Benjamin D. Wandelt

We present a simple and robust framework to assess the information content of the power spectrum of a marked dark matter density field within the effective field theory of large scale structure, providing a physically motivated regime of validity of perturbation theory for such fields. We optimize the choice of mark to maximize the constraining power on cosmological parameters, focusing on the resulting reduction of parameter uncertainties. After marginalizing over the small-scale counterterms, we find improvements in the parameter error bars by a factor of approximately 1.30–2.3, 1.3–8.3, and 1.2–2.5 for Ω m , σ 8 , and h , respectively, depending on redshift and smoothing scale. The optimized mark exhibits a simple functional form, for which we provide a physical interpretation in terms of its response to the underlying density field. The results presented in this work, which are valid for dark matter in real space, demonstrate the potential of marked statistics as a tool to extract additional cosmological information beyond standard two-point analyses and open a pathway for further exploration of nonlinear transformations of the density field.

Primordial non-Gaussianity is predicted by various inflationary models, and N-body simulations are a crucial tool for studying its imprints on large-scale structure. In this work, we present GENGARS (GEnerator of Non-Gaussian ARbitrary Shapes), a framework for generating accurate non-Gaussian initial conditions for N-body simulations. It builds upon the formulation introduced by Wagner & Verde (2012), enabling to generate a primordial gravitational potential with a desired separable bispectrum B _Φ ( k ₁ , k ₂ , k ₃ ). For the local, equilateral and orthogonal non-Gaussian templates, we benchmark our method against the well-established 2LPT-PNG code. We show that GENGARS achieves improved accuracy and lower noise by suppressing spurious contributions to the primordial power spectrum. This paper aims at presenting the method, quantifying its performance and illustrating the benefits and applicable use cases over existing approaches.

The advent of Stage IV galaxy redshift surveys such as DESI and Euclid marks the beginning of an era of precision cosmology, with one key objective being the detection of primordial non-Gaussianities (PNG), which are potential signatures of inflationary physics. In particular, constraining the amplitude of local-type PNG, parametrised by f _NL , with σ f _NL ∼ 1, would provide a critical test of single-versus-multi-field inflation scenarios. While current large-scale structure and cosmic microwave background analyses have achieved σ f _NL ∼ 5–9, further improvements demand novel data compression strategies. We propose a hybrid estimator that hierarchically combines standard two-point and three-point statistics with a field-level neural summary, motivated by recent theoretical works that have indicated that such a combination is nearly optimal in effectively disentangling primordial from late-time non-Gaussianity. We employed P ATCH N ET , a convolutional neural network that extracts small-scale information from sub-volumes (i.e. patches) of the halo number density field, while large-scale information is retained via the power spectrum and bispectrum. Using Q UIJOTE -PNG simulations, we evaluated the Fisher information of this combined estimator across various redshifts, halo mass cuts, and scale cuts. Our results demonstrate that the inclusion of patch-based field-level compression always enhances constraints on f _NL , reaching gains of 30–45% at low k _max (∼ 0.1 h Mpc ⁻¹ ) and of 15–25% when the standard summary statistics include k modes comparable to those probed by the patches ( k _max ∼ 0.4 h Mpc ⁻¹ ). This shows that, even in this configuration, information from beyond the bispectrum can be captured. This approach offers a computationally efficient and scalable pathway to tightening the PNG constraints with forthcoming survey data.

What is the cosmological information content of a cubic Gigaparsec of dark matter? Extracting cosmological information from the non-linear matter distribution has high potential to tighten parameter constraints in the era of next-generation surveys such as Euclid, DESI, and the Vera Rubin Observatory. Traditional approaches relying on summary statistics like the power spectrum and bispectrum, though analytically tractable, fail to capture the full non-Gaussian and non-linear structure of the density field. Simulation-Based Inference (SBI) provides a powerful alternative by learning directly from forward-modeled simulations. In this work, we apply SBI to the Quijote dark matter simulations and introduce a hierarchical method that integrates small-scale information from field sub-volumes or patches with large-scale statistics such as power spectrum and bispectrum. This hybrid strategy is efficient both computationally and in terms of the amount of training data required. It overcomes the memory limitations associated with full-field training. We show that our approach enhances Fisher information relative to analytical summaries and matches that of a very different approach (wavelet-based statistics), hinting that we are estimating most of the information content of the dark matter density field at the resolution of ∼ 7.8 Mpc/ h .

The advent of increasingly advanced surveys and cosmic tracers has motivated the development of new inference techniques and novel approaches to extracting information from cosmic fields. A central challenge in this endeavor is to quantify the information content carried by these summary statistics in cosmic fields. In particular, how should we assess which statistics are more informative than others and assess the exact degree of complementarity of the information from each statistic? Here, we introduce mutual information (MI), which provides, from an information-theoretic perspective, a natural framework for assessing the sufficiency and complementarity of summary statistics in cosmological data. We demonstrate how MI can be applied to typical inference tasks to make information-theoretic evaluations, using two representative examples: the cosmic microwave background map, from which the power spectrum (PS) extracts almost all information as is expected for a Gaussian random field, and the 21 cm brightness temperature map, from which the scattering transform extracts the most non-Gaussian information but which is complementary to the PS and bispectrum. Our results suggest that MI offers a robust theoretical foundation for evaluating and improving summaries, thereby enabling a deeper understanding of cosmic fields from an information-theoretic perspective.

In this study, we investigate the impact of covariance within uncertainties on the inference of cosmological and astrophysical parameters, specifically focusing on galaxy stellar mass functions derived from the CAMELS simulation suite. Utilizing both Fisher analysis and implicit likelihood inference, we explore how different covariance structures, including simple toy models and physics-motivated uncertainties, affect posterior distributions and parameter variances. Our methodology utilizes forward modeling via emulators that are trained on CAMELS simulations to produce stellar mass functions based on input parameters, subsequently incorporating Gaussian noise as defined by covariance matrices. We examine both toy model covariance matrices and physically motivated covariance matrices derived from observational factors like the stellar initial mass function and photometric aperture size. Our results demonstrate that covariance terms significantly influence parameter inference, often leading to tighter constraints or revealing complex, multimodal posterior distributions. These findings underscore the necessity of accounting for covariance when interpreting astrophysical observations, especially in fields where accurate parameter estimation is critical for model validation and hypothesis testing.

Context. While cosmic voids are now recognized as a valuable cosmological probe, it is challenging to identify them in a galaxy catalog for multiple reasons: Observational effects such as holes in the mask or magnitude selection hinder the detection process; galaxies are biased tracers of the underlying dark matter distribution; and it is nontrivial to estimate the detection significance and parameter uncertainties for individual voids. Aims. Our goal is to extract a catalog of voids from constrained simulations of the large-scale structure that are consistent with the observed galaxy positions and effectively represent statistically independent realizations of the probability distribution of the cosmic web. This allows us to carry out a full Bayesian analysis of the structures emerging in the Universe. Methods. We used 50 posterior realizations of the large-scale structure in the Manticore-Local suite, obtained from the 2M++ galaxies, with z ≲ 0.1 and a sky area between ∼23 000 − 36 000 deg ² . Running the VIDE void finder on each realization, we extracted 50 independent void catalogs. We performed a posterior clustering analysis to identify high-significance voids at the 5 σ level, and we assessed the probability distribution of their properties by combining the contributions of independent large-scale structure realizations. Results. We produced a publicly available catalog of 100 voids with a high statistical significance, including the probability distributions of the centers and the radii of the voids. We characterized the morphology of these regions and effectively produced a template for density environments that can be used in astrophysical applications such as galaxy evolution studies. Conclusions. While providing the community with a detailed catalog of voids in the nearby Universe, this work also constitutes an approach to identifying cosmic voids from galaxy surveys that allows us to rigorously account for the observational systematics intrinsic to direct detection, and to provide a Bayesian characterization of their properties.

How many simulations do we need to train machine learning methods to extract information available from summary statistics of the cosmological density field? Neural methods have shown the potential to extract nonlinear information available from cosmological data. To achieve this requires appropriate network architectures and a sufficient number of simulations for training the networks. This is the first detailed convergence study in which a neural network (NN) is trained to extract maximally informative summary statistics for cosmological inference. We show that currently available simulation suites, such as the Quijote Latin Hypercube with 2000 simulations, do not provide sufficient training data for a generic NN to reach the optimal regime. We present a case study in which we train a moment network to infer cosmological parameters from the nonlinear dark matter power spectrum, where the optimal information content can be computed through asymptotic analysis using the Cramér-Rao information bound. We find an empirical neural scaling law that predicts how much information a NN can extract from highly informative summary statistics as a function of the number of simulations used to train the network, for a wide range of architectures and hyperparameters. Looking beyond two-point statistics, we find a similar scaling law for the training of neural posterior inference using wavelet scattering transform coefficients. To verify our method, we created the largest publicly released suite of cosmological simulations, the B IG S OBOL S EQUENCE (BSQ), consisting of 32 768 Λ cold dark matter N-body simulations uniformly covering the Λ cold dark matter parameter space. Our method enables efficient planning of simulation campaigns for machine learning applications in cosmology, while the BSQ dataset provides an unprecedented resource for studying the convergence behavior of NNs in cosmological parameter inference. Our results suggest that new large simulation suites or new training approaches will be necessary to infer information-optimal parameters from nonlinear simulations.

The rapid advancement of large-scale cosmological simulations has opened new avenues for cosmological and astrophysical research. However, the increasing diversity among cosmological simulation models presents a challenge to the robustness. In this work, we develop the Model-Insensitive ESTimator (Miest), a machine that can robustly estimate the cosmological parameters, Ω_m and σ ₈, from neural hydrogen maps of simulation models in the Cosmology and Astrophysics with MachinE Learning Simulations project—IllustrisTNG, SIMBA, Astrid, and SWIFT -Eagle. An estimator is considered robust if it possesses a consistent predictive power across all simulations, including those used during the training phase. We train our machine using multiple simulation models and ensure that it only extracts common features between the models while disregarding the model-specific features. This allows us to develop a novel model that is capable of accurately estimating parameters across a range of simulation models, without being biased toward any particular model. Upon the investigation of the latent space—a set of summary statistics, we find that the implementation of robustness leads to the blending of latent variables across different models, demonstrating the removal of model-specific features. In comparison to a standard machine lacking robustness, the average performance of Miest on the unseen simulations during the training phase has been improved by ∼17% for Ω_m and 38% for σ ₈. By using a machine learning approach that can extract robust, yet physical features, we hope to improve our understanding of galaxy formation and evolution in a (subgrid) model-insensitive manner, and ultimately, gain insight into the underlying physical processes responsible for robustness.

The marked power spectrum — a two-point correlation function of a weighted density field — has emerged as a promising tool for extracting cosmological information from the large-scale structure of the Universe. In this work, we present the first comprehensive analytical study of the marked power spectrum's sensitivity to primordial non-Gaussianity (PNG) of the non-local type. We extend previous effective field theory frameworks to incorporate PNG, developing a complete theoretical model that we validate against the Quijote simulation suite. Through a systematic Fisher analysis, we compare the constraining power of the marked power spectrum against traditional approaches combining the power spectrum and bispectrum (P+B). We explore different choices of mark parameters to evaluate their impact on parameter constraints, particularly focusing on equilateral and orthogonal PNG as well as neutrino masses. Our analysis shows that while marking up underdense regions yields optimal constraints in the low shot-noise regime, the marked power spectrum's performance for discrete tracers with BOSS-like number densities does not surpass that of P+B analysis at mildly non-linear scales (k ≲ 0.25 h/Mpc). However, the marked approach offers several practical advantages, including simpler estimation procedures and potentially more manageable systematic effects. Our theoretical framework reveals how the marked power spectrum incorporates higher-order correlation information through terms resembling tree-level bispectra and power spectrum convolutions. This work establishes a robust foundation for applying marked statistics to future large-volume surveys.