New high-precision microwave spectroscopic measurements and analysis of rotational energy level transitions in the ground vibronic state of the open-shell BaF molecule are reported with the purpose of contributing to studies of physics beyond the Standard Model. BaF is currently among the key candidate molecules being examined in the searches for a measurable electron electric dipole moment, eEDM, as well as the nuclear anapole moment. Employing Fourier-transform microwave spectroscopy, these new pure rotational transition frequencies for the 138Ba19F, 137Ba19F, 136Ba19F, 135Ba19F, and 134Ba19F isotopologues are analyzed here in a combined global fit with previous microwave data sets for 138Ba19F (v = 0 - 4), 137Ba19F, and 136Ba19F using the program SPFIT. As a result, hyperfine parameters are significantly improved, and we observe a distinctive structure in a Born-Oppenheimer breakdown (BOB) analysis of the primary rotational constant. This can be understood using the nuclear field shifts due to the known isotopic variation in the size of barium nuclei and in combination with the smaller linear mass-dependent BOB terms.

We present numerical relativity simulations of cosmological scenarios in which the universe is smoothed and flattened by undergoing a phase of slow contraction and test their sensitivity to a wide range of initial conditions. Our numerical scheme enables the variation of all freely specifiable physical quantities that characterize the initial spatial hypersurface, such as the initial shear and spatial curvature contributions as well as the initial field and velocity distributions of the scalar that drives the cosmological evolution. In particular, we include initial conditions that are far outside the perturbative regime of the well-known attractor scaling solution. We complement our numerical results by analytically performing a complete dynamical systems analysis and show that the two approaches yield consistent results.

We track the evolution of entropy and black holes in a cyclic universe that undergoes repeated intervals of expansion followed by slow contraction and a smooth (non-singular) bounce. In this kind of cyclic scenario, there is no big crunch and no chaotic mixmaster behavior. We explain why the entropy following each bounce is naturally partitioned into near-maximal entropy in the matter-radiation sector and near-minimal in the gravitational sector, satisfying the Weyl curvature conditions conjectured to be essential for a cosmology consistent with observations. As a result, this kind of cyclic universe can undergo an unbounded number of cycles in the past and/or the future.

We exploit red- and blue-detuned magneto optical trapping (MOT) of $^{87}$Rb benefitting from a simplified setup based on liquid crystal variable retarders (LCVR). To maintain the trapping forces when switching from a red- to a blue-detuned MOT, the circularity of the cooling beams needs to be reversed. LCVRs allow fast polarization control and represent compact, simple and cost-efficient components which can easily be implemented in existing laser systems. This way, we achieve a blue-detuned type-II MOT for $^{87}$Rb atoms with sub-Doppler temperatures of 44.5 $\mu$K. The phase space density is increased by more than two orders of magnitude compared to the standard red-detuned type-I MOT. The setup can readily be transferred to any other system working with $^{87}$Rb.

Observations of the rotational spectrum of lead monofluoride, PbF, have been extended up to transitions in the \textit{v} = 7 level for $^{208}$PbF in the lowest $X_1\,^2\Pi_{1/2}$ state of the radical and \textit{v} = 5 for the $^{207}$Pb and $^{206}$Pb isotopologues. The data also include a few measurements for $^{204}$PbF in \textit{v} = 0. These new measurements have been combined with existing near-IR measurements of the $X_2 - X_1$ fine-structure transition and a simultaneous multi-isotope fit of the data to an effective isotope-independent ro-vibronic Hamiltonian has been carried out. The resulting parameters fully characterize the vibrational, rotational and hyperfine structure of the combined $X_1 \, / \, X_2$ state of the radical. A pair of opposite parity levels with total angular momentum quantum number, $F=1/2$, in the lowest rotational level, $J=1/2$ of \PbF \,are close in energy and their spacing decreases with vibrational excitation. The experimental results show the spacing decreases to less than 20 MHz at $v=7$ and 8. The experimental work is complemented by new \textit{ab initio} calculations which support the results and allow predictions outside the experimental data range. The calculated radiative lifetimes of the relevant vibrationally excited states are of the order of 50 ms. This work was motivated by interest in using \PbF\, as a vehicle for future probes of the standard model of physics such as placing limits on the electron's electric dipole moment (\eEDM), molecular charge-parity non-conservation and Born-Oppenheimer breakdown effects for example.