Cosmological large-scale structure using a semi-classical Schrödinger description
Supervisor: Dr. Cornelius Rampf
Contact information: cornelius.rampf@univie.ac.at
Co-supervisor: Prof. Dr. Oliver Hahn
Expected duration: 9 months
Project description & Goals:
The cosmic large-scale structures of the Universe are mainly the result of the gravitational instability of initially small density fluctuations in the dark-matter distribution. Cold dark matter can accumulate very efficiently at focused locations, leading to a highly non-linear filamentary network with extreme matterdensities. Traditionally, the evolution of the dark-matter distribution can be determined using analytical or numerical techniques, both based on classical physics.
Recently, however, there is increasing interest in employing complementary techniques based on a semi-classical Schrödinger description [1-3]. These initial approaches provide very efficient and reliable results during the early gravitational evolution, but they need to be revised once non-linear structures emerge. The most stringent problem is the determination of the gravitational potential at late times within this approach.
In this project, we will develop novel methods to accurately determine the gravitational potential within the Schrödinger method. While the techniques in [1-3] were executed in the interaction picture of quantum mechanics, other descriptions such as the Heisenberg picture might be more suited for such avenues.
Working plan & Milestones (including final thesis):
- Literature study to cosmic large-scales and related basic methods (numerical techniques and perturbation theory)
- Establish connection between classical fluid mechanics and the Heisenberg picture.
- Develop an optimal strategy for solving the gravitational potential
- Validate the method by numerical implementation, e.g., using Python or advanced programming languages
- Write thesis (and, depending on the progress, a short paper on the results)
Requirements / special skills: 1) Should have followed lectures on cosmology and/or cosmic large-scale structure, 2) Some prior experience with semi-analytical techniques is a plus, 3) Advanced (Python) programming skills are a bonus
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