timzi

Tim Zimmermann, Massimo Pietroni, Javier Madroñero, Luca Amendola, and Sandro Wimberger (Nov. 2019). “A Quantum Model for the Dynamics of Cold Dark Matter”. In: Condensed Matter 4.4, p. 89. DOI: 10.3390/condmat4040089.

Tim Zimmermann, Nico Schwersenz, Massimo Pietroni, and Sandro Wimberger (n.d.). “One Dimensional Fuzzy Dark Matter Models: Structure Growth and Asymptotic Dynamics”. submitted to: Physical Review D. DOI: 10.1103/PhysRevD.103.083018.

• Zimmermann, Tim; Alvey, James; Marsh, David J. E.; Fairbairn, Malcolm & Read, Justin I. (2025). Dwarf Galaxies Imply Dark Matter Is Heavier than 2.2x10^-21 eV. Physical Review Letters. ISSN 0031-9007. 134(15). doi: 10.1103/physrevlett.134.151001. Full text in Research Archive Show summary

  It is widely established that a lower bound on the dark matter particle mass, m , can be obtained by demanding that the de Broglie wavelength in a given galaxy must be smaller than the virial radius of the galaxy, leading to m ≳ 10 − 22     eV when applied to typical dwarf galaxies. This lower limit has never been derived precisely or rigorously. We use stellar kinematical data for the Milky Way satellite galaxy Leo II to self-consistently reconstruct a statistical ensemble of dark matter wave functions and corresponding density profiles. By comparison to a data-driven, model-independent reconstruction, and using a variant of the maximum mean discrepancy as a statistical measure, we determine that a self-consistent description of dark matter in the local Universe requires m > 2.2 × 10 − 21     e V   ( C L > 95 % ). This lower limit is free of any assumptions pertaining to cosmology, microphysics (including spin), or dynamics of dark matter, and only assumes that it is predominantly composed of a single bosonic particle species.

• Zimmermann, Tim; Marsh, D.J.E.; Rogers, K.K.; Winther, Hans Arnold & Shen, Sijing (2025). Interference in fuzzy dark matter filaments: Idealized models and statistics. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 696. doi: 10.1051/0004-6361/202554232. Full text in Research Archive Show summary

  Fuzzy (wave) dark matter (FDM), the dynamical model underlying an ultralight bosonic dark matter species, produces a rich set of nongravitational signatures that distinguishes it markedly from the phenomenologically related warm (particle) dark matter (WDM) scenario. The emergence of extended interference fringes hosted by cosmic filaments is one such phenomenon reported by cosmological simulations, and a detailed understanding of such may strengthen existing limits on the boson mass but also break the degeneracy with WDM, and provide a unique fingerprint of interference in cosmology. In this paper, we provide initial steps toward this goal. In particular, we show in a bottom-up approach, how the presence of interference in an idealized filament population can lead to a non-suppressive feature in the matter power spectrum – an observation supported by cosmological FDM simulations. To this end, we build on a theoretically motivated and numerically observed steady-state approximation for filaments and express the equilibrium dynamics of such in an expansion of FDM eigenstates. We optimize the size of the expansion by incorporating classical phase-space information. Ellipsoidal collapse considerations were used to construct a fuzzy filament mass function which, together with the reconstructed FDM wave function, allowed us to efficiently compute the one-filament power spectrum. We showcase our non-perturbative interference model for a selection of boson masses and confirm our approach is able to produce the matter power boost observed in fully cosmological FDM simulations. More precisely, we find an excess in correlation between the spatial scale associated with the FDM ground state and the quantum pressure scale. We speculate about applications of this effect in data analysis.

• Schwersenz, Nico; Loaiza, Victor; Zimmermann, Tim; Madroñero, Javier & Wimberger, Sandro (2024). Comparison of two different integration methods for the (1+1)-dimensional Schrödinger-Poisson equation. Computer Physics Communications. ISSN 0010-4655. 300. doi: 10.1016/j.cpc.2024.109192. Full text in Research Archive Show summary

  We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schrödinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schrödinger equation with an auto-gravitating potential created by the wave function density itself. The latter is determined as a solution of Poisson's equation modelling, e.g., non-relativistic gravity. For reasons of complexity, we treat a one-dimensional version of the problem whose numerical integration is still challenging because of the extreme long-range forces (being constant in the asymptotic limit). Both of our methods, a Strang splitting scheme and a basis function approach using B-splines, are compared in numerical convergence and effectivity. Overall, our Strang-splitting evolution compares favourably with the B-spline method. In particular, by using an adaptive time-stepper rather large one-dimensional boxes can be treated. These results give hope for extensions to two spatial dimensions for not too small boxes and large evolution times necessary for describing, for instance, dark matter formation over cosmologically relevant scales.

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• Zimmermann, Tim; Shen, Sijing & Winther, Hans Arnold (2025). On the wave-like nature of fuzzy dark matter. Modeling, phenomenology, and limits from the bottom up. Universitetet i Oslo. Full text in Research Archive Show summary

  Cold dark matter (CDM), a thermally produced, nonrelativistic form of matter, has established itself as a successful effective theory for the abundant nonluminous matter in the universe, accurately describing the large-scale structure of the universe. At the same time, null results of direct detection efforts emphasize that the microphysical nature of DM remains elusive. With hard detection limits approaching and a plethora of phenomenological degeneracies lurking on galactic scales, looking beyond CDM remains a vital effort in constraining the nature of DM. This thesis investigates ultralight or fuzzy dark matter (FDM) as a theoretically well-motivated alternative to CDM and focuses on its astrophysical implications due to its wave-like nature. To this end, we adopt a bottom-up methodology and examine the behavior of FDM dimension-by-dimension, state-by-state, and filament-by-filament. The results of this thesis are (i) a deepened understanding of its numerical modeling, (ii) a new, robust limit for its mass, and (iii) first steps towards a principled understanding of the emerging wave phenomena in cosmic filaments.

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