Random Matrix Product States RMPS Unlock Early Cosmology
A Seoul National University-MIT physics collaboration produced a research in December 2025 that significantly changed our understanding of the early universe. Using Random Matrix Product States (RMPS), researchers Sunghoon Jung, Sungjung Kim, Jiwoo Park, and Seokhyeon Song have been able to study the universe's "initial state" when Einstein's General Relativity's smooth geometry disintegrates into a turbulent "quantum foam."
Breakthrough: Quantum Foam Mapping
This discovery centres on “gravitationally prepared states”. In quantum field theory, these states represent a closed world's quantum wave function. They are constructed by visualising a universe where gravity has boundary limitations but matter does not. These states preserve the whole history of gravitational events, which is vital for universe evolution.
Researching these states has been difficult due to their intricacy. Standard scientific methods struggle to explain “higher topologies” or “Wormhole Phase Transition,” complex spacetime geometries with many holes and bridges. Before this study, traditional semiclassical techniques were assumed to be unable to determine the contributions of these complex structures to the universe.
Understanding Gravity-Ready States
The research team solved these problems with Random Matrix Product States. The “tensor network” apparatus was designed for many-body quantum systems, including atom behaviour in crystals. The researchers added randomness to these matrices to represent quantum gravity's statistical behaviour.
The RMPS approach is unprecedentedly accurate. It can construct complex geometric configurations, including quantum entanglement "replica geometries," to all orders of approximation. With this precision, scientists may study how past gravitational history affects matter fields now.
Innovation: Random Matrix Product States
Key findings include the “bra-ket wormhole phase transition” confirmation. “Bra” and “ket” are the two sides of a quantum probability computation. These two sides are connected gravitationally by a Wormhole Phase Transition.
As the universe's geometry alters fundamentally, this phase shift may be mathematically assured, the researchers found. This is guaranteed if the RMPS "transfer matrix" fits the spectral gapping property. This conclusion is essential because it provides a rigorous mathematical basis for understanding why and when wormholes dominate early cosmic physics, moving the issue from theoretical speculation to mathematics.
Bra-Ket Wormhole Phase Transition
The “off-shell” wormhole revelations were astounding. Classical physics calls configurations that follow equations of motion “on-shell” like a tossed ball. However, “off-shell” structures are quantum fluctuations and do not follow classical paths.
Because gravity models lack stable classical solutions, they often miss off-shell wormholes, whereas the RMPS model can include them. The researchers found that off-shell structures lead to nonzero long-distance correlations in gravitationally prepared states. This shows that a wormhole's quantum presence connects distant portions of the cosmos even if it isn't a fixed “bridge” and may leave quantitative evidence for researchers to locate.
Long-distance correlations and off-shell wormholes
The researchers extended their model from two-dimensional to continuous space to study de Sitter gravitationally prepared states. This is relevant to our reality because de Sitter space provides the mathematical model for accelerated expansion, like cosmic inflation.
By applying matrix models to de Sitter space, the group created a new “toolkit” for studying quantum gravity events with non-perturbative effects that are too powerful or sophisticated for step-by-step approximation. This research sheds light on quantum phenomena and spatial geometry.
Cosmological Implications: de Sitter Space and Inflation
Information theory, condensed matter physics, and high-energy physics are the key scientific fields involved. The “holographic” view of the cosmos posits that spacetime emerges from quantum entanglement rather than being a basic “fabric.”
The following are key study pillars:
An anti-de Sitter space conformal field theory-gravity duality: the AdS/CFT Correspondence.
The structure of spacetime can be understood using quantum entanglement and entropy.
Information Scrambling: The “butterfly effect” suggests that qubits, quantum events like black holes, can scramble information.
Even without a "Theory of Everything," this RMPS framework can guide future study. Future studies will focus on:
The Nature of Time: How previous gravitational history encodes the current quantum state.
Cosmic Inflation: Investigating whether long-distance correlations explain early universe matter distribution.
Quantum Error Correction: Comparing computational quantum coding to Wormhole Phase Transition mathematically.
By showing that wormhole phase transitions are inherent to quantum matrices, the vast, expanding universe is linked to them.
