Quantum Physics in de Sitter Spacetime

Summary

A de Sitter spacetime is the maximally symmetric solution to Einstein’s field equations endowed with a positive value for the cosmological constant. It describes a universe undergoing exponential expansion in time. Due to the exponential expansion, different regions of the de Sitter spacetime can become causally disconnected. Thus, de Sitter space bears resemblance to, though being distinct from, the properties of black hole horizons.

There are two cosmological epochs wherein a de Sitter phase appears to be of physical relevance. According to the inflationary scenario, at early times the universe underwent a period of primordial quasiexponential expansion. The current evolution of the large-scale universe appears to be driven by a cosmological constant causing a second epoch of accelerated expansion. In both cases, the large-scale structure of spacetime is well approximated by the idealized de Sitter model.

Moreover, both periods of exponential expansion necessitate an understanding at the quantum level. During inflation, quantum fluctuations of light fields, including those of the spacetime metric, must be understood. The cosmological constant receives quantum contributions from the vacuum energy of all quantum fields present in the universe.

Due to its highly symmetric character, the de Sitter spacetime constitutes a natural theoretical laboratory to study quantum properties of fields and gravity in a cosmological setting. The properties of quantum fields can be organized in a form structured around the maximally large isometry group of de Sitter space. This governs the mathematical properties of their respective late-time correlation functions.

A complete mathematical framework for a quantum theory of gravity encoding de Sitter vacua is an ongoing task. An important avenue is to understand, in as precise a form as possible, the construction of de Sitter solutions within the framework of string theory. Further to this, lessons stemming from more general methods and theoretical toolkits—notably Euclidean quantum gravity and lower-dimensional models of quantum gravity—are argued to play a key role in the study of the de Sitter space and its quantum features.