σ8 or the dark energy equation of state parameter w0. We find similar levels of improvement on the constraints of the baryonic feedback parameters, which strengthens the prospects for cosmic shear data to obtain tight constraints not only on cosmology but also on astrophysical feedback models. These encouraging results motivate future works on the integrated shear 3-point correlation function towards applications to real survey data.

We show how to estimate in a robust and conservative way the sensitivity of an Euclid-like survey to the parameters of a minimal ΛCDM and the total neutrino mass for a Euclid-like survey.To include as much information as possible, and use the mildly non-linear scales in a meaningful way, we present a method for including theoretical errors.Two sets of errors are considered: (i) one to account for uncertainties in the modelling of the effect of neutrinos on the non-linear galaxy power spectrum and (ii) one to parametrise the overall residual uncertainties in modelling the non-linear galaxy power spectrum at small scales.We discuss how the inclusion of these errors impact the error on M ν by comparing different ansatz, and we mention the effect of taking into account data from smaller scales considering our current understanding of non-linearities.We also discuss how this method can be extended to other probes to have a reliable estimate of the current and achievable sensitivity to the total neutrino mass.

Kernel-based emulator for the 3D matter power spectrum from CLASS

Many of the most exciting questions in astrophysics and cosmology, including the majority of observational probes of dark energy, rely on an understanding of the nonlinear regime of structure formation. In order to fully exploit the information available from this regime and to extract cosmological constraints, accurate theoretical predictions are needed. Currently such predictions can only be obtained from costly, precision numerical simulations. This paper is the third in a series aimed at constructing an accurate calibration of the nonlinear mass power spectrum on Mpc scales for a wide range of currently viable cosmological models, including dark energy. The first two papers addressed the numerical challenges, and the scheme by which an interpolator was built from a carefully chosen set of cosmological models. In this paper we introduce the "Coyote Univers"' simulation suite which comprises nearly 1,000 N-body simulations at different force and mass resolutions, spanning 38 wCDM cosmologies. This large simulation suite enables us to construct a prediction scheme, or emulator, for the nonlinear matter power spectrum accurate at the percent level out to k~1 h/Mpc. We describe the construction of the emulator, explain the tests performed to ensure its accuracy, and discuss how the central ideas may be extended to a wider range of cosmological models and applications. A power spectrum emulator code is released publicly as part of this paper.

We investigate the impact that warm dark matter (WDM) has in terms of 21 cm intensity mapping in the post-reionization Universe at z=3−5. We perform hydrodynamic simulations for 5 different models: cold dark matter and WDM with 1,2,3,4 keV (thermal relic) mass and assign the neutral hydrogen a-posteriori using two different methods that both reproduce observations in terms of column density distribution function of neutral hydrogen systems. Contrary to naive expectations, the suppression of power present in the linear and non-linear matter power spectra, results in an increase of power in terms of neutral hydrogen and 21 cm power spectra. This is due to the fact that there is a lack of small mass halos in WDM models with respect to cold dark matter: in order to distribute a total amount of neutral hydrogen within the two cosmological models, a larger quantity has to be placed in the most massive halos, that are more biased compared to the cold dark matter cosmology. We quantify this effect and address significance for the telescope SKA1-LOW, including a realistic noise modeling. The results indicate that we will be able to rule out a 4 keV WDM model with 5000 hours of observations at z>3, with a statistical significance of >3 σ, while a smaller mass of 3 keV, comparable to present day constraints, can be ruled out at more than 2 σ confidence level with 1000 hours of observations at z>5.

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

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations.We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β2, with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications.

Extracting precise cosmology from weak lensing surveys requires modelling the non-linear matter power spectrum, which is suppressed at small scales due to baryonic feedback processes. However, hydrodynamical galaxy formation simulations make widely varying predictions for the amplitude and extent of this effect. We use measurements of Dark Energy Survey Year 3 weak lensing (WL) and Atacama Cosmology Telescope DR5 kinematic Sunyaev–Zel’dovich (kSZ) to jointly constrain cosmological and astrophysical baryonic feedback parameters using a flexible analytical model, ‘baryonification’. First, using WL only, we compare the $S_8$ constraints using baryonification to a simulation-calibrated halo model, a simulation-based emulator model, and the approach of discarding WL measurements on small angular scales. We find that model flexibility can shift the value of $S_8$ and degrade the uncertainty. The kSZ provides additional constraints on the astrophysical parameters, with the joint WL + kSZ analysis constraining $S_8=0.823^{+0.019}_{-0.020}$. We measure the suppression of the non-linear matter power spectrum using WL + kSZ and constrain a mean feedback scenario that is more extreme than the predictions from most hydrodynamical simulations. We constrain the baryon fractions and the gas mass fractions and find them to be generally lower than inferred from X-ray observations and simulation predictions. We conclude that the WL + kSZ measurements provide a new and complementary benchmark for building a coherent picture of the impact of gas around galaxies across observations.

Future large scale structure observations are expected to be sensitiveto small neutrino masses, of the order of 0.05 eV or more. However,forecasts are based on the assumption that by the time at which thesedatasets will be available, the non-linear spectrum in presence ofneutrino mass will be predicted with an accuracy at least equal to theneutrino mass effect itself, i.e. about 3%. Motivated by theseconsiderations, we present the computation of the non-linear powerspectrum of ΛCDM models in the presence of massive neutrinosusing the Renormalization Group (RG) time-flow approach, which amounts to aresummation of perturbative corrections to thematter power spectrum to all orders. We compare our results with those obtained withother methods, i.e. linear theory, one-loop perturbation theory andN-body simulations and show that the time-RG method improvesthe one-loop method in fitting the N-body data, especially in determining the suppression of the matter power spectrum when neutrinoare massive with respect to the linear power spectrum.

Nonlinear gravitational evolution induces strong nonlinearities in the observed cosmological density fields, leading to positive off-diagonal correlations in the power spectrum covariance. This has caused the information saturation in the power spectrum, e.g., the neutrino mass constraints from the nonlinear power spectra are lower than their linear counterparts by a factor of ∼2 at z = 0. In this paper, we explore how nonlinear reconstruction methods improve the cosmological information from nonlinear cosmic fields. By applying nonlinear reconstruction to cold dark matter fields from the Quijote simulations, we find that nonlinear reconstruction can improve the constraints on cosmological parameters significantly, nearly reaching the linear theory limit. For neutrino mass, the result is only 12% lower than the linear power spectrum, i.e., the theoretical best result. This makes nonlinear reconstruction an efficient and useful method to extract neutrino information from current and upcoming galaxy surveys.

We measure the covariance of the non-linear matter power spectrum from N-body simulations using two methods. In the first case, the covariance of power is estimated from the scatter over many random realizations of the density field. In the second, we use a novel technique to measure the covariance matrix from each simulation individually by re-weighting the density field with a carefully chosen set of functions. The two methods agree at linear scales, but unexpectedly they disagree substantially at increasingly non-linear scales. Moreover, the covariance of non-linear power measured using the re-weightings method changes with box size. The numerical results are consistent with an explanation given in a companion paper, which argues that the cause of the discrepancy is beat-coupling, in which products of Fourier modes separated by a small wavevector couple by gravitational growth to the large-scale beat mode between them. We calculate the information content of the non-linear power spectrum (about the amplitude of the initial, linear power spectrum) using both methods and confirm the result of a previous paper, that at translinear scales the power spectrum contains little information over and above that in the linear power spectrum, but that there is a marked increase in information at non-linear scales. We suggest that, in real galaxy surveys, the covariance of power at non-linear scales is likely to be dominated by beat-coupling to the largest scales of the survey and that, as a result, only part of the information potentially available at non-linear scales is actually measurable from real galaxy surveys.