Alexander Eggemeier

Stage-IV galaxy surveys will provide the opportunity to test cosmological models and the underlying theory of gravity with unparal-leled precision. In this context, it is crucial for the Euclid mission to leverage its spectroscopic and photometric probes to systematically investigate and incorporate non-standard cosmological models, including modified gravity, alternative dark energy scenarios, massive neutrinos, and primordial non-Gaussianity. For this, we produce and release publicly simulated galaxy catalogues from a broad suite of non-standard cosmological simulations, which we processed through a model-independent analytical pipeline, making use of ROCKSTAR for halo identification, and a modified version of the SciPic library for the galaxy-halo connection using the halo occupation distribution framework. One of the goals of this paper is also to test the validity of the template-fitting method for galaxy clustering analyses, even in cases where the template significantly differ from data. For this purpose, we investigate the multipoles of the two-point correlation function in redshift space and VDG _∞ , a highly performant, state-of-the-art model for galaxy clustering. Across a wide range of models, the linear growth rate multiplied by the matter density within spheres of radius of 12 Mpc, fσ ₁₂ , exhibits a notable robustness to the choice of cosmological template. Compared to previous works, our study extends this result to numerous scenarios with markedly distinct gravitational or dark energy dynamics. We find that the most of the scatter in cosmological parameter inference already appears when using the cosmological model of the simulations as templates. Using a ‘wrong’ template can also introduce an additional scatter, although with smaller amplitude. Often, we find deviations much larger than error bars, meaning that the Gaussian approximation for the covariance might need to be further studied. Looking ahead, future cosmological investigations must broaden their scope to include a diverse array of non-standard theoretical frameworks extending beyond ΛCDM and rudimentary dynamic dark energy models.

We present the first end-to-end validation of the Euclid baryon acoustic oscillation (BAO) analysis pipeline, encompassing density-field reconstruction, two-point correlation function measurement, and cosmological parameter inference. Using eight Euclid -like mock catalogues extracted from each of the four snapshots of the Flagship 1 (FS1) simulation, which is designed to replicate the statistical properties of the first Euclid data release (DR1), we assessed the performance of the two standard BAO reconstruction methods based on the Zeldovich approximation, R EC S YM and R EC I SO , in four redshift snapshots (0.9 ≤ z ≤ 1.8). The pipeline introduces several methodological advances: an emulator-based model evaluator ( Bora.jl ) combined with a Hamiltonian Monte Carlo sampler ( NUTS ), achieving a speed-up of more than 500 times relative to standard Monte Carlo Markov chains, and a semi-analytical covariance estimator ( BeXiCov+WinCov ) that enables robust error estimates with only eight mock realisations and remains stable under variations in the fiducial cosmology. Together, these components ensure computational efficiency while significantly reducing the risk of underestimating the parameter uncertainties. The two reconstruction schemes yield unbiased BAO measurements for all redshifts and user-defined choices, including the smoothing scale and fiducial cosmology. In each snapshot, reconstruction enhances the figure of merit for {Ω _m , H ₀ r _s } by a factor of ∼3, which is equivalent to tripling the effective survey volume. When we combined the four redshift bins, the improvement remained substantial, with BAO-only constraints reaching ∼10% precision on Ω _m and ∼3% on H ₀ r _s . The results from R EC S YM and R EC I SO are consistent within the uncertainties, but we recommend R EC S YM during testing because its sensitivity to covariance variations is lower. These findings establish the accuracy, robustness, and scalability of the Euclid BAO pipeline for DR1 and provide a solid foundation for future cosmological analyses.

Context. Simulation-based inference (SBI) has emerged as a powerful framework for extracting cosmological information from complex, nonlinear data where analytical likelihoods are unavailable. Its reliability is commonly assessed using coverage-based diagnostics, which test whether posterior credible regions contain the true parameter with the expected frequency under the prior predictive distribution. However, these tests probe calibration only in an averaged sense and do not constrain posterior behavior at a fixed parameter value, which is the regime relevant for practical inference where the data are generated at a single (unknown) truth. Aims. We investigated these limitations in the context of constraining primordial non-Gaussianity, parameterized by f _NL , using simulations of the dark matter halo field. In particular, we assessed whether calibration under standard diagnostics ensures reliable uncertainty quantification at a fixed parameter value. Methods. We compared SBI based on contrastive neural ratio estimation (CNRE) with likelihood-based inference (LBI) using three complementary summary statistics: the power spectrum, bispectrum, and wavelet scattering transform (WST) coefficients. Posterior distributions were evaluated across 1000 independent test simulations. Results. SBI and LBI agree well on posterior means and skewness, while the variance agrees on average but it shows a weaker realization-by-realization consistency. Larger differences arise in the kurtosis, indicating discrepancies in the posterior tails. These effects are already present for the power spectrum – where the Gaussian likelihood assumed in our LBI analysis is best justified – and they are most pronounced for the combined power spectrum and bispectrum, where SBI posteriors are often underconfident and can yield weaker constraints than either statistic individually, despite passing coverage tests. WST coefficients further tighten constraints on f _NL even when restricting the analysis to large scales ( k _max = 0.141 h Mpc ⁻¹ ). Conclusions. Our results highlight both the potential of higher-order statistics for probing primordial non-Gaussianity and the limitations of current validation strategies for SBI. Diagnostics sensitive to posterior shape and behavior at a fixed parameter value will be necessary for robust uncertainty quantification in precision cosmology.

Accurate modelling of redshift-space distortions (RSD) in galaxy clustering is essential for extracting cosmological information from current and forthcoming large-scale structure surveys. While perturbation theory is reliable on large scales, much of the constraining power lies at intermediate and small separations, where non-linear dynamics within and between dark matter haloes dominate. We present a halo streaming model for non-linear galaxy clustering in redshift space that is accurate and physically interpretable. Our framework combines the streaming model for RSD with a halo-model decomposition of the galaxy clustering into central/satellite and one-/two-halo contributions. We build dedicated emulators for the key physical ingredients, trained on a suite of N-body simulations: halo mass functions, real-space halo two-point correlation functions, and pairwise velocity moments. By emulating these modular building blocks rather than the final redshift-space observable, this approach preserves physical transparency, enables targeted optimization for each ingredient, and remains flexible to changes in tracer populations and galaxy–halo connection models. The resulting halo streaming model reproduces the simulated non-linear anisotropic clustering signal down to highly non-linear scales, while achieving the computational efficiency required for cosmological parameter inference. This framework is designed to support full-shape RSD analyses for surveys such as DESI and Euclid, facilitating precision measurements of structure growth and tests of gravity. All codes and trained emulators are publicly available in the freyja repository (https://github.com/chzruan/freyja).

The Euclid satellite will measure spectroscopic redshifts for tens of millions of emission-line galaxies, allowing for one of the most precise tests of the cosmological model. In the context of Stage-IV surveys such as Euclid, the 3D clustering of galaxies plays a key role, providing both geometrical and dynamical cosmological constraints. In this paper, we conduct a comprehensive model comparison campaign for the multipole moments of the galaxy 2-point correlation function (2PCF) in redshift space. We tested state-of-the-art models, in particular the effective field theory of large-scale structure (EFT), a model based on the velocity difference generating function (VDG_∞), and variants of the Lagrangian perturbation theory (LPT), namely convolutional Lagrangian perturbation theory (CLPT) and convolutional Lagrangian effective field theory (CLEFT). We analysed the first three even multipole moments of the 2PCF in the simulation of emission-line galaxies, which consists of four snapshots at z∈ 1.2, 1.5, 1.8 covering the redshift range of the Euclid spectroscopic sample. We studied template-fitting and full-shape approaches and compared the different models in terms of three performance metrics: reduced ̧hi^2, a figure of merit, and a figure of bias. We find that with the template-fitting approach, only the VDG_∞ model is able to reach a minimum fitting scale of smin=20 at z=0.9 without biasing the recovered parameters. Indeed, the EFT model becomes inaccurate already at smin=30 Conversely, in the full-shape analysis, the CLEFT and VDG_∞ models perform similarly well, but only the CLEFT model can reach smin=20 while the VDG_∞ model is unbiased down to smin=25 at the lowest redshift. Overall, in order to achieve the accuracy required by Euclid, non-perturbative modelling, such as in the VDG_∞ or CLEFT models, should be considered. At the highest redshift probed by Euclid, the CLPT model is sufficient to describe the data with a high figure of merit. This comparison selects baseline models that perform best in ideal conditions and sets the stage for an optimal analysis of Euclid data in configuration space.

We present the strategy used to identify and mitigate potential sources of angular systematics in the spectroscopic galaxy survey, and we quantify their impact on galaxy clustering measurements and cosmological parameter estimation. We first surveyed the processing pipeline to identify all evident, potential sources of systematics, and classified them into two broad classes: angular systematics, which modulate the galaxy number density across the sky, and catastrophic redshift errors, which lead to interlopers in the galaxy sample. We then used simulated spectroscopic surveys to test our ability to mitigate angular systematics by constructing a random catalogue that represents the `visibility mask' of the survey; this is a dense set of intrinsically unclustered objects, subject to the same selection effects as the data catalogue. The construction of this random catalogue relies on a detection model, which gives the probability of reliably measuring the galaxy redshift as a function of the signal-to-noise ratio (S/N) of its emission lines. We demonstrate that, in the ideal case of a perfect knowledge of the visibility mask, the galaxy power spectrum in the presence of systematics is recovered, to within sub-per cent accuracy, by convolving a theory power spectrum with a window function obtained from the random catalogue itself. In the case of only approximate knowledge of the visibility mask, we test the stability of power spectrum measurements and cosmological parameter posteriors by using perturbed versions of the random catalogue. We find that significant effects are limited to very large scales, and parameter estimation remains robust; the most impacting effects are connected to the calibration of the detection model. Euclid Euclid

We investigated the accuracy and range of validity of the perturbative model for the two-point (2PCF) and three-point (3PCF) correlation functions in real space in view of the forthcoming analysis of the Euclid mission spectroscopic sample. We took advantage of clustering measurements from four snapshots of the Flagship I N -body simulations at z = {0.9,1.2,1.5,1.8}, which mimic the expected galaxy population in the ideal case, i.e. in the absence of observational effects such as purity and completeness. For the 3PCF we considered all available triangular configurations given a minimal separation ( r _min ). We first assessed the model performance by fixing the cosmological parameters and evaluating the goodness of fit provided by the perturbative bias expansion in the joint analysis of the two statistics, finding an overall agreement with the data down to separations of 20 h ⁻¹ Mpc. Subsequently, we built on the state-of-the-art analysis and extended it to include the dependence on three cosmological parameters: the amplitude of scalar perturbations ( A _s ), the matter density ( ω _cdm ), and the Hubble parameter ( h ). To achieve this goal, we developed an emulator capable of generating fast and robust modelling predictions for the two summary statistics, which thus enables an efficient sampling of the joint likelihood function. We therefore present the first joint full-shape analysis of the real-space 2PCF and 3PCF, testing the consistency and constraining power of the perturbative model across both probes and assessing its performance in a combined likelihood framework. We explored possible systematic uncertainties induced by the perturbative model at small scales, finding an optimal scale cut of r _min = 30 h ⁻¹ Mpc for the 3PCF when imposing an additional limitation on the nearly isosceles triangular configurations included in the data vector. This work is part of a series of papers in which we validate theoretical models for galaxy clustering measurements in preparation for the Euclid mission.

We introduce an extension of the evolution mapping framework to cosmological models that include massive neutrinos. The original evolution mapping framework exploits a degeneracy in the linear matter power spectrum when expressed in Mpc units, which compresses its dependence on cosmological parameters into those that affect its shape and a single extra parameter σ 12 , defined as the rms linear variance in spheres of radius 12 Mpc. We show that by promoting the scalar amplitude of fluctuations, A s , to a shape parameter, we can additionally describe the suppression due to massive neutrinos at any redshift to sub-0.01% accuracy across a wide range of masses and for different numbers of mass eigenstates. This methodology has been integrated into the public package, enhancing its ability to emulate predictions of state-of-the-art perturbative models for galaxy clustering, such as the effective field theory (EFT) model. Additionally, the updated software now accommodates a broader cosmological parameter space for the emulator, enables the simultaneous generation of multiple predictions to reduce computation time, and incorporates analytic marginalization over nuisance parameters to expedite posterior estimation. Finally, we explore the impact of different infrared resummation techniques on galaxy power spectrum multipoles, demonstrating that any discrepancies can be mitigated by EFT counterterms without impacting the cosmological parameters.