The stability of empty space, or the ‘false vacuum’, is a fundamental question in cosmology, and understanding how it might decay is crucial for our understanding of the universe. Victor Ivo from Princeton University, alongside colleagues, investigates this decay by examining the contribution of Coleman-de Luccia instantons, theoretical solutions describing the process of vacuum decay, at a more refined level of detail. The team computes these contributions at the ‘one-loop’ level, a significant step towards greater accuracy, and demonstrates that, under certain conditions, the calculation neatly separates into contributions from pure gravity and the matter fields within it. This work clarifies the behaviour of previously ambiguous calculations, proposes a formula for calculating the rate of false vacuum decay using gravitational path integrals, and importantly, shows this formula aligns with established results from particle physics in certain limits, offering a powerful new approach to understanding the fate of the universe.
One loop aspects of Coleman de Luccia instantons at small backreaction Scientists investigate the behaviour of Coleman-de Luccia instantons, solutions describing transitions between vacuum states, by computing their contribution to decay rates at the one-loop level with small gravitational effects. The research demonstrates that, at this level of approximation, the contribution from these instantons separates into distinct components representing gravity and matter, simplifying calculations and providing new insight into their interplay. This factorization clarifies how quantum fluctuations influence these spacetime solutions and advances understanding of false vacuum decay, a process with implications for the stability of the universe.
The team also proposes a formula for calculating the rate of false vacuum decay, expressed in terms of gravitational path integrals, a mathematical technique for summing over all possible spacetime geometries. This definition aligns with standard quantum field theory results when gravity is weak, confirming its consistency with established physics. Finally, scientists propose a method to track how the phase of the path integral changes as theoretical parameters are altered, offering a practical way to analyze the decay process.
False Vacuum Decay and Quantum Gravity Links
This research explores the intersection of quantum mechanics and gravity, particularly in the context of the early universe and the stability of the vacuum state. Scientists investigate false vacuum decay and the mathematical tools used to describe it, known as instantons. A central challenge is ensuring these instantons remain mathematically consistent and physically meaningful when gravity is involved, addressing recurring issues with negative modes that signal instability in calculations.
The calculations rely heavily on path integrals and partition functions, fundamental tools in quantum field theory, to accurately compute probabilities even in complex gravitational backgrounds. De Sitter space, a model for the expanding universe, serves as a key background, and understanding quantum fields near its horizon is crucial. The research also touches on black hole thermodynamics, exploring corrections to classical results due to quantum effects, and ensuring the quantum theory remains consistent and preserves probability.
Early work by Hawking and Moss, Coleman, and Callan laid the groundwork for understanding phase transitions and tunneling in the early universe. More recent contributions from Tanaka, Sasaki, and others focus on resolving the negative mode problem in false vacuum decay. Anninos, Denef, and Law have made significant contributions to calculating entropy in de Sitter space, while Law’s work provides a compendium of sphere path integrals. Donnelly and Wall have explored the unitarity of Maxwell theory on curved spacetimes, and Kapec, Sheta, Strominger, and Toldo have investigated logarithmic corrections to black hole thermodynamics.
Witten’s recent work focuses on background-independent algebras in quantum gravity, and a collaboration between Chandrasekaran, Longo, Penington, and Witten has developed an algebra of observables for de Sitter space. Key concepts employed include instantons, path integrals, partition functions, negative modes, and renormalization. Euclidean quantum gravity and background independence are also central to the research.
This collection of research papers represents the cutting edge of theoretical physics, grappling with some of the most challenging problems in our understanding of the universe. The recurring themes of negative modes, instability, and the need for background independence highlight the difficulties in constructing a consistent and complete theory of quantum gravity.
False Vacuum Decay, Factorization and Clutch Prescription
This research advances understanding of false vacuum decay, a process with implications for the stability of the universe, through detailed calculations of gravitational path integrals around Coleman-de Luccia instantons. Scientists computed the contribution of these instantons to decay rates at a high level of approximation, revealing that this contribution neatly separates into components representing pure gravity and matter effects. This factorization simplifies calculations and clarifies the interplay between gravitational and quantum effects in false vacuum decay.
The team also developed a novel method, termed the “Clutch prescription”, to track changes in the phase of the path integral as theoretical parameters are altered, offering a practical way to analyze the decay process. While acknowledging the limitations of this prescription, particularly its sensitivity to zero eigenvalues, the researchers demonstrate its effectiveness through illustrative examples. Furthermore, they extended this work by investigating how to incorporate semiclassical observers into the expanding spacetime resulting from bubble nucleation, examining geodesic paths within these geometries and comparing them to those in de Sitter space. This exploration lays groundwork for future investigations into the role of observation within these complex cosmological scenarios and provides a basis for more fundamental definitions of phase changes in coupled systems.