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**UNC-CH Physics and Astronomy Thesis Proposal Presentation**

*Isaac Waldstein*

**“Kinetic decoupling of dark matter in the early Universe, and The motion of extended bodies in curved spacetime”**

We study the effects of dark matter temperature and dark matter interactions with relativistic particles on the growth of dark matter density perturbations during an early matter-dominated era (EMDE). An EMDE occurs when the energy content of the Universe is dominated by either massive particles or an oscillating scalar field before Big Bang nucleosynthesis. An EMDE enhances the small-scale matter power spectrum and increases the abundance of microhalos. These microhalos substantially boost the dark matter annihilation rate. However, estimates of this boost show that it is highly sensitive to the free-streaming cutoff scale in the matter power spectrum, which is set by the kinetic decoupling temperature of dark matter. We show that dark matter kinetic decoupling is radically different in an EMDE than it is in a radiation-dominated era: dark matter enters a quasidecoupled state in an EMDE, during which the dark matter temperature cools faster than the plasma temperature, but slower than it would cool if the dark matter were fully decoupled. Moreover, radiation perturbations do not oscillate during an EMDE. We establish that elastic-scattering interactions between dark matter and relativistic particles during an EMDE do not significantly suppress the growth of dark matter perturbations on small scales, in contrast to the impact of these interactions in a radiation-dominated era.

Self-force describes the effect of an object’s own field on its motion. If we model a physical object as a point particle with no size or internal structure, then the self-force diverges when evaluated at the particle’s location. One way to avoid this difficulty is to model the physical object as an extended body with detailed internal structure. We consider an extended body, modeled as an isolated elastic material moving in an arbitrary background gravitational field. We express the spacetime coordinates of each point in the body in terms of the local inertial frame of an observer in the neighborhood of the body. The inertial frame allows us to extract physical effects as seen in the rest frame of the body. We construct the action and equations of motion for the elastic body – expanding in powers of the inertial frame coordinates – and we use a center-of-mass condition to tie the motion of the observer to the body. We show (a) that the elastic body follows a geodesic at leading order in the expansion and (b) we recover the generalized Jacobi equation at first order in the case of dust particles. These results suggest that our model – which includes a physically realistic treatment of the internal interactions – (i) represents an improvement over earlier models of extended bodies in spacetime and (ii) has the potential to yield spin and self-force effects on extended bodies in a mathematically self–consistent way.