Cosmic Structures

All particles of any size, nature or location feel gravitation in the same way. Despite this simple law, gravity and the structures it forms are hard to understand, in particular the almost universal mass density profiles caused by Newtonian gravity found in simulations in the 1990s. These structures emerge from particles non-relativistically moving in their own gravitational field, so that the description of this evolution process raises many questions which this project tackles. Here are a few of them, leading to the first paper on an analytical derivation of the famous Navarro-Frenk-White profile: 

• How to describe the evolution of a self-gravitating set of particles?

We assume that the particle positions determine the gravitational potential of the set of all these masses, the particles move in this gravitational potential to the next time step, and the gravitational potential is updated then. This is a valid mean field theory for slowly moving particles and therefore valid for the non-relativistic particles usually considered in such simulations. But when does it break down from a conceptual point of view and not only from a numerical one?

• How to separate structure description from structure evolution?

Particle positions and their evolution seem to contain complementary and sometimes redundant information. Taking a snapshot of the particle set at one moment in cosmic time, we can set up a structure description without taking into account any velocity information. Vice versa, the equations of motion of a particle ensemble track the evolution for any given initial particle positions. Since the self-gravitational interaction seems to lead to one common long-term stable final state for a multitude of initial conditions, is it necessary to understand and follow the entire evolution of a particle set if we are only interested in a description of their final state? And how should we convert the set of discrete particles into a continuous mass density profile?

• What role do conservation laws and symmetries play in forming the final state?

Position and velocity information can easily be converted into each other by means of conservation laws like energy conservation for each particle. In addition, most simulations assume a spherically symmetric distribution of particles. Does assuming conservation laws for average properties of the entire particle set and dropping the spherical symmetry of the final state change the interpretation of simulated particle sets? More generally, what information gets lost when coarse-graining the "microscopic" particle set into a "macroscopic" mass density representation?

• How to set up a thermodynamics for scale-free self-gravity?

Thermodynamics is based on deviations from an equilibrium state taking into account perturbations with respect to the preferred scale of the problem at hand. Yet, a description of the coarse-grained self-gravitating mass density suffers from being scale-free and lacking a thermodynamical equilibrium. What adaptations need to be made to conventional thermodynamics to account for these specialties of gravity?

Answers to these questions are not only useful to gain a deeper understanding of our interpretations of cosmic structures, but can be employed more generally to model any phenomenon in which gravitational interactions dominate all other processes. 

This project started with one naive mathematical calculation but has led to many valuable insights so far, in particular how to overcome the conceptual problems of conventional statistical physics approaches to capture the features of simulated particle sets and their relation to continuous mass densities. The Gravity Research Foundation found my essay submitted in 2020 worth a "honorable mention". The approach tailored for the description of dark matter halo profiles is called DAEMON for DArk Emergent Matter halO explanatioN.

I am highly grateful to all inspirations and motivations to continue this line of thought from many people. To name a few: George F. R. Ellis, Xinzhong Er, Robert Grand, Jens Hjorth, Angela Lahee, Roy Maartens, Andrea Maccio, Shude Mao, Carlo Rovelli, Volker Springel, Max Tegmark, Liliya L. R. Williams, Rüdiger Vaas, Dandan Xu and the entire "Peebles Fan club" of philosophers of physics.