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Deep-dive physics
Study — the physics behind the campaign
A ground-up tutorial series covering everything needed to understand our fuzzy-dark-matter research — from the expanding universe to solitons, halo mass functions, wave simulations, and the observational tension. 10 of 55 articles published; the rest are on the way.
1. The expanding universe & ΛCDM
2. Dark matter: evidence, problems & candidates
2.4 Ultralight bosons: the axiverse & misalignment soon
2.5 Why ‘fuzzy’: the de Broglie wavelength as a galactic scale soon
3. The quantum mechanics you need
3.1 Wavefunction, Schrödinger equation & probability current soon
3.2 Free particles, wave packets & dispersion soon
3.3 The uncertainty principle and quantum pressure soon
3.4 Bose–Einstein condensates & the Gross–Pitaevskii equation soon
3.5 The Madelung (hydrodynamic) formulation soon
4. The Schrödinger–Poisson system
4.1 From a classical scalar field to Schrödinger–Poisson soon
4.2 The coupled equations: wave + self-gravity soon
4.3 Scaling symmetry and dimensionless units soon
4.4 The quantum Jeans scale and instability soon
4.5 The SP → Vlasov–Poisson correspondence soon
5. Solitons: the cored ground state
5.1 The self-gravitating ground state soon
5.3 The M⁴ scaling and the soliton family soon
5.4 A soliton inside a halo: core + envelope soon
5.5 Computing a soliton: imaginary-time relaxation soon
6. Linear growth, P(k) & the FDM cutoff
6.1 Growth of perturbations and the growth factor soon
6.2 The transfer function soon
6.3 The FDM cutoff: Hu–Barkana–Gruzinov & the half-mode soon
6.4 σ(M), σ₈ and window functions soon
6.5 Boltzmann codes: CAMB and axionCAMB soon
7. The halo mass function
7.1 Spherical collapse and the critical overdensity soon
7.3 Excursion set and Sheth–Tormen soon
7.4 The FDM mass function: suppression below the cutoff soon
7.5 Measuring the HMF: halo finders (FOF vs SO) soon
8. Halo structure: NFW, cusps, cores & core–halo
8.1 The NFW profile soon
8.2 The concentration–mass relation soon
8.3 Cusp vs core: the observational problem soon
8.4 The FDM halo: soliton core + NFW envelope soon
8.5 The core–halo relation (β≈⅓) and its debate soon
9. Simulating dark matter
9.1 N-body simulation and GADGET-4 soon
9.2 Initial conditions: from P(k) to particles soon
9.3 Wave solvers I: pseudo-spectral (JAXiON) soon
9.4 Wave solvers II: adaptive mesh (GAMER/ELBDM) soon
9.5 The de Broglie wall and the fluid shortcut soon
9.6 Differentiable simulation & gradient-based inference soon
10. Observations & the boson-mass tension
10.1 Dwarf-galaxy cores: a light-boson signal soon
10.2 The Lyman-α forest: a heavy-boson bound soon
10.3 Substructure, satellites & stellar streams soon
10.4 The mass tension: combining the probes soon
10.5 Statistical inference: likelihoods, SBI & calibration soon
11. Frontier methods
11.1 Quantum algorithms for cosmological simulation soon
11.2 Analog gravity: cold-atom simulation soon
11.3 Hydrodynamics + FDM; mixed dark matter soon
11.4 Open problems & our contribution soon