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We describe and test a family of new numerical methods to solve the Schrodinger equation in self-gravitating systems, e.g. Bose-Einstein condensates or fuzzy/ultra-light scalar field dark matter. The methods are finite-volume Godunov schemes with stable, higher-order accurate gradient estimation, based on a generalization of recent mesh-free finite-mass Godunov methods. They couple easily to particle-based N-body gravity solvers (with or without other fluids, e.g. baryons), are numerically stable, and computationally efficient. Different sub-methods allow for manifest conservation of mass, momentum, and energy. We consider a variety of test problems and demonstrate that these can accurately recover solutions and remain stable even in noisy, poorly-resolved systems, with dramatically reduced noise compared to some other proposed implementations (though certain types of discontinuities remain challenging). This is non-trivial because the quantum pressure is neither isotropic nor positive-definite and depends on higher-order gradients of the density field. We implement and test the method in the code GIZMO.
Dark matter (DM) may have its origin in a pre-Big Bang epoch, the cosmic inflation. Here, we consider for the first time a broad class of scenarios where a massive free scalar field unavoidably reaches an equilibrium between its classical and quantum
We derive non-relativistic equations of motion for the formation of cosmological structure in a Scalar Field Dark Matter (SFDM) model corresponding to a complex scalar field endowed with a quadratic scalar potential. Starting with the full equations
This paper aims to put constraints on the parameters of the Scalar Field Dark Matter (SFDM) model, when dark matter is described by a free real scalar field filling the whole Universe, plus a cosmological constant term. By using a compilation of 51 $
The dynamics of a cosmological model fueled by scalar field dark matter with a cosh-like potential plus a cosmological constant is investigated in detail. It is revealed that the late-time attractor is always the de Sitter solution, and that, dependi
Massive scalar fields provide excellent dark matter candidates, whose dynamics are often explored analytically and numerically using nonrelativistic Schr{o}dinger-Poisson (SP) equations in a cosmological context. In this paper, starting from the nonl