Quantum Instability Linked to Universe Expansion

Kazuki Ikeda and Yaron Oz, reveal a competition between redshift and the electric term, creating a pseudo-critical line that governs excitation growth and loss of adiabaticity. Their analysis, utilising exact diagonalization and matrix-product states, connects curved-space gauge dynamics, near-critical spectral structure, and the emergence of operational irreversibility, potentially offering insights into fundamental physics at the intersection of quantum field theory and cosmology. Matrix-product states were key in disentangling different physical scales within this research, representing the quantum state of the system as a network of interconnected mathematical objects and enabling efficient simulation of many-body systems. This approach allows for a tensor network representation, effectively capturing the entanglement structure inherent in quantum many-body problems, which is crucial when dealing with interacting quantum fields in curved spacetime.

By employing matrix-product states, the team separated the effects of a finite system size from the behaviour as the system becomes infinitely large, a process vital for identifying genuine physical phenomena rather than artefacts of the simulation. They used matrix-product states to study quantum electrodynamics in de Sitter space, a theoretical framework combining quantum mechanics with cosmology, to disentangle finite system size effects from behaviour at infinite scales. The de Sitter space is characterised by a constant positive curvature, mimicking the accelerated expansion observed in our universe. Simulations used a fixed mass parameter, separating thermodynamic limits from continuum extrapolations, and data currently suggests a critical time of approximately 3.1, though the dip depth requires further investigation. The fixed mass parameter allows for a systematic study of the system’s behaviour without introducing additional complexities related to mass variations, facilitating a clearer understanding of the interplay between redshift and the electric term. The thermodynamic limit refers to the behaviour of the system as its size approaches infinity, while continuum extrapolations involve taking the lattice spacing to zero to recover the true continuum physics.

Spectral dip survival and irreversibility fronts in infinite volume QED2

The late-time spectral dip in quantum electrodynamics (QED2) now persists in simulations with infinitely large physical volumes, representing a substantial advancement over earlier, finite-size limited work. The spectral dip refers to a reduction in the density of states at certain energies, indicating a suppression of particle production. Establishing behaviour at infinite scales previously proved elusive, but this survival was confirmed by extrapolating data to zero lattice spacing, demonstrating a continuum limit and solidifying the reliability of the findings. A ‘pseudo-critical line’ at approximately τ* ≈ 3.1 governs excitation growth and the loss of adiabaticity within de Sitter space, a model used to represent an expanding universe. Adiabaticity refers to the slow, gradual change of a system, and its loss signifies the onset of rapid excitation growth and potentially, instability. The pseudo-critical line represents a boundary in parameter space beyond which the system deviates significantly from adiabatic behaviour. This line is crucial for understanding the dynamics of quantum fields in expanding universes, as it dictates the conditions under which quantum effects become dominant.

Matrix-product states distinguished between the fixed-cutoff thermodynamic limit and the continuum extrapolation, improving resolution and detail. This line also defines an ‘irreversibility front’ in relative entropy, detectable through locally accessible measurements, and offers a novel probe of quantum field theory in curved spacetime. Relative entropy is a measure of the difference between two probability distributions, and its increase indicates a loss of information and the emergence of irreversibility. The detection of this front through local measurements provides a practical way to observe the breakdown of adiabaticity and the onset of quantum irreversibility. Increasing the physical box size, followed by lattice resolution refinement, enabled this persistence. Alignment of this ‘irreversibility front’ with the pseudo-critical line suggests a link between curved spacetime, spectral structure, and thermodynamic irreversibility, although the precise depth of the spectral dip remains less certain, and translating these findings into practical applications, such as understanding real-world cosmological phenomena, still requires significant further investigation. The depth of the spectral dip is a key parameter that determines the rate of particle production and the overall energy density of the universe.

Modelling quantum field behaviour in de Sitter space reveals insights into early universe dynamics

Reconciling quantum mechanics with cosmology increasingly focuses on understanding how quantum field theories behave in expanding universes. QED2 within de Sitter space established a controlled setting to explore this interaction; however, fully characterising the depth of the late-time spectral dip remains a key limitation, hindering a complete picture of excitation growth. The challenge lies in accurately modelling the complex interplay between quantum fluctuations and the expansion of spacetime, which can lead to significant deviations from standard flat-space quantum field theory. Quantum chromodynamics, the theory describing the strong nuclear force, has also been successfully modelled within a rapidly expanding space, allowing exploration of conditions shortly after the Big Bang and offering insights into the fundamental forces governing matter. This allows researchers to investigate the behaviour of quarks and gluons in the extreme conditions of the early universe, potentially shedding light on the origin of matter and the formation of hadrons. A competition between the effects of cosmic redshift and the electric force within the quantum field has been demonstrated by identifying a ‘pseudo-critical line’. This establishes a framework for understanding how expanding space impacts quantum field theory, utilising QED2 within a de Sitter space model, which represents a universe undergoing accelerated expansion. The redshift effect, caused by the stretching of spacetime, tends to decrease the energy of particles, while the electric force, mediated by photons, tends to bind them together. The pseudo-critical line represents the point where these two effects balance each other, leading to a qualitative change in the system’s behaviour. Future work will explore similar scenarios with increased complexity and precision, potentially revealing new physics. This includes investigating the effects of gravity on other quantum field theories, such as those describing dark matter and dark energy, and exploring the possibility of detecting these effects through cosmological observations.

The research identified a ‘pseudo-critical line’ within a model of quantum electrodynamics in de Sitter space, demonstrating how expanding space impacts quantum field theory. This line governs the loss of adiabaticity and excitation growth, revealing a connection between curved-space gauge dynamics and operational irreversibility. Researchers used matrix-product states and exact diagonalization to analyse the system, finding a late-time dip in the spectrum at approximately τ* = 3.1. The study establishes a controlled setting for linking cosmological expansion with quantum dynamics, and the authors intend to explore similar scenarios with increased complexity and precision.