Quantum Expanding Spacetimes

This award supports the research activities of Professor Alexey Milekhin at the University of Kentucky. Modern physics rests on two extraordinarily successful theories: quantum mechanics, which describes matter and information at very small scales, and general relativity, which describes gravity and the structure of space and time. Yet these theories appear to be in tension in settings where space itself expands, such as our universe and the interiors of black holes. Quantum mechanics requires information to be preserved, while general relativity allows space to expand and black-hole interiors to grow, raising difficult questions about where and how quantum information is stored. This project asks a fundamental question: Can expanding spacetimes be described by quantum systems that preserve information? In this research, Professor Milekhin will address this question from two complementary directions. First, he will study de Sitter space --- the simplest model of an accelerating universe and a close approximation to our own --- using tools from quantum information theory and controllable models of many interacting quantum components. Second, the project will develop new ways to study black-hole interiors and Hawking radiation. In particular, it will investigate “deep thermalization,” which probes more detailed properties than ordinary thermal equilibrium, and “entanglement in time,” a new measure of quantum correlations between events occurring at different times. Together, these approaches will clarify how the growth of spacetime can be reconciled with the fundamental principles of quantum mechanics. Research in this area will advance the national interest by deepening our fundamental understanding of gravity, one of the fundamental interactions of nature, while producing conceptual and mathematical tools relevant to quantum information science and quantum many-body physics. The project will also strengthen quantum science research at the University of Kentucky by supporting and training graduate students and postdoctoral researchers. Results will be disseminated through publications, conferences, and seminars that connect the quantum gravity and quantum computing communities. The project also includes accessible popular science articles and public lectures throughout Kentucky, designed to communicate modern ideas about quantum physics, black holes, and cosmology to broad audiences and to encourage students to pursue careers in science. More technically, this project investigates whether expanding spacetimes, including de Sitter space and black-hole interiors, admit a fully unitary quantum-mechanical description. It combines model-independent tools from quantum information theory with analytically tractable holographic models based on the Sachdev–Ye–Kitaev family. For de Sitter space, the research will analyze two- and higher-point correlation functions, operator growth, out-of-time-ordered correlators, scrambling, and super-diffusive transport, with the goal of identifying the quantum many-body universality class capable of reproducing cosmological-horizon dynamics. The project will also test and extend proposed de Sitter/SYK correspondences by comparing correlation functions, thermodynamics, entropy, and late-time behavior, and by constructing deformations that may realize de Sitter or related “centaur” geometries. For black holes, the project will develop two fine-grained probes of interior dynamics: deep thermalization, which studies the full distribution of observables conditioned on the environment, and entanglement in time, which characterizes quantum correlations between time-separated subsystems. These tools will be used to examine deviations of Hawking radiation from thermality, the possible role of replica wormholes, and whether the growth of black-hole interiors is consistent with unitary quantum dynamics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.