Cosmology and Causal Structure in 2+1d Spin-foam Quantum Gravity

• Applicant: Dr. José Diogo de Figueiredo e Simão
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 551576920

This project considers the application of spin-foam quantum gravity to cosmology, with an emphasis on Lorentzian signature and causal structure. Spin-foams are a non-perturbative and background-independent approach to quantum gravity, derived from a state-sum formulation. A general spin-foam model involves two ingredients: 1) a characterization of the states at the boundary of the relevant space-time, frequently in terms of spin-networks (as in loop quantum gravity); and 2) an amplitude map as a function of those very states. Recently a new spin-foam model for 3-dimensional Lorentzian quantum gravity was proposed. The model assigns a quantum amplitude to a polyhedral graph once a causal character (i.e. space- or time-like) is assigned to every edge of the polyhedron. The mathematical structure and semiclassical limit of the model are well under control for all causal cases, and in such a way that the new model may be applied to cosmological scenarios where the causal structure is thought to play an important role. The main goal of this project is therefore to develop a semiclassical cosmological framework based on the new 3d spin-foam model. The project is divided in two parts: 1) (Main) To implement a numerical simulation of the spin-foam amplitude without cosmological constant, adapted to the cosmological principle of spatial homogeneity and isotropy, and to study the possibility of a cosmological bounce. A cosmological constant is to be added to the theory, as well as a free scalar field. The dependence of the dynamics on the assignment of causal character is to be scrutinized in detail. B) (Exploratory) To couple a self-interacting scalar field to the theory, so as to model Starobinsky inflation. Moreover, starting from the 3d model, an analysis and possible improvement of the so-called EPRL spin-foam amplitude for 4-dimensional Lorentzian quantum gravity will be performed.

• DFG Programme: WBP Fellowship
• International Connection: Portugal
• Host: Professor Dr. João Rosa