Sang-Eon Bak

Verlinde and Zurek (VZ) have proposed that quantum gravity fluctuations in causal diamonds lead to observable effects. In particular, they argued that in quantum gravity causal diamonds have an uncertainty in their size that scales as δ L ∼ ℓ p L , i.e. fluctuations are enhanced from the Planck scale. In this work, we explore the origin of the VZ scaling by studying scalar perturbations in inflationary cosmology. We reinterpret these cosmological perturbations as fluctuations of the modular Hamiltonian associated with a causal diamond, establishing a connection between modular fluctuations and observable primordial perturbations. Independent of assumptions about the modular Hamiltonian or the background spacetime, our results show that—whenever an (effective) spherically symmetric perturbation is quantized—it can lead to the VZ scaling. However, whether such a mode exists in the vacuum of any theory of quantum gravity remains an open question.

In this study, we calculate the m − 1 correction to the reflected entropy for two adjacent intervals on a half-infinite line within the AdS 3 / BCFT 2 framework, where m is a Renyi index for a canonical purification. We utilize the doubling trick and compute the leading terms in the large central charge expansion of correlation functions in the holographic boundary conformal field theory (BCFT). In the corresponding anti–de Sitter (AdS) space with an end of the world brane, we analyze the entanglement wedge cross section, the dual counterpart of reflected entropy. This AdS/BCFT setup allows us to explore a richer set of phases in the entanglement wedge cross section. The m − 1 correction in the holographic BCFT manifests as modifications in the entanglement wedge cross section induced by cosmic branes. For the adjacent intervals anchored to the boundary of BCFT, we show the duality between the entanglement wedge cross section with the backreaction from a cosmic brane and Renyi reflected entropy at all orders in m − 1 . Furthermore, by analyzing the entanglement wedge cross section for general adjacent intervals, we provide guidance for an ε expansion of five-point functions in the holographic conformal field theory (CFT), where ε is the rescaled conformal dimension by the central charge.

We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by such fluctuations. For the gravitational field in its vacuum state, we find that quantum gravity contributes a correction to the null Raychaudhuri equation which is of the same sign as the classical terms. We thus derive a quantum-gravitational focusing theorem valid for linearized quantum gravity.

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.

We consider a timelike geodesic congruence in the presence of perturbative quantum fluctuations of the spacetime metric. We calculate the change in the volume of a bundle of geodesics due to such fluctuations and thereby obtain a quantum-gravitationally modified timelike Raychaudhuri equation. Quantum gravity generically increases the convergence of congruences and the production of caustics.

We consider a timelike geodesic congruence in the presence of perturbative quantum fluctuations of the spacetime metric. We calculate the change in the volume of a bundle of geodesics due to such fluctuations and thereby obtain a quantum-gravitationally modified timelike Raychaudhuri equation. Quantum gravity generically increases the convergence of congruences and the production of caustics.