We present galaxy luminosity functions (LFs) for the Dark Energy Spectroscopic Instrument (DESI) DR2 Bright Galaxy Survey (BGS) in the g, r, z, and wl bands over 0.002 < z < 0.6 Our analysis uses updated k-corrections and evolutionary corrections, including new polynomial kcorrection fits derived from BGS Year 1 data that supersede earlier GAMA-based prescriptions. Exploiting the statistical power of DESI, we measure LFs to very faint magnitudes, reaching M-0.1(r)- 5 logh similar to -10. Independent measurements from the North and South survey regions show excellent agreement around the LF knee, but the very small statistical uncertainties reveal that simple analytic forms fail to capture the full LF shape. The bright end departs from a pure exponential decline, while the faint end exhibits complex, non-powerlaw behaviour, including a pronounced upturn at M-0.1(r) - 5 log(h) greater than or similar to - 15, which is stronger for red galaxies than for blue. We show that our LFs are largely complete for galaxies with surface brightness mu(50) < 25 and that an apparent steepening fainter than -13 is driven primarily by local overdensity and fragmentation of large galaxies. A systematic North-South offset at the brightest magnitudes is traced to red galaxies and may reflect shallower North photometry underestimating extended earlytype profiles, although this remains inconclusive. We therefore also provide LFs based on model Petrosian magnitudes. Redshift splitting reveals small but significant residuals, indicating limitations of a simple global evolutionary model. Using the redshift limits of J. Loveday et al. (2012), we find excellent agreement with GAMA, with substantially reduced statistical errors. These measurements provide a precise reference for studies of environmental and population-dependent LFs and for testing galaxy formation models.

The Wide-field Spectroscopic Telescope (WST) is a concept for a dedicated 12-m spectroscopic survey facility designed to address some of the most important questions in astrophysics in the 2040s. The WST will provide unprecedented spectroscopic survey capabilities by operating simultaneously over a 2-degree diameter field of view with 54 low-resolution spectrographs fed by 30,000 fibres, 8-16 high-resolution spectrographs fed by 2,000 fibres, and a large panoramic low-resolution integral-field spectrograph. Supported by Horizon Europe, the concept study has refined the science cases, facility architecture, operations model, sustainability strategy, and technology roadmap. The resulting reference design demonstrates that the WST is both scientifically transformative and technically feasible, while identifying the developments required to mitigate the remaining risks. The WST is designed as an ESO flagship facility for the post-ELT construction era and a key spectroscopic complement to the major imaging, time-domain, and multi-messenger facilities of the coming decades.

Our Local Group, dominated in mass by the Milky Way (MW) and M31, provides a unique laboratory for testing ΛCDM cosmology on small scales owing to its proximity. However, its connection to the surrounding large-scale environment, which is essential for interpreting its properties, is inadequately understood. In this work, we explore the connection between Local Group analogues (LGAs) and their surrounding large-scale environments using the ABACUSSUMMIT simulation suite, highlighting the key role of the coupling energy of the MW-M31 orbit, E_ coupling. We find that LGAs with high E_ coupling preferentially reside in denser regions, whereas those with low E_ coupling tend to occupy low-density environments. Furthermore, LGAs with low E_ coupling exhibit strong alignment with cosmic filaments, manifested as a pronounced polar anisotropy in the distribution of tracer haloes. By contrast, LGAs with high E_ coupling show a weaker polar anisotropy but an enhanced azimuthal anisotropy, with large-scale tracer haloes preferentially lying in the plane spanned by the halo pair and the orbital spin vector. Within this framework, our Local Group is characterised by typical E_ coupling residing in a relatively under-dense environment, yet it remains consistent with the 95% range of analogue systems identified in the simulation.

We present a unified physical framework for the fundamental metallicity relation (FMR), based on the mass-continuity equations. The FMR is not merely the anti-correlation between star formation rate (SFR) and gas metallicity (Z_ g) at fixed stellar mass (M_⋆); it is a redshift-invariant surface in the (M_⋆, SFR,Z_ g) space. We construct a minimal cosmological gas flow model, calibrated to reproduce the mass-metallicity relation, star-forming main sequence, and stellar-to-halo mass relation at z=0-3, and show that the FMR emerges as a prediction of the calibrated physics. Through controlled experiments that progressively simplify the model, we reveal that in a universe where both the star formation efficiency (ε) and mass-loading factor (η) are constants, the FMR reduces to a universal scaling between Z_ g and M_⋆/SFR, whose shape traces the transition from inflow-driven regime to equilibrium. The specific parameterisation of the observed FMR is not a fundamental symmetry but a contingent consequence of how ε and η depend on stellar mass and redshift. We show that the gaseous FMR (gFMR), defined in the (M_⋆,M_ g,Z_ g) space, is more fundamental than the standard FMR: in the inflow-driven limit, Z_ g is proportional to M_⋆/M_ g, and the approach to equilibrium is governed by M_⋆/M_ g and η alone. We derive an analytic solution for an idealised version of the model that provides closed-form expressions relating Z_ g, M_ g/M_⋆, and η, and show this framework accurately reproduces the cosmological gas flow model. By establishing the physical origin of the FMR and its connection to the more fundamental gFMR, we provide the theoretical foundation to turn metallicity scaling relations into precision probes of the baryon cycle over cosmic history.

Galaxy mergers drive both the size growth and the transformation from discs to spheroids, yet the prescriptions used to model these processes in semi-analytic frameworks have not been tested against the realistic merger population in cosmological hydrodynamical simulations. Using ≈ 4,500 mergers identified in the EAGLE simulation, we test an energy-conservation estimator for post-merger galaxy sizes and quantify merger-driven morphological transformation. The predicted remnant half-stellar-mass radius matches the simulated descendant size with a scatter of ≈ 0.12-0.15 dex and no significant systematic dependence on progenitor properties, while a commonly used dissipation correction applied to gas-rich mergers under-predicts the post-merger size by up to ≈ 0.4 dex in a cosmological context and increases the overall scatter. The per-merger size growth increases monotonically with the stellar mass ratio of the merging pair, from ≲ 0.03 dex for minor mergers to ≈ 0.10 dex for equal-mass mergers. From the energy-conservation estimator, we analytically derive the size growth efficiency per unit accreted stellar mass, η≡dlog_10 r_⋆/dlog_10 M_⋆, and show that η reaches ≈ 2 only in the idealised limit of collisionless minor mergers with zero orbital energy; as η is highly sensitive to the orbital energy at the time of merging, the minor merger channel cannot be established as the driver of the rapid size growth of massive galaxies without better constraints on this quantity. Beyond the size growth, mergers systematically reduce rotational support and increase triaxiality in proportion to mass ratio, but even the most nearly equal-mass mergers do not always fully destroy the disc, in tension with the complete disc destruction assumed in several semi-analytic models.

We present results from a set of high-fidelity simulated lightcones for the DESI One-Percent Survey, created from the Uchuu simulation. This 8 (Gpc/h)^3 N-body simulation comprises 2.1 trillion particles and provides high-resolution dark matter (sub)haloes in the framework of the Planck base-LCDM cosmology. Employing the subhalo abundance matching (SHAM) technique, we populate the Uchuu (sub)haloes with all four DESI tracers (BGS, LRG, ELG and QSO) to z = 2.1. Our method accounts for redshift evolution as well as the clustering dependence on luminosity and stellar mass. The two-point clustering statistics of the DESI One-Percent Survey align reasonably well with our predictions from Uchuu across scales ranging from 0.1 Mpc/h to 100 Mpc/h. Some discrepancies arise due to cosmic variance, incompleteness in the massive end of the stellar mass function, and a simplified galaxy-halo connection model. We find that the Uchuu BGS and LRG samples are adequately described using the standard 5-parameter halo occupation distribution model, while the ELGs and QSOs show agreement with an adopted Gaussian distribution for central halos with a power law for satellites. We observe a fair agreement in the large-scale bias measurements between data and mock samples, although the data exhibits smaller bias values, likely due to cosmic variance. The bias dependence on absolute magnitude, stellar mass and redshift aligns with that of previous surveys. These results improve simulated lightcone construction from cosmological models and enhance our understanding of the galaxy-halo connection, with pivotal insights from the first DESI data for the success of the final survey.

Assembly bias is the variation in the clustering of dark matter halos and galaxies that arises from correlations between the halo assembly history and the large-scale environment at fixed halo mass. In this work, we use the cosmological magnetohydrodynamical simulation TNG300 to investigate how assembly bias affects the environment-dependent galaxy luminosity function (LF). We measure the LFs in bins of large-scale environment for the original simulated galaxy sample and for a shuffled sample, where the galaxies are randomly reassigned among halos of similar mass to remove assembly bias. By comparing them, we find distinct signatures, showing variations in the number of galaxies at the ∼10% level across all luminosities. Assembly bias increases the tendency of galaxies to reside in denser environments and further dilutes underdense regions, beyond the trends governed by halo mass. When separating by color, we see that assembly bias has a much bigger effect on red galaxies fainter than M r − 5 log h = − 18.5 , which accounts for a ∼20% increase in the number of galaxies in the densest environment and a remarkable 50% decrease in the least dense regions. The ratio of these measurements for the densest and least dense regions provides a significant assembly bias signal for the faint red galaxies, larger than a factor of 2. Overall, our results provide a novel sensitive measure of assembly bias, offering valuable insight for modeling the effect and a potential new route to detect it in observations.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

The analysis of state-of-the-art cosmological surveys like the Dark Energy Spectroscopic Instrument (DESI) survey requires high-resolution, large-volume simulations. However, the computational cost of hydrodynamical simulations at these scales is prohibitive. Instead, dark matter (DM)-only simulations are used, with galaxies populated a posteriori, typically via halo occupation distribution (HOD) models. While effective, HOD models are statistical in nature and lack full physical motivation. In this work, we explore using neural networks (NNs) to learn the complex, physically motivated relationships between DM haloes and galaxy properties. Trained on small-volume, high-resolution hydrodynamical simulations, our NN predicts galaxy properties in a larger DM-only simulation and determines which galaxies should be classified as luminous red galaxies (LRGs). Comparing the original LRG sample to the one generated by our NN, we find that, while the subhalo mass distributions are similar, our NN selects fewer low-mass subhaloes as LRG hosts, possibly due to the absence of baryonic feedback effects in DM-only simulations. This feedback could brighten or redden galaxies, altering their classification. Finally, we generate a new LRG sample by fitting an HOD model to the NN-generated LRG sample. We verify that both the HOD- and NN-generated samples preserve a set of bias parameter relations, which assume that the higher-order parameters, b_s2 and b_3nl, are determined by the linear bias parameter b_1. These relations are commonly used to simplify clustering analyses.

We introduce a new scheme based on the marked correlation function to probe gravity using the large-scale structure of the Universe. We illustrate our approach by applying it to simulations of the metric-variation f(R) modified gravity theory and general relativity (GR). The modifications to the equations in f(R) gravity lead to changes in the environment of large-scale structures that could, in principle, be used to distinguish this model from GR. Applying the Monte Carlo Markov Chain algorithm, we use the observed number density and two-point clustering to fix the halo occupation distribution (HOD) model parameters and build mock galaxy catalogues from both simulations. To generate a mark for galaxies when computing the marked correlation function we estimate the local density using a Voronoi tessellation. Our approach allows us to isolate the contribution to the uncertainty in the predicted marked correlation function that arises from the range of viable HOD model parameters, in addition to the sample variance error for a single set of HOD parameters. This is critical for assessing the discriminatory power of the method. In a companion paper, we apply our new scheme to a current large-scale structure survey.

We use the GALFORM semi-analytical galaxy formation model implemented in the Planck Millennium N-body simulation to build a mock galaxy catalogue on an observer's past lightcone. The mass resolution of this N-body simulation is almost an order of magnitude better than in previous simulations used for this purpose, allowing us to probe fainter galaxies and hence build a more complete mock catalogue at low redshifts. The high time cadence of the simulation outputs allows us to make improved calculations of galaxy properties and positions in the mock. We test the predictions of the mock against the Physics of the Accelerating Universe Survey, a narrow-band imaging survey with highly accurate and precise photometric redshifts, which probes the galaxy population over a lookback time of 8 billion years. We compare the model against the observed number counts, redshift distribution, and evolution of the observed colours and find good agreement; these statistics avoid the need for model-dependent processing of the observations. The model produces red and blue populations that have similar median colours to the observations. However, the bimodality of galaxy colours in the model is stronger than in the observations. This bimodality is reduced on including a simple model for errors in the GALFORM photometry. We examine how the model predictions for the observed galaxy colours change when perturbing key model parameters. This exercise shows that the median colours and relative abundance of red and blue galaxies provide constraints on the strength of the feedback driven by supernovae used in the model.

We apply the marked correlation function test proposed by Armijo et al. (Paper I) to samples of luminous red galaxies (LRGs) from the final data release of the Sloan Digital Sky Survey (SDSS) III. The test assigns a density-dependent mark to galaxies in the estimation of the projected marked correlation function. Two gravity models are compared: general relativity (GR) and $f(R)$ gravity. We build mock catalogues which, by construction, reproduce the measured galaxy number density and two-point correlation function of the LRG samples, using the halo occupation distribution model (HOD). A range of HOD models give acceptable fits to the observational constraints, and this uncertainty is fed through to the error in the predicted marked correlation functions. The uncertainty from the HOD modelling is comparable to the sample variance for the SDSS-III LRG samples. Our analysis shows that current galaxy catalogues are too small for the test to distinguish a popular $f(R)$ model from GR. However, upcoming surveys with a better measured galaxy number density and smaller errors on the two-point correlation function, or a better understanding of galaxy formation, may allow our method to distinguish between viable gravity models.

The Dark Energy Spectroscopic Instrument (DESI) completed its five-month Survey Validation in May 2021. Spectra of stellar and extragalactic targets from Survey Validation constitute the first major data sample from the DESI survey. This paper describes the public release of those spectra, the catalogs of derived properties, and the intermediate data products. In total, the public release includes good-quality spectral information from 466,447 objects targeted as part of the Milky Way Survey, 428,758 as part of the Bright Galaxy Survey, 227,318 as part of the Luminous Red Galaxy sample, 437,664 as part of the Emission Line Galaxy sample, and 76,079 as part of the Quasar sample. In addition, the release includes spectral information from 137,148 objects that expand the scope beyond the primary samples as part of a series of secondary programs. Here, we describe the spectral data, data quality, data products, Large-Scale Structure science catalogs, access to the data, and references that provide relevant background to using these spectra.

The Dark Energy Spectroscopic Instrument (DESI) was designed to conduct a survey covering 14,000 deg ^2 over 5 yr to constrain the cosmic expansion history through precise measurements of baryon acoustic oscillations (BAO). The scientific program for DESI was evaluated during a 5 month survey validation (SV) campaign before beginning full operations. This program produced deep spectra of tens of thousands of objects from each of the stellar Milky Way Survey (MWS), Bright Galaxy Survey (BGS), luminous red galaxy (LRG), emission line galaxy (ELG), and quasar target classes. These SV spectra were used to optimize redshift distributions, characterize exposure times, determine calibration procedures, and assess observational overheads for the 5 yr program. In this paper, we present the final target selection algorithms, redshift distributions, and projected cosmology constraints resulting from those studies. We also present a One-Percent Survey conducted at the conclusion of SV covering 140 deg ^2 using the final target selection algorithms with exposures of a depth typical of the main survey. The SV indicates that DESI will be able to complete the full 14,000 deg ^2 program with spectroscopically confirmed targets from the MWS, BGS, LRG, ELG, and quasar programs with total sample sizes of 7.2, 13.8, 7.46, 15.7, and 2.87 million, respectively. These samples will allow exploration of the Milky Way halo, clustering on all scales, and BAO measurements with a statistical precision of 0.28% over the redshift interval z < 1.1, 0.39% over the redshift interval 1.1 < z < 1.9, and 0.46% over the redshift interval 1.9 < z < 3.5.

Accurate mock galaxy catalogues are crucial to validate analysis pipelines used to constrain dark energy models. We present a fast HOD-fitting method which we apply to the AbacusSummit simulations to create a set of mock catalogues for the DESI Bright Galaxy Survey, which contain r-band magnitudes and g-r colours. The halo tabulation method fits HODs for different absolute magnitude threshold samples simultaneously, preventing unphysical HOD crossing between samples. We validate the HOD fitting procedure by fitting to real-space clustering measurements and galaxy number densities from the MXXL BGS mock, which was tuned to the SDSS and GAMA surveys. The best-fitting clustering measurements and number densities are mostly within the assumed errors, but the clustering for the faint samples is low on large scales. The best-fitting HOD parameters are robust when fitting to simulations with different realisations of the initial conditions. When varying the cosmology, trends are seen as a function of each cosmological parameter. We use the best-fitting HOD parameters to create cubic box and cut sky mocks from the AbacusSummit simulations, in a range of cosmologies. As an illustration, we compare the Mr<-20 sample of galaxies in the mock with BGS measurements from the DESI one-percent survey. We find good agreement in the number densities, and the projected correlation function is reasonable, with differences that can be improved in the future by fitting directly to BGS clustering measurements. The cubic box and cut-sky mocks in different cosmologies are made publicly available.

We present FITCOV an approach for accurate estimation of the covariance of two-point correlation functions that requires fewer mocks than the standard mock-based covariance. This can be achieved by dividing a set of mocks into jackknife regions and fitting the correction term first introduced in Mohammad & Percival (2022), such that the mean of the jackknife covariances corresponds to the one from the mocks. This extends the model beyond the shot-noise limited regime, allowing it to be used for denser samples of galaxies. We test the performance of our fitted jackknife approach, both in terms of accuracy and precision, using lognormal mocks with varying densities and approximate EZmocks mimicking the Dark Energy Spectroscopic Instrument LRG and ELG samples in the redshift range of z = [0.8, 1.1]. We find that the Mohammad-Percival correction produces a bias in the two-point correlation function covariance matrix that grows with number density and that our fitted jackknife approach does not. We also study the effect of the covariance on the uncertainty of cosmological parameters by performing a full-shape analysis. We demonstrate that our fitted jackknife approach based on 25 mocks can recover unbiased and as precise cosmological parameters as the ones obtained from a covariance matrix based on 1000 or 1500 mocks, while the Mohammad-Percival correction produces uncertainties that are twice as large. The number of mocks required to obtain an accurate estimation of the covariance for the two-point correlation function is therefore reduced by a factor of 40-60. The FITCOV code that accompanies this paper is available at this GitHub repository

Over the next 5 yr, the Dark Energy Spectroscopic Instrument (DESI) will use 10 spectrographs with 5000 fibers on the 4 m Mayall Telescope at Kitt Peak National Observatory to conduct the first Stage IV dark energy galaxy survey. At z < 0.6, the DESI Bright Galaxy Survey (BGS) will produce the most detailed map of the universe during the dark-energy-dominated epoch with redshifts of >10 million galaxies spanning 14,000 deg(2). In this work, we present and validate the final BGS target selection and survey design. From the Legacy Surveys, BGS will target an r < 19.5 mag limited sample (BGS Bright), a fainter 19.5 < r < 20.175 color-selected sample (BGS Faint), and a smaller low-z quasar sample. BGS will observe these targets using exposure times scaled to achieve homogeneous completeness and cover the footprint three times. We use observations from the Survey Validation programs conducted prior to the main survey along with simulations to show that BGS can complete its strategy and make optimal use of "bright" time. BGS targets have stellar contamination <1%, and their densities do not depend strongly on imaging properties. BGS Bright will achieve >80% fiber assignment efficiency. Finally, BGS Bright and BGS Faint will achieve >95% redshift success over any observing condition. BGS meets the requirements for an extensive range of scientific applications. BGS will yield the most precise baryon acoustic oscillation and redshift-space distortion measurements at z < 0.4. It presents opportunities for new methods that require highly complete and dense samples (e.g., N-point statistics, multitracers). BGS further provides a powerful tool to study galaxy populations and the relations between galaxies and dark matter.

We introduce a new scheme based on the marked correlation function to probe gravity using the large-scale structure of the Universe. We illustrate our approach by applying it to simulations of the metric-variation $f(R)$ modified gravity theory and general relativity (GR). The modifications to the equations in $f(R)$ gravity lead to changes in the environment of large-scale structures that could, in principle, be used to distinguish this model from GR. Applying the Monte Carlo Markov Chain algorithm, we use the observed number density and two-point clustering to fix the halo occupation distribution (HOD) model parameters and build mock galaxy catalogues from both simulations. To generate a mark for galaxies when computing the marked correlation function we estimate the local density using a Voronoi tessellation. Our approach allows us to isolate the contribution to the uncertainty in the predicted marked correlation function that arises from the range of viable HOD model parameters, in addition to the sample variance error for a single set of HOD parameters. This is critical for assessing the discriminatory power of the method. In a companion paper we apply our new scheme to a current large-scale structure survey.

We use sparse regression methods (SRM) to build accurate and explainable models that predict the stellar mass of central and satellite galaxies as a function of properties of their host dark matter halos. SRM are machine learning algorithms that provide a framework for modelling the governing equations of a system from data. In contrast with other machine learning algorithms, the solutions of SRM methods are simple and depend on a relatively small set of adjustable parameters. We collect data from 35,459 galaxies from the EAGLE simulation using 19 redshift slices between z=0 and z=4 to parameterize the mass evolution of the host halos. Using an appropriate formulation of input parameters, our methodology can model satellite and central halos using a single predictive model that achieves the same accuracy as when predicted separately. This allows us to remove the somewhat arbitrary distinction between those two galaxy types and model them based only on their halo growth history. Our models can accurately reproduce the total galaxy stellar mass function and the stellar mass-dependent galaxy correlation functions (ξ(r)) of EAGLE. We show that our SRM model predictions of ξ(r) is competitive with those from sub-halo abundance matching and might be comparable to results from extremely randomized trees. We suggest SRM as an encouraging approach for populating the halos of dark matter only simulations with galaxies and for generating mock catalogues that can be used to explore galaxy evolution or analyse forthcoming large-scale structure surveys.