Baojiu Li

The modelling of the power spectrum of biased tracers has become a central topic in the analysis of modern cosmological galaxy surveys. Perturbative templates formulated in both Eulerian and Lagrangian frameworks have been extensively developed over the last decades, with their implementation in ΛCDM thoroughly investigated and validated. In parallel, approaches combining perturbation theory with the output of dark-matter-only simulations have emerged as powerful tools for modelling the nonlinear regime, most notably the Hybrid Effective Field Theory (HEFT) framework [ Mon. Not. Roy. Astron. Soc. 492 (2020) 5754]. In this work, we discuss the perturbative biased expansion within the local Lagrangian bias scheme and its implementation in the HEFT framework for modified gravity cosmologies. We focus on f ( R ) gravity, a theory characterized by scale-dependent growth and chameleon screening, making it one of the most challenging scenarios for the computation of Lagrangian Perturbation Theory growth functions and for the generation of accurate numerical simulations. We present a detailed overview of the ingredients required to compute loop-corrected biased power spectra analytically and compare these predictions against fully non-perturbative simulation results. Finally, we propose a strategy to extend existing HEFT-based ΛCDM emulators, such as bacco and Aemulus , to beyond-ΛCDM cosmologies.

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).

We investigate the errors in modeling the redshift-space distortion (RSD) effect at large linear scales, using data from the Millennium simulation. While standard theoretical templates, such as the Kaiser formula and the TNS method, could precisely model RSD for individual large-scale modes, we find that for tracers with number densities lower than ∼ 10 ^-3 (Mpc/ h ) ^-3 , there is a few-percent level bias in the predicted power spectrum. This error arises due to the amplification of intrinsic Poisson noise during RSD modeling from real-space power spectrum. This amplified noise can be analytically expressed as 1 + ϵ /[ n̅P (1 + ϵ )], with ϵ = 2 β /3 + β ² /5, where P denotes the real-space tracer power spectrum and β ≡ f / b . Specifically, for halos with a number density of around 5 × 10 ^-4 (Mpc/ h ) ^-3 , this phenomenon results in an additional systematic error of 2.5%. Our result suggests that caution is necessary when directly modeling redshift-space distortions (RSD) using real-space power spectra of tracers obtained from simulations or actual surveys. This caution is particularly pertinent in scenarios where emulators trained on simulation data forecast the real-space tracer power spectrum, as well as in baryon acoustic oscillation (BAO) reconstruction using galaxy samples, for which we estimate that shot noise could introduce random errors of about one-third in the displacement field, potentially diminishing the effectiveness of the BAO peak sharpening.

The large variety and number of dark energy (DE) theories make it impractical to perform detailed analyses on a case-by-case basis, which has motivated proposals to “parameterize” theories to reduce the size of theory space. The leading approach to do this is the effective field theory of dark energy (EFTofDE), which can describe general Horndeski-type theories with a small number of observationally accessible time-dependent functions. However, the EFTofDE primarily works for linear perturbations, and extending it to obtain a fully non-linear description of DE theories, which is critical for theories with screening mechanisms, is challenging. In this paper, we present a general method for reconstructing the non-linear DE Lagrangian from the background expansion history and certain linear-perturbation quantities, building upon the EFTofDE framework. Using numerical examples, we demonstrate that this method is applicable to a wide range of single-scalar-field dark energy and modified gravity theories, including quintessence, scalar-tensor theory, k -essence, and generalized cubic Galileon with shift symmetry. For each of these theories, we discuss the validity of the method and factors affecting its results. While this method involves solving differential equations, we find that the initial conditions are not important for quintessence, scalar-tensor theory and k -essence, while for shift-symmetric cubic Galileon, the generic tracker solution can help transform differential equations into algebraic equations. This offers a useful framework to connect cosmological observations at the background and linear-perturbation levels to the underlying non-linear dynamics of dark energy, and will enable cosmological simulations to analyze and examine DE theories systematically and in much greater detail.

The Euclid mission will measure cosmological parameters with unprecedented precision. To distinguish between cosmological models, it is essential to generate realistic mock observables from cosmological simulations that were run in both the standard Λ-cold-dark-matter (ΛCDM) paradigm and in many non-standard models beyond ΛCDM. We present the scientific results from a suite of cosmological N-body simulations using non-standard models including dynamical dark energy, k-essence, interacting dark energy, modified gravity, massive neutrinos, and primordial non-Gaussianities. We investigate how these models affect the large-scale-structure formation and evolution in addition to providing synthetic observables that can be used to test and constrain these models with Euclid data. We developed a custom pipeline based on the Rockstar halo finder and the nbodykit large-scale structure toolkit to analyse the particle output of non-standard simulations and generate mock observables such as halo and void catalogues, mass density fields, and power spectra in a consistent way. We compare these observables with those from the standard ΛCDM model and quantify the deviations. We find that non-standard cosmological models can leave large imprints on the synthetic observables that we have generated. Our results demonstrate that non-standard cosmological N-body simulations provide valuable insights into the physics of dark energy and dark matter, which is essential to maximising the scientific return of Euclid.