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Major improvements in the theoretical understanding of LSS have been possible due to the effective field theory approach. After an overview of the perturbation theory applications for LSS, I will discuss how to go beyond the one-loop calculation, presenting novel two-loop results and their information content (both for clustering and lensing). I will also show how to extract information from higher-loop orders using renormalization group equations.

Big Bang Nucleosynthesis (BBN) provides a powerful probe of hadronic injection from new physics that modifies the neutron-to-proton ratio, thanks to the precisely measured primordial helium-4 abundance. In this talk, I apply this probe to long-lived particles, specifically heavy QCD axions which are well-motivated candidates that can address the strong CP problem and predominantly decay into hadrons. We compute the axion-induced modification of the neutron-to-proton ratio and derive robust upper bounds on the axion lifetime, as short as 0.017 seconds, well before 1 second, the onset of BBN. While motivated by the axion study, we also make several significant and broadly applicable advances in the treatment of hadronic injection during BBN. These include new or updated hadronic cross sections, scattering processes involving energetic neutral kaons (KL), and the effects of secondary hadrons. Neglecting these effects can lead to significant misestimates of the primordial helium-4 abundance. In addition, we derive a semi-analytic solution that allows us to estimate theoretical uncertainties and demonstrate the robustness of our bounds.

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There have been growing interests in quantum states of photons (and gravitons) produced, say, from conversion of axion dark matter (and binary black holes). With high luminosity (or large occupation number), they are well described as classical waves. On the other hand, as luminosity decreases, quantum nature gets more significant. A half century ago, Roy Glauber showed that photons produced by a classical source follow the coherent state. We generalize this notion of Glauber including quadratic non-linearity and show that photons follow the displaced squeezed state. We compare our full treatment with a simplified treatment found in the literature.

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