Development of a Renormalisation Group approach to Kinetic Field Theory for the study of cosmic structure formation

• Applicant: Dr. Elena Kozlikin
• Subject Area: Astrophysics and Astronomy ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 452923686

The objective of this project is to apply well-established methods from quantum and statistical field theory to the analytical framework of Kinetic Field Theory designed to describe the formation of cosmic large-scale structure. The question addressed with this research is: How do we get from the tiny density fluctuations observed in the Cosmic Microwave Background in the early Universe to the highly pronounced filamentary (web-like) structures, which largely consist of dark matter and galaxies, we observe in our Universe today? In the framework of Kinetic Field Theory, the full information of an ensemble of N classical particles is encoded in a generating functional – the field-theory equivalent of the partition function known from statistical physics – making the application of field-theoretical tools, such as renormalisation group techniques, possible. The dynamics of the particle ensemble is determined by a few physical quantities on microscopic scales only, such as the interaction potential between particles, their initial phase-space distribution, and their equations of motion, which we understand well. On macroscopic scales, however, the microscopic dynamics leads to a high degree of complexity which results in the well-known filamentary structure that is observed in the universe today. In order to understand the transition from the simple microscopic physics to the complexity of macroscopic physics, one needs to bridge the gap between the known microscopic interactions and such quantities which embody the effective macroscopic laws that govern the many-body system on scales where observations are actually made. Functional renormalisation group techniques allow us to study this transition to complexity. A suitable theoretical tool to do that is provided by the Wetterich equation which acts like a microscope with variable resolution.The objective of this project is to apply the well-established procedure that leads to the Wetterich equation to Kinetic Field Theory and to construct solutions for the Wetterich equation, and thus to study the transition from microscopic to macroscopic scales. With this three major goals are pursued: (1) The project will allow us to gain a better qualitative understanding of the formation of structure in self-gravitating particle systems that we have in cosmology. (2) It will allow us to obtain more accurate quantitative results for the statistical quantities which characterise structures, i.e. correlation functions, especially in the regime where non-linear dynamics dominates the evolution of structures. (3) It will provide us with methods to study the relation between the particle-based approach of Kinetic Field Theory and established approaches for cosmic structure formation based on fluid dynamics.

• DFG Programme: Research Grants