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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.

Primordial black holes (PBHs) are believed to form through the gravitational collapse of overdense regions in the early Universe. They may serve as seeds for galaxy formation and are also considered one of the important candidates for cold dark matter (DM). In particular, I will focus on several representative toy models of single-field inflation. The enhanced primordial perturbations in these models can not only produce PBHs, but also generate gravitational waves through higher-order effects. I will further extend the discussion to the possibility of a PBH-dominated era, which could leave observable signatures if PBH evaporation produces stable relics. These studies demonstrate the significant potential of PBHs as probes of the early Universe, naturally leading to the important question of how to accurately estimate the PBH abundance. In the latter part of the talk, I will introduce a method based on peaks theory for estimating the abundance of primordial black holes. Our approach works well for arbitrary forms of the power spectrum, and by incorporating more systematic statistical methods, we expect it to provide useful cross-checks in combination with future gravitational-wave observations and related cosmological probes.

Black holes pose sharp consistency questions at the interface of gravity, quantum mechanics, and thermodynamics. It is widely believed that resolving problems such as providing a microscopic account of Bekenstein–Hawking entropy, understanding the origin of black hole thermodynamics, and resolving the information paradox posed by Hawking radiation will provide valuable insights to the construction of the theory of quantum gravity. In this talk, I discuss a recent proposal [1,2] of a quantum mechanics of quantized space as a model of quantum black hole and quantum gravity in 4-dimensions. Our construction was motivated by the bottom-up approach [3,4]. As a system of quantum bits of quantum space, our model reproduces not only the needed macroscopic properties of the Schwarzschild black hole [1] and the rotating Kerr black hole [2], it also provides a microscopic counting of the Bekenstein-Hawking entropy of black hole [1,2] and explains the origin of Hawking radiation in terms of a tunneling process of emission of monopole in the quantum mechanics [5]. As application, I discuss how the well-known membrane paradigm of black hole is modified by quantum gravity effects [6]. In classical general relativity, the black hole membrane is an electrical conductor with a constant vacuum resistivity. We identify new quantum gravity effects and show that the quantum black hole membrane has also a frequency dependent inductance and a chiral Hall conductance. We propose to test these new effects with the observation of quasi-normal modes.

1. Matrix model proposal for quantum gravity and the quantum mechanics of black holes, Phys.Rev.D 112 (2025) 6, 066001, Chong-Sun Chu
2. Quantum Kerr black hole from matrix theory of quantum gravity, Phys.Rev.D 112 (2025) 4, 046014, Chong-Sun Chu
3. Fermi model of a quantum black hole, Phys.Rev.D 110 (2024) 4, 046001, Chong-Sun Chu
4. Tunneling of Bell particles, page curve and black hole information, Phys.Lett.B 865 (2025) 139486, Chong-Sun Chu
5. Hawking Radiation from Tunneling in Black Hole Quantum Mechanics, e- Print: 2603.12199 [hep-th], Chong-Sun Chu
6. Membrane Paradigm for Quantum Black Hole, to appear, Chong-Sun Chu

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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