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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.

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.

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.

The intrinsic alignment (IA) of observed galaxy shapes with the underlying cosmic web is a source of contamination in weak lensing surveys. Sensitive methods to identify the IA signal will therefore need to be included in the upcoming weak lensing analysis pipelines. Hydrodynamical cosmological simulations allow us to directly measure the intrinsic ellipticities of galaxies, and thus provide a powerful approach to predict and understand the IA signal. Here we employ the novel, large-volume hydrodynamical simulation MTNG740, a product of the MillenniumTNG (MTNG) project, to study the IA of galaxies. We measure the projected correlation functions between the intrinsic shape/shear of galaxies and various tracers of large-scale structure, w+g, w+m, w++ over the radial range $r_{\rm p} \in [0.02 , 200]\, h^{-1}{\rm Mpc}$ and at redshifts z = 0.0, 0.5, and 1.0. We detect significant signal-to-noise IA signals with the density field for both elliptical and spiral galaxies. We also find significant intrinsic shear–shear correlations for ellipticals. We further examine correlations of the intrinsic shape of galaxies with the local tidal field. Here we find a significant IA signal for elliptical galaxies assuming a linear model. We also detect a weak IA signal for spiral galaxies under a quadratic tidal torquing model. Lastly, we measure the alignment between central galaxies and their host dark-matter haloes, finding small to moderate misalignments between their principal axes that decline with halo mass.

The early release science results from JWST have yielded an unexpected abundance of high-redshift luminous galaxies that seems to be in tension with current theories of galaxy formation. However, it is currently difficult to draw definitive conclusions form these results as the sources have not yet been spectroscopically confirmed. It is in any case important to establish baseline predictions from current state-of-the-art galaxy formation models that can be compared and contrasted with these new measurements. In this work, we use the new large-volume ($L_\mathrm{box}\sim 740 \, \mathrm{cMpc}$) hydrodynamic simulation of the MillenniumTNG project, suitably scaled to match results from higher resolution – smaller volume simulations, to make predictions for the high-redshift (z ≳ 8) galaxy population and compare them to recent JWST observations. We show that the simulated galaxy population is broadly consistent with observations until z ∼ 10. From z ≈ 10–12, the observations indicate a preference for a galaxy population that is largely dust-free, but is still consistent with the simulations. Beyond z ≳ 12, however, our simulation results underpredict the abundance of luminous galaxies and their star-formation rates by almost an order of magnitude. This indicates either an incomplete understanding of the new JWST data or a need for more sophisticated galaxy formation models that account for additional physical processes such as Population III stars, variable stellar initial mass functions, or even deviations from the standard ΛCDM model. We emphasize that any new process invoked to explain this tension should only significantly influence the galaxy population beyond z ≳ 10, while leaving the successful galaxy formation predictions of the fiducial model intact below this redshift.

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.

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.

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.

Cosmological simulations are an important theoretical pillar for understanding non-linear structure formation in our Universe and for relating it to observations on large scales. In several papers, we introduce our MillenniumTNG (MTNG) project that provides a comprehensive set of high-resolution, large-volume simulations of cosmic structure formation aiming to better understand physical processes on large scales and to help interpret upcoming large-scale galaxy surveys. We here focus on the full physics box MTNG740 that computes a volume of $740\, \mathrm{Mpc}^3$ with a baryonic mass resolution of $3.1\times ~10^7\, \mathrm{M_\odot }$ using arepo with 80.6 billion cells and the IllustrisTNG galaxy formation model. We verify that the galaxy properties produced by MTNG740 are consistent with the TNG simulations, including more recent observations. We focus on galaxy clusters and analyse cluster scaling relations and radial profiles. We show that both are broadly consistent with various observational constraints. We demonstrate that the SZ-signal on a deep light-cone is consistent with Planck limits. Finally, we compare MTNG740 clusters with galaxy clusters found in Planck and the SDSS-8 RedMaPPer richness catalogue in observational space, finding very good agreement as well. However, simultaneously matching cluster masses, richness, and Compton-y requires us to assume that the SZ mass estimates for Planck clusters are underestimated by 0.2 dex on average. Due to its unprecedented volume for a high-resolution hydrodynamical calculation, the MTNG740 simulation offers rich possibilities to study baryons in galaxies, galaxy clusters, and in large-scale structure, and in particular their impact on upcoming large cosmological surveys.

We employ the hydrodynamical simulation illustrisTNG to inform the galaxy–halo connection of the Luminous Red Galaxy (LRG) and Emission Line Galaxy (ELG) samples of the Dark Energy Spectroscopic Instrument (DESI) survey at redshift z ∼ 0.8. Specifically, we model the galaxy colours of illustrisTNG and apply sliding DESI colour–magnitude cuts, matching the DESI target densities. We study the halo occupation distribution (HOD) model of the selected samples by matching them to their corresponding dark matter haloes in the illustrisTNG dark matter run. We find the HOD of both the LRG and ELG samples to be consistent with their respective baseline models, but also we find important deviations from common assumptions about the satellite distribution, velocity bias, and galaxy secondary biases. We identify strong evidence for concentration-based and environment-based occupational variance in both samples, an effect known as ‘galaxy assembly bias’. The central and satellite galaxies have distinct dependencies on secondary halo properties, showing that centrals and satellites have distinct evolutionary trajectories and should be modelled separately. These results serve to inform the necessary complexities in modelling galaxy–halo connection for DESI analyses and also prepare for building high-fidelity mock galaxies. Finally, we present a shuffling-based clustering analysis that reveals a 10–15 ${{\ \rm per\ cent}}$ excess in the LRG clustering of modest statistical significance due to secondary galaxy biases. We also find a similar excess signature for the ELGs, but with much lower statistical significance. When a larger hydrodynamical simulation volume becomes available, we expect our analysis pipeline to pinpoint the exact sources of such excess clustering signatures.