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__Title:__

**KINETIC DECOUPLING OF DARK MATTER IN THE EARLY UNIVERSE AND GEODESIC DEVIATION IN CURVED SPACETIME**

Speaker — Isaac Raj Waldstein

__Abstract:__

Our understanding of the origins and behavior of dark matter is limited by our ignorance of the epoch bridging the end of inflation and the onset of Big Bang Nucleosynthesis. One possibility is that the Universe’s energy density was dominated by a scalar field that rapidly oscillates about the minimum of a quadratic potential and has the same dynamics as a pressureless fluid of nonrelativistic matter. We show that the evolution of the dark matter temperature leads to a fundamentally new state of (quasidecoupled) dark matter during an early matter-dominated era (EMDE). We extend the conditions for quasidecoupling to other nonstandard cosmologies, and resolve a disagreement in the literature over the correct way to define the dark matter kinetic decoupling temperature during an EMDE. Next, we probe dark matter kinetic decoupling during an EMDE by studying the effects of interactions (drag) between dark matter and relativistic particles on the evolution of dark matter density perturbations during an EMDE. In the limit of heavy dark matter, we find that drag during an EMDE does not significantly suppress the growth of dark matter density perturbations on small scales, even if the dark matter stays coupled to the plasma well into an EMDE. Consequently, the small-scale cutoff in the matter power spectrum is set exclusively by dark matter free- streaming effects if dark matter drops out of kinetic equilibrium with the plasma during an EMDE. This is a surprising result, since in a standard radiation-dominated universe, the small-scale cutoff in the matter power spectrum is determined by two effects: drag and free streaming. Separately, we investigate a central result in general relativity called the geodesic deviation equation (GDE). This equation determines the relative acceleration between neighboring geodesics in curved spacetime. The GDE, which is difficult to solve exactly, assumes that nearby geodesics have a small rate of separation, compared to the speed of light, that is treated as the same order in smallness as the separation itself, compared to the radius of curvature of spacetime. This assumption is discussed in various papers, but is not discussed in any standard textbooks on general relativity. Relaxing this assumption yields the generalized geodesic deviation equation (GGDE). We were first introduced to the GGDE by deriving it from the action for an isolated elastic body in curved spacetime. We elucidate the distinction between the GDE and the GGDE by explicitly computing the relative acceleration between timelike geodesics in two-dimensional de Sitter spacetime.

When: Friday June 3^{rd} at 1 pm

Where: Phillips 277, or remotely on Zoom

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https://unc.zoom.us/j/96656226621?pwd=QmQ2MzlLQjllbGJmcEFnVm1BUTA4QT09

Meeting ID: 966 5622 6621

Passcode: 716115