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Abstract

The dynamics of quantum fields in curved spacetime give rise to various intriguing phenomena. Among them is the production of particles in an expanding spacetime. This process is likely responsible for seeding the Universe's large-scale structure, which, in turn, causes the temperature fluctuations in the cosmic microwave background and grows into the distribution of galaxies and galaxy clusters we observed today. In this work, we simulate this process in an ultracold quantum gas. The simulation is based on a novel and particularly straightforward mapping between a mass-less, free, relativistic scalar field in a curved spacetime and the phononic excitations of a Bose-Einstein condensate. Here, the density distribution and speed of sound of the background condensate determine the geometry of the spacetime.

Additionally, this thesis introduces a new ultracold atom machine that creates and controls a quasi-two-dimensional Bose-Einstein condensate of potassium-39. This experimental system combines a high control over the condensate's density with the possibility to dynamically adjust the atomic interaction -- and thus the speed of sound -- via a broad Feshbach resonance. We use this control to implement the two aspects of a Friedmann-Lemaître-Robertson-Walker (FLRW) metric: spatial curvature and the expansion of space.

To demonstrate spatial curvature, we probe wave packet dynamics and show that a harmonically trapped Bose-Einstein condensate approximates a hyperbolically curved space.

For the expansion of space, we perform a global change of the speed of sound. We realize three different power-law expansions, corresponding to accelerated, uniform, and decelerated expansion. For all three, we observe the emergence of fluctuations equivalent to cosmological particle production. To characterize these fluctuations, we compute their correlation function and power spectrum. In the time evolution of these quantities after the expansion, we identify an intriguing feature. It is connected to a complex phase of the produced quantum state and shows a clear dependence on the expansion history. Understanding if and how such a feature can be used in real cosmological observations is an intriguing prospect for future research.

Additionally, a good agreement between our experimental results and analytical predictions confirms that our experimental system simulates the dynamics of a quantum field in a curved and expanding space. This is the starting point for the future investigation of more complex spacetime geometries.