Making (dark matter) waves: Untangling wave interference for multi-streaming dark matter (2206.11918v2)

Abstract: The classical dynamics of collisionless cold dark matter, commonly described by fluid variables or a phase-space distribution, can be captured in a single semiclassical wavefunction. We illustrate how classical multi-streaming creates wave interference in a toy model corresponding to the dynamics of the Zel'dovich approximation and link it to diffraction optics. Wave interference dresses the classical skeleton of cold dark matter with universal features akin to the physical imprints of wavelike (or fuzzy) dark matter. We untangle this wave interference to obtain single-stream wavefunctions corresponding to the classical fluid streams, by writing the wavefunction in an integral form. Our wave decomposition captures the full phase-space information and isolates the multi-stream phenomena related to vorticity and velocity dispersion. We link the wave interference features of our system to the standard forms of diffraction catastrophe integrals, which produce bright caustics in optical fields analogous to the cold dark matter density field. Our two complementary descriptions of dark matter wave-fields present rich universal features that can unlock new ways of modelling and probing wavelike dark matter on the scales of the cosmic web.

• The paper proposes a new semiclassical wavefunction method to model dark matter interference in multi-stream regions using principles from diffraction optics.
• It decomposes complex wave interference with numerical techniques like the stationary phase approximation to connect quantum effects to classical trajectories.
• The study links wave caustic phenomena with catastrophe theory, offering a framework to enhance simulations of cosmic structures and mitigate classical divergences.

Analysis of "Making (dark matter) waves: Untangling wave interference for multi-streaming dark matter"

The research paper "Making (dark matter) waves: Untangling wave interference for multi-streaming dark matter" offers a comprehensive paper of the wave-mechanical approach to modeling cold dark matter (CDM), particularly addressing the complexities arising from multi-streaming and caustics in the formation of the cosmic web. This paper is of great interest to researchers focusing on large-scale structure formation and theoretical cosmology.

Overview and Methodology

The authors propose an innovative method to simulate the behavior of CDM by utilizing a semiclassical wavefunction approach rather than the traditional fluid dynamics or the Vlasov-Poisson framework. The paper bridges the dynamics of CDM with wave interference phenomena, drawing analogies to diffraction optics. By analyzing wave interference patterns, the paper unpacks classical caustic phenomena and demonstrates how classical trajectories can be extracted from quantum mechanical models.

Key to this paper is the use of a wavefunction obeying the Schrödinger equation without potential, mimicking the free-particle motion under the Zel'dovich approximation. This approximation is significant in tracing large-scale structures where simplifying assumptions about the gravitational collapse can be leveraged. The authors further develop the wavefunction into a form where interference effects, typically problematic in multi-stream regions, can be decomposed to regain classical insights.

Numerical Techniques and Analytical Tools

The paper employs a variety of numerical techniques to verify theoretical predictions. Using methods such as domain coloring and contour shifting, the paper presents a vivid representation of the complex wavefunction behavior across different stages of cosmic structure formation. The introduction of stationary phase approximation (SPA) allows the authors to decompose the wavefunction into individual streams, each corresponding to classical trajectories.

The theoretical implications extend into the field of catastrophe theory, where the paper connects wave interference structures to well-classified phenomena such as fold and cusp catastrophes. These connections enable the exploration of universal features of wave caustics beyond the details of initial conditions, offering a robust approach to understanding the regularization of classical divergences by quantum effects.

Implications and Future Directions

The implications of this research are potent, both in refining theoretical understandings of dark matter dynamics and in potentially influencing computational approaches in cosmology. By presenting a new way of probing CDM systems, this work proposes alternative methodologies for understanding the filamentary nature of cosmic structures and the phenomena occurring on scales where traditional methods struggle.

This approach could pave the way for improved simulations of the early universe's large-scale structures and the dynamics of multi-stream regions post-shell-crossing. Future research might expand these findings to more comprehensive models, incorporating realistic cosmological conditions and larger simulations that extend beyond the current scale limitations. Utilizing the insights from diffraction catastrophes could enhance predictive tools in astrophysical surveys, connecting theoretical models with observable cosmic signatures.

Conclusion

The paper "Making (dark matter) waves: Untangling wave interference for multi-streaming dark matter" contributes significantly to modern cosmology by providing a framework that unites semiclassical wave mechanics with classical cosmological perturbations. As the paper identifies universal features of wave phenomena around caustics, it opens avenues for further exploration and practical application in the interpretation of cosmological data and the computational modeling of the universe's structure at vast scales.