| Summary: | Inflation, an extension to the standard ΛCDM model which posits a brief, accelerated expansion early in the Universe, naturally solves the horizon and flatness problems with the standard model and provides a source of the initial perturbations that seed large-scale structure. Most inflationary models predict a stochastic background of gravitational waves which would imprint a unique B-mode pattern in the polarization of the Cosmic Microwave Background (CMB) that peaks at degree angular scales. The strength of this signature is parametrized by the tensor-to-scalar ratio r. A nonzero measurement of r would provide direct evidence for inflation. The BICEP/Keck series of CMB experiments has been observing the polarized CMB from the Amundsen-Scott South Pole Station since 2006, using small-aperture, on-axis refractors. Continuous integration of a low-foreground, ~1-2% patch of the sky has produced maps over multiple frequencies that lead to world-leading constraints on r from B-mode measurements: r_0.05 0.034 and σ_r = 0.009 using data through the 2018 observing season. The BICEP/Keck telescopes measure polarization by taking the difference between two co-located, orthogonally polarized detectors. A prominent systematic that must be controlled is the leakage from the bright CMB temperature sky into the polarization measurement due to mismatch in the angular response patterns (beams) of the two detectors within a pair. In this dissertation, we use high-fidelity in-situ measurements of the per-detector beam response in conjunction with specialized simulations to quantify the level of temperature-to-polarization (T-P) leakage expected in the BK18 data set, and the associated impact on the r constraint. We also use Fourier transform spectrometer measurements of the spectral response to constrain the bias on r from band center uncertainties. We introduce simple metrics evaluated only from the beam maps (without simulations) that estimate the T-P leakage and other optical properties, and discuss progress of optical modeling of small-aperture telescope beams, including their ability to predict T-P leakage. Finally, we assess the utility of these simulations, metrics, and optical models as we move forward to the next generation of CMB experiments with hundreds of thousands of detectors.
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