Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
Modular Fluctuations in Cosmology
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abstract
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 $\delta L \sim \sqrt{\ell_p L}$, 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.
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hep-th 2years
2026 2representative citing papers
Quantum width of spherically symmetric black hole horizons is defined by signal escape timing and calculated in perturbative quantum gravity to often greatly exceed the Planck length, scaling as sqrt(l_P r_s^2 / sigma_perp) for Schwarzschild patches.
citing papers explorer
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Relative entropy for $\lambda \phi^4$ in the Rindler wedge
Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
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Quantum Fluctuations of the Black Hole Horizon
Quantum width of spherically symmetric black hole horizons is defined by signal escape timing and calculated in perturbative quantum gravity to often greatly exceed the Planck length, scaling as sqrt(l_P r_s^2 / sigma_perp) for Schwarzschild patches.