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Abstract
Diffusion damping of the cosmic microwave background (CMB) power spectrum results from imperfect photon-baryon coupling in the pre-recombination plasma. Energy release at redshifts $5 \times 10^4 < z < 2 \times 10^6$ can create $\mu$-type spectral distortions of the CMB. These $\mu$-distortions trace the underlying photon density fluctuations, probing the primordial power spectrum in short-wavelength modes $k_\mathrm{S}$ over the range $50 \ \mathrm{Mpc}^{-1} \lesssim k \lesssim 10^4 \ \mathrm{Mpc}^{-1}$. In this thesis, I will discuss my work on using $\mu$-distortions to probe inflation. First, I will discuss how models that seek to greatly enhance small scale power in order to form primordial black holes (PBHs) will induce a local curvature in the plasma and spatially modulate the beginning of the $\mu$ era, thus producing anisotropic $\mu$-distortions. Another method of generating $\mu$-anisotropies is if small-scale power modulated by long-wavelength modes originates from squeezed-limit non-Gaussianities, parameterized by $f_\mathrm{NL}$. My second work will forecast how well the Cosmic Microwave Background - Stage IV (CMB-S4) experiment can constrain cross-correlations between $\mu$-anisotropies and temperature anisotropies from \fnl. Then, I will discuss how $\mu$-distortions will modify the thermal Sunyaev-Zel’dovich (tSZ) effect, a spectral distortion of the CMB resulting from inverse Compton scattering of CMB photons with electrons in the medium of galaxy clusters, and the ability of CMB experiments to measure $\mu$-distortions from this effect. Lastly, I will discuss a novel idea of using the Square Kilometer Array (SKA) to measure $\mu$-anisotropies at radio wavelengths in order to improve constraints on $f_\mathrm{NL}$ compared to traditional CMB experiments.