Dark Matter modelling
Using the Schrödinger-Poisson equations to model dark matter
Dark matter is the hypothesised invisible, non-baryonic matter whose presence is inferred from (among other pieces of evidence) the difference between the visible and gravitational mass of galaxy clusters in the Universe. The nature of dark matter is a major unsolved problem in Cosmology and Particle Physics. Many proposed particles are viable, varying in mass from primordial black holes (or the less speculative Weakly-Interacting Massive Particles; WIMPs) to axions. Dark matter is generally assumed to be cold (CDM), i.e., without velocity dispersion. This is known to be only an approximation as non-linear gravitational dynamics will introduce non-zero velocity dispersion even if it is initially zero1.
In this work, I model the dynamics of the system of dark matter particles using the Schrödinger-Poisson system of equations. This approach was first suggested by Widrow and Kaiser in 19932. The motivation behind this approach is the observation that CDM seems to have trouble explaining observational effects on subgalactic scales. Briefly, CDM overpredicts the amount of structure on subgalactic scales. A DM particle following Schrödinger-Poisson dynamics can reproduce the behaviour of CDM on extragalactic scales, and suppresses structure formation on subgalactic scales, and thus alleviates the problems with CDM. This modulation is governed by the `de-Broglie wavelength' of the particle. This is a semi-classical system such that the Schrödinger equation is merely a classical wave equation with ℏ being a parameter that controls the de-Broglie wavelength.