With recent Lyα forest data from BOSS and XQ-100, some studies suggested that the lower mass limit on the fuzzy dark matter (FDM) particles is lifted up to . However, such a limit was obtained by ΛCDM simulations with the FDM initial condition and the quantum pressure (QP) was not taken into account, which could have generated non-trivial effects in large-scale structures. We investigate the QP effects in cosmological simulations systematically, and find that the QP leads to further suppression of the matter power spectrum at small scales, as well as the halo mass function in the low-mass end. We estimate the suppressing effect of QP in the 1D flux power spectrum of Lyα forest and compare it with data from BOSS and XQ-100. The rough uncertainties of thermal gas properties in the flux power spectrum model calculation were discussed. We conclude that more systematic studies, especially with QP taken into account, are necessary to constrain FDM particle mass using Lyα forest.

Ultralight axion is a dark matter candidate with mass and de Broglie wavelength of order kiloparsec. Such an axion, also called fuzzy dark matter (FDM), thermalizes via gravitational force and forms a Bose–Einstein condensate. Recent studies suggested that the quantum pressure from FDM can significantly affect structure formation in small scales, thus alleviating the so-called “small-scale crisis.” In this paper, we develop a new technique to discretize the quantum pressure and illustrate the interactions among FDM particles in an N-body simulation that accurately simulates the formation of the dark matter halo and its inner structure in the region outside the softening length. In a self-gravitationally bound virialized halo, we find a constant density solitonic core, which is consistent with theoretical prediction. The existence of the solitonic core reveals the nonlinear effect of quantum pressure and impacts structure formation in the FDM model.

Fuzzy Dark Matter (FDM), motivated by string theory, has recently become a hot candidate for dark matter. The rest mass of FDM is believed to be ~10⁻²²eV and the corresponding de-Broglie wave length is ~1kpc. Therefore, the quantum effect of FDM plays an important role in structure formation. In order to study the cosmological structure formation in FDM model, several simulation techniques have been introduced. We review the current status and challenges in the cosmological simulation for the FDM model in this paper.

In this second paper in a series studying galaxy–galaxy lensing signals using Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we present our measurement and modeling of the lensing signals around groups of galaxies. We divide the groups into four halo mass bins and measure the signals around four different halo-center tracers: brightest central galaxies (BCGs), luminosity-weighted centers, number-weighted centers, and X-ray peak positions. For groups cross-identified in both X-ray and SDSS DR7, we further split the groups into low and high X-ray emission subsamples, both of which are assigned to two halo-center tracers, BCGs and X-ray peak positions. The galaxy–galaxy lensing signals show that BCGs, among the four candidates, are the best halo-center tracers. We model the lensing signals using a combination of four contributions: the off-center NFW host halo profile, subhalo contribution, stellar contribution, and projected two-halo term. We sample the posterior of five parameters, i.e., the halo mass, concentration, off-centering distance, subhalo mass, and fraction of subhalos, via a Monte Carlo Markov Chain (MCMC) package using the galaxy–galaxy lensing signals. After taking into account the sampling effects (e.g., Eddington bias), we found that the best-fit halo masses obtained from lensing signals are quite consistent with those obtained in the group catalog based on an abundance matching method, except in the lowest mass bin.

We devise a fully self-consistent simulation pipeline for the first time to study the interaction between dark matter and dark energy. We perform convergence tests and show that our code is accurate on different scales. Using the parameters constrained by Planck, Type Ia Supernovae, baryon acoustic oscillations (BAO) and Hubble constant observations, we perform cosmological N-body simulations. We calculate the resulting matter power spectra and halo mass functions for four different interacting dark energy models. In addition to the dark matter density distribution, we also show the inhomogeneous density distribution of dark energy. With this new simulation pipeline, we can further refine and constrain interacting dark energy models.

The interacting dark energy (IDE) model, which considers the interaction between dark energy and dark matter, provides a natural mechanism to alleviate the coincidence problem and can also relieve the observational tensions under the ΛCDM model. Previous studies have put constraints on IDE models by observations of cosmic expansion history, cosmic microwave background, and large-scale structures. However, these data are not yet enough to distinguish IDE models from ΛCDM effectively. Because the non-linear structure formation contains rich cosmological information, it can provide additional means to differentiate alternative models. In this paper, based on a set of N-body simulations for IDE models, we investigate the formation histories and properties of dark matter haloes and compare with their ΛCDM counterparts. For the model with dark matter decaying into dark energy and the parameters being the best-fitting values from previous constraints, the structure formation is markedly slowed down, and the haloes have systematically lower mass, looser internal structure, higher spin, and anisotropy. This is inconsistent with the observed structure formation, and thus this model can be safely ruled out from the perspective of non-linear structure formation. Moreover, we find that the ratio of halo concentrations between IDE and ΛCDM counterparts depends sensitively on the interaction parameter and is independent of halo mass. This can act as a powerful probe to constrain IDE models. Our results concretely demonstrate that the interaction of the two dark components can affect the halo formation considerably, and therefore the constraints from non-linear structures are indispensable.