Andrew Eberhardt

Current Research and Scholarly Interests

Determining the particle nature of dark matter remains one of the major outstanding problems in cosmology. A global effort combines observational, theoretical, and numerical work to investigate the problem across nearly one hundred orders of magnitude in mass. At the lowest mass end, m ~ 1e-19 eV, simulations of structure provide a powerful tool to constrain the lower bound on the dark matter mass. Crucially, in this ultra light regime, high occupation numbers are though to motivate the use of classical field theory. The wavelike phenomena associated with this model influences the abundance of small scale structure, produces soliton over densities, and impacts the dispersion relation of stellar streams, and coherence times for haloscope experiments. All of these effects have been employed to exclude decades of mass parameter space. Many efforts rely on the accuracy of the classical field description at over all length and time scales. And while classical field simulations provide a powerful tool to analyze dark matter phenomena in this mass regime, appropriate interpretation of the results is essential to understanding these constraints.

Recently, there has been debate in the community whether the classical field theory can make accurate predictions at all scales relevant to the constraints discussed above. While classical field theory describes well high occupied systems freely propagating, like electromagnetism, it is also known that non-linearities, such as those due to gravity or to axion like self interactions, cause the classical field theory to admit quantum corrections. Understanding where the classical field theory is accurate, and finding the time scales on which quantum corrections become important, called the ``quantum breaktime", has been an ongoing effort. Previous efforts have addressed this question by simulating the quantum evolution of very small systems, or by approximating the time scale of non classical processes. However, a dynamical simulation of the quantum corrections for realistic system had not existed in the literature.

My research has focused on providing simulations that directly integrate the evolution of quantum corrections as relevant to ultra light astrophysical dark matter. I investigated this problem in a number of stages. First, I investigated how the classical field and n-body dark matter simulations differed and how simulating multiple classical fields effected this correspondence. Following this, I developed a massively parallel algorithm to simulate the full quantum evolution of small systems, resulting in the treatment of quantum coherent states many times larger than had been previously simulated in the literature. I then designed a solver that dynamically evolved the leading order quantum correction term to the mean field theory, and used this to track the size of quantum corrections in an astrophysical test problem in one spatial dimension. Currently, we are working on developing simulations that approximate the evolution of the quantum Wigner function. These will allow us to simulate much larger cosmological systems in three spatial dimensions and track the quantum corrections throughout. The result of these efforts should be an unprecedented understanding of the behavior of quantum corrections for scalar field dark matter simulations in astrophysical and cosmology contexts and a thorough understanding of the regimes of accuracy of the classical field theory and how quantum effects may influence existing scalar field dark matter calculations.