De Sitter Holography and Excited States via Boundary Conditions

Research establishes a method for defining excited states within de Sitter spacetime using a holographic approach. By introducing a boundary and applying Dirichlet conditions, the study demonstrates consistency between point correlation functions and modified late-time cosmological observables, advancing the holographic dictionary for de Sitter space.

The enduring challenge of reconciling quantum mechanics with general relativity continues to receive attention through explorations of holographic duality, a theoretical framework that connects gravity in a given spacetime to a quantum field theory on its boundary. Recent research focuses on adapting this approach, specifically the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, to de Sitter spacetime, a model frequently used to describe the accelerating expansion of the universe. A novel investigation by Botta-Cantcheff, Cruz, and Martínez, all from the Instituto de Física La Plata (IFLP-CONICET) in Argentina, examines the ‘no boundary proposal’ – an approach defining quantum states without requiring a conventional boundary in spacetime – and extends it to encompass excited states within de Sitter holography. Their work, entitled “The (No) Boundary Proposal and excited states in de Sitter holography”, demonstrates the consistency of point correlation functions with the presence of these excited states and predicts modifications to cosmological late-time observables, potentially refining the holographic dictionary for de Sitter spacetimes.

Recent research investigates the creation of universes from a quantum vacuum, utilising the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence and extending it to de Sitter holography. The AdS/CFT correspondence is a theoretical framework positing a duality between gravitational theories in Anti-de Sitter space—a spacetime with constant negative curvature—and conformal field theories, which are quantum field theories without a characteristic length scale, residing on the boundary of that space. This work explores how excited states of the universe arise and are described by imposing specific conditions on the boundaries of spacetime.

Researchers employ the ‘no boundary proposal’, a method defining the universe’s ground state through a path integral—a mathematical tool used in quantum mechanics to calculate the probability of a particular quantum state—over smooth, Euclidean geometries. Euclidean geometry differs from the familiar geometry of our everyday experience by postulating parallel lines always converge or diverge, rather than remaining parallel. This approach avoids both past singularities—points where physical quantities become infinite—and the need for additional boundaries. The proposal is extended to define a family of excited states by introducing an artificial boundary in the Euclidean region and applying arbitrary Dirichlet boundary conditions. Dirichlet boundary conditions specify the values of fields—such as temperature or density—on the boundary, effectively defining the state of the universe.

Calculations demonstrate consistency between the calculated point correlation functions—mathematical functions describing the statistical relationship between points in spacetime—and the presence of these excited states, providing mathematical validation of the methodology. Crucially, the research reveals that cosmological late-time observables—quantities measurable at very late times in the universe’s evolution—undergo significant modifications in these states, suggesting the universe’s evolution differs depending on its initial quantum state. This offers a potential explanation for observed cosmological phenomena, such as the accelerated expansion of the universe.

This work contributes to the development of a holographic dictionary for de Sitter spacetimes—spacetimes with constant positive curvature, resembling our own universe—a crucial step towards a complete understanding of the universe’s quantum gravity. By establishing a correspondence between gravitational phenomena in de Sitter space and quantum field theory on its boundary, the research provides a new avenue for calculating quantities that are otherwise intractable using traditional methods. This approach effectively adapts techniques from AdS/CFT correspondence to the context of de Sitter space, offering a novel means of exploring the nature of quantum cosmology.

Future research will focus on exploring the implications of these findings for understanding the early universe and the nature of dark energy—a mysterious force driving the accelerated expansion of the universe. Scientists plan to investigate the possibility of using these techniques to develop new models of inflation—a period of rapid expansion in the early universe—and the cosmic microwave background—the afterglow of the Big Bang. They also intend to explore the connection between de Sitter holography and other approaches to quantum gravity, such as string theory and loop quantum gravity, and further refine the holographic dictionary to provide a more complete and accurate description of the relationship between gravity and quantum mechanics.