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Weak gravitational lensing is a powerful tool for precision tests of cosmology. As the expected deflection angles are small, predictions based on non-linear N -body simulations are commonly computed with the Born approximation. Here, we examine this assumption using DORIAN, a newly developed full-sky ray-tracing scheme applied to high-resolution mass-shell outputs of the two largest simulations in the MillenniumTNG suite, each with a 3000 Mpc box containing almost 1.1 trillion cold dark matter particles in addition to 16.7 billion particles representing massive neutrinos. We examine simple two-point statistics like the angular power spectrum of the convergence field, as well as statistics sensitive to higher order correlations such as peak and minimum statistics, void statistics, and Minkowski functionals of the convergence maps. Overall, we find only small differences between the Born approximation and a full ray-tracing treatment. While these are negligibly small at power-spectrum level, some higher order statistics show more sizeable effects; ray-tracing is necessary to achieve per cent level precision. At the resolution reached here, full-sky maps with 0.8 billion pixels and an angular resolution of 0.43 arcmin, we find that interpolation accuracy can introduce appreciable errors in ray-tracing results. We therefore implemented an interpolation method based on non-uniform fast Fourier transforms (NUFFT) along with more traditional methods. Bilinear interpolation introduces significant smoothing, while nearest grid point sampling agrees well with NUFFT, at least for our fiducial source redshift, |$z_s=1.0$|⁠ , and for the 1 arcmin smoothing we use for higher order statistics. [ABSTRACT FROM AUTHOR]

Extracting information from the total matter power spectrum with the precision needed for upcoming cosmological surveys requires unraveling the complex effects of galaxy formation processes on the distribution of matter. We investigate the impact of baryonic physics on matter clustering at z  = 0 using a library of power spectra from the Cosmology and Astrophysics with MachinE Learning Simulations project, containing thousands of |$(25\, h^{-1}\, {\rm Mpc})^3$| volume realizations with varying cosmology, initial random field, stellar and active galactic nucleus (AGN) feedback strength and subgrid model implementation methods. We show that baryonic physics affects matter clustering on scales |$k \gtrsim 0.4\, h\, \mathrm{Mpc}^{-1}$| and the magnitude of this effect is dependent on the details of the galaxy formation implementation and variations of cosmological and astrophysical parameters. Increasing AGN feedback strength decreases halo baryon fractions and yields stronger suppression of power relative to N -body simulations, while stronger stellar feedback often results in weaker effects by suppressing black hole growth and therefore the impact of AGN feedback. We find a broad correlation between mean baryon fraction of massive haloes (M 200c > 1013.5 M⊙) and suppression of matter clustering but with significant scatter compared to previous work owing to wider exploration of feedback parameters and cosmic variance effects. We show that a random forest regressor trained on the baryon content and abundance of haloes across the full mass range 1010 ≤ M halo/M⊙<1015 can predict the effect of galaxy formation on the matter power spectrum on scales k  = 1.0–20.0  |$h\, \mathrm{Mpc}^{-1}$|⁠. [ABSTRACT FROM AUTHOR]

Sunyaev–Zel'dovich (SZ) measurements can dramatically improve our understanding of the intergalactic medium and the role of feedback processes in galaxy formation, allowing us to calibrate important astrophysical systematics in cosmological constraints from weak lensing galaxy clustering surveys. However, the signal is only measured in a two-dimensional projection, and its correct interpretation relies on understanding the connection between observable quantities and the underlying intrinsic properties of the gas, in addition to the relation between the gas and the underlying matter distribution. One way to address these challenges is through the use of hydrodynamical simulations such as the high-resolution, large-volume MillenniumTNG suite. We find that measurements of the optical depth, τ, and the Compton- y parameter, Y , receive large line-of-sight contributions that can be removed effectively by applying a compensated aperture photometry filter. In contrast with other τ probes (e.g. X-rays and fast radio bursts), the kinematic SZ-inferred τ receives most of its signal from a confined cylindrical region around the halo due to the velocity decorrelation along the line of sight. Additionally, we perform fits to the Y – M and τ– M scaling relations and report best-fitting parameters adopting the smoothly broken power law formalism. We note that subgrid physics modelling can broaden the error bar on these by 30 per cent for intermediate-mass haloes (⁠|${\sim }10^{13} \, {\rm M}_{\odot }$|⁠). The scatter of the scaling relations can be captured by an intrinsic dependence on concentration and an extrinsic dependence on tidal shear. Finally, we comment on the effect of using galaxies rather than haloes in observations, which can bias the inferred profiles by ∼20 per cent for L * galaxies. [ABSTRACT FROM AUTHOR]

Upcoming large galaxy surveys will subject the standard cosmological model, Lambda Cold Dark Matter, to new precision tests. These can be tightened considerably if theoretical models of galaxy formation are available that can predict galaxy clustering and galaxy–galaxy lensing on the full range of measurable scales, throughout volumes as large as those of the surveys, and with sufficient flexibility that uncertain aspects of the underlying astrophysics can be marginalized over. This, in particular, requires mock galaxy catalogues in large cosmological volumes that can be directly compared to observation, and can be optimized empirically by Monte Carlo Markov Chains or other similar schemes, thus eliminating or estimating parameters related to galaxy formation when constraining cosmology. Semi-analytic galaxy formation methods implemented on top of cosmological dark matter simulations offer a computationally efficient approach to construct physically based and flexibly parametrized galaxy formation models, and as such they are more potent than still faster, but purely empirical models. Here, we introduce an updated methodology for the semi-analytic L-Galaxies code, allowing it to be applied to simulations of the new MillenniumTNG project, producing galaxies directly on fully continuous past lightcones, potentially over the full sky, out to high redshift, and for all galaxies more massive than |$\sim 10^8\, {\rm M}_\odot$|⁠. We investigate the numerical convergence of the resulting predictions, and study the projected galaxy clustering signals of different samples. The new methodology can be viewed as an important step towards more faithful forward-modelling of observational data, helping to reduce systematic distortions in the comparison of theory to observations. [ABSTRACT FROM AUTHOR]

Feedback from active galactic nuclei and stellar processes changes the matter distribution on small scales, leading to significant systematic uncertainty in weak lensing constraints on cosmology. We investigate how the observable properties of group-scale haloes can constrain feedback's impact on the matter distribution using Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS). Extending the results of previous work to smaller halo masses and higher wavenumber, k , we find that the baryon fraction in haloes contains significant information about the impact of feedback on the matter power spectrum. We explore how the thermal Sunyaev Zel'dovich (tSZ) signal from group-scale haloes contains similar information. Using recent Dark Energy Survey weak lensing and Atacama Cosmology Telescope tSZ cross-correlation measurements and models trained on CAMELS, we obtain 10 per cent constraints on feedback effects on the power spectrum at |$k \sim 5\, h\, {\rm Mpc}^{-1}$|⁠. We show that with future surveys, it will be possible to constrain baryonic effects on the power spectrum to |$\mathcal {O}(\lt 1~{{\ \rm per\ cent}})$| at |$k = 1\, h\, {\rm Mpc}^{-1}$| and |$\mathcal {O}(3~{{\ \rm per\ cent}})$| at |$k = 5\, h\, {\rm Mpc}^{-1}$| using the methods that we introduce here. Finally, we investigate the impact of feedback on the matter bispectrum, finding that tSZ observables are highly informative in this case. [ABSTRACT FROM AUTHOR]

We study weak gravitational lensing convergence maps produced from the MillenniumTNG simulations by direct projection of the mass distribution on the past backwards lightcone of a fiducial observer. We explore the lensing maps over a large dynamic range in simulation mass and angular resolution, allowing us to establish a clear assessment of numerical convergence. By comparing full physics hydrodynamical simulations with corresponding dark-matter-only runs, we quantify the impact of baryonic physics on the most important weak lensing statistics. Likewise, we predict the impact of massive neutrinos reliably far into the non-linear regime. We also demonstrate that the 'fixed & paired' variance suppression technique increases the statistical robustness of the simulation predictions on large scales not only for time slices but also for continuously output lightcone data. We find that both baryonic and neutrino effects substantially impact weak lensing shear measurements, with the latter dominating over the former on large angular scales. Thus, both effects must explicitly be included to obtain sufficiently accurate predictions for stage IV lensing surveys. Reassuringly, our results agree accurately with other simulation results where available, supporting the promise of simulation modelling for precision cosmology far into the non-linear regime. [ABSTRACT FROM AUTHOR]

Approximate methods to populate dark-matter haloes with galaxies are of great utility to galaxy surveys. However, the limitations of simple halo occupation models (HODs) preclude a full use of small-scale galaxy clustering data and call for more sophisticated models. We study two galaxy populations, luminous red galaxies (LRGs) and star-forming emission-line galaxies (ELGs), at two epochs, z  = 1 and z  = 0, in the large-volume, high-resolution hydrodynamical simulation of the MillenniumTNG project. In a partner study we concentrated on the small-scale, one-halo regime down to r ∼ 0.1  h −1 Mpc, while here we focus on modelling galaxy assembly bias in the two-halo regime, r ≳ 1  h −1 Mpc. Interestingly, the ELG signal exhibits scale dependence out to relatively large scales (r ∼ 20  h −1 Mpc), implying that the linear bias approximation for this tracer is invalid on these scales, contrary to common assumptions. The 10–15 per cent discrepancy is only reconciled when we augment our halo occupation model with a dependence on extrinsic halo properties ('shear' being the best-performing one) rather than intrinsic ones (e.g. concentration, peak mass). We argue that this fact constitutes evidence for two-halo galaxy conformity. Including tertiary assembly bias (i.e. a property beyond mass and 'shear') is not an essential requirement for reconciling the galaxy assembly bias signal of LRGs, but the combination of external and internal properties is beneficial for recovering ELG the clustering. We find that centrals in low-mass haloes dominate the assembly bias signal of both populations. Finally, we explore the predictions of our model for higher order statistics such as nearest neighbour counts. The latter supplies additional information about galaxy assembly bias and can be used to break degeneracies between halo model parameters. [ABSTRACT FROM AUTHOR]

Luminous red galaxies (LRGs) and blue star-forming emission-line galaxies (ELGs) are key tracers of large-scale structure used by cosmological surveys. Theoretical predictions for such data are often done via simplistic models for the galaxy–halo connection. In this work, we use the large, high-fidelity hydrodynamical simulation of the MillenniumTNG project (MTNG) to inform a new phenomenological approach for obtaining an accurate and flexible galaxy-halo model on small scales. Our aim is to study LRGs and ELGs at two distinct epochs, z  = 1 and z  = 0, and recover their clustering down to very small scales, |$r \sim 0.1 \ h^{-1}\, {\rm Mpc}$|⁠ , i.e. the one-halo regime, while a companion paper extends this to a two-halo model for larger distances. The occupation statistics of ELGs in MTNG inform us that (1) the satellite occupations exhibit a slightly super-Poisson distribution, contrary to commonly made assumptions, and (2) that haloes containing at least one ELG satellite are twice as likely to host a central ELG. We propose simple recipes for modelling these effects, each of which calls for the addition of a single free parameter to simpler halo occupation models. To construct a reliable satellite population model, we explore the LRG and ELG satellite radial and velocity distributions and compare them with those of subhaloes and particles in the simulation. We find that ELGs are anisotropically distributed within haloes, which together with our occupation results provides strong evidence for cooperative galaxy formation (manifesting itself as one-halo galaxy conformity); i.e. galaxies with similar properties form in close proximity to each other. Our refined galaxy-halo model represents a useful improvement of commonly used analysis tools and thus can be of help to increase the constraining power of large-scale structure surveys. [ABSTRACT FROM AUTHOR]

Cosmological inference with large galaxy surveys requires theoretical models that combine precise predictions for large-scale structure with robust and flexible galaxy formation modelling throughout a sufficiently large cosmic volume. Here, we introduce the millenniumTNG (MTNG) project which combines the hydrodynamical galaxy formation model of illustrisTNG with the large volume of the millennium simulation. Our largest hydrodynamic simulation, covering |$(500 \, h^{-1}{\rm Mpc})^3 \simeq (740\, {\rm Mpc})^3$|⁠ , is complemented by a suite of dark-matter-only simulations with up to 43203 dark matter particles (a mass resolution of |$1.32\times 10^8 \, h^{-1}{\rm M}_\odot$|⁠) using the fixed-and-paired technique to reduce large-scale cosmic variance. The hydro simulation adds 43203 gas cells, achieving a baryonic mass resolution of |$2\times 10^7 \, h^{-1}{\rm M}_\odot$|⁠. High time-resolution merger trees and direct light-cone outputs facilitate the construction of a new generation of semi-analytic galaxy formation models that can be calibrated against both the hydro simulation and observation, and then applied to even larger volumes – MTNG includes a flagship simulation with 1.1 trillion dark matter particles and massive neutrinos in a volume of |$(3000\, {\rm Mpc})^3$|⁠. In this introductory analysis we carry out convergence tests on basic measures of non-linear clustering such as the matter power spectrum, the halo mass function and halo clustering, and we compare simulation predictions to those from current cosmological emulators. We also use our simulations to study matter and halo statistics, such as halo bias and clustering at the baryonic acoustic oscillation scale. Finally we measure the impact of baryonic physics on the matter and halo distributions. [ABSTRACT FROM AUTHOR]

We introduce a novel technique for constraining cosmological parameters and galaxy assembly bias using non-linear redshift-space clustering of galaxies. We scale cosmological N -body simulations and insert galaxies with the SubHalo Abundance Matching extended (SHAMe) empirical model to generate over 175 000 clustering measurements spanning all relevant cosmological and SHAMe parameter values. We then build an emulator capable of reproducing the projected galaxy correlation function at the monopole, quadrupole, and hexadecapole level for separations between |$0.1\, h^{-1}\, {\rm Mpc}$| and |$25\, h^{-1}\, {\rm Mpc}$|⁠. We test this approach by using the emulator and Monte Carlo Markov Chain (MCMC) inference to jointly estimate cosmology and assembly bias parameters both for the MTNG740 hydrodynamic simulation and for a semi-analytical model (SAM) galaxy formation built on the MTNG740-DM dark matter-only simulation, obtaining unbiased results for all cosmological parameters. For instance, for MTNG740 and a galaxy number density of |$n\sim 0.01 h^{3}\, {\rm Mpc}^{-3}$|⁠ , we obtain |$\sigma _{8}=0.799^{+0.039}_{-0.044}$| and |$\Omega _\mathrm{M}h^2= 0.138^{+ 0.025}_{- 0.018}$| (which are within 0.4 and 0.2σ of the MTNG cosmology). For fixed Hubble parameter (h), the constraint becomes |$\Omega _\mathrm{M}h^2= 0.137^{+ 0.011}_{- 0.012}$|⁠. Our method performs similarly well for the SAM and for other tested sample densities. We almost always recover the true amount of galaxy assembly bias within 1σ. The best constraints are obtained when scales smaller than |$2\, h^{-1}\, {\rm Mpc}$| are included, as well as when at least the projected correlation function and the monopole are incorporated. These methods offer a powerful way to constrain cosmological parameters using galaxy surveys. [ABSTRACT FROM AUTHOR]

To extract information from the clustering of galaxies on non-linear scales, we need to model the connection between galaxies and haloes accurately and in a flexible manner. Standard halo occupation distribution (HOD) models make the assumption that the galaxy occupation in a halo is a function of only its mass, however, in reality; the occupation can depend on various other parameters including halo concentration, assembly history, environment, and spin. Using the IllustrisTNG hydrodynamical simulation as our target, we show that machine learning tools can be used to capture this high-dimensional dependence and provide more accurate galaxy occupation models. Specifically, we use a random forest regressor to identify which secondary halo parameters best model the galaxy–halo connection and symbolic regression to augment the standard HOD model with simple equations capturing the dependence on those parameters, namely the local environmental overdensity and shear, at the location of a halo. This not only provides insights into the galaxy formation relationship but also, more importantly, improves the clustering statistics of the modelled galaxies significantly. Our approach demonstrates that machine learning tools can help us better understand and model the galaxy–halo connection, and are therefore useful for galaxy formation and cosmology studies from upcoming galaxy surveys. [ABSTRACT FROM AUTHOR]