# Quantum theory and gravity

Our research covers many aspects of quantum gravity and quantum field theory in curved spacetimes.

A major interest of our research group is the theory of quantum fields in curved spacetime, often in the framework of algebraic quantum field theory, which provides a synergy between rigorous mathematics and conceptual clarity.

Our work involves rigorous techniques drawn from areas of pure mathematics such as functional analysis, operator algebras, differential geometry, microlocal analysis and category theory.

Specific interests include:

### Effective quantum gravity and the problem of relational observables

We approach the quantisation of gravity from a QFT perspective, with metric perturbations as a quantum field on a curved background. This theory is not renormalisable in the usual sense but can be understood as an effective theory valid up to a given energy scale. This allows one to describe phenomena where quantum gravity effects are relatively weak. An important issue is to identify physical observables of the theory, which must be diffeomorphism-invariant, and are hence non-local. The most promising approach is to use relational observables.

### Quantum energy inequalities

Unlike most classical forms of matter, quantum fields can have locally negative energy densities. We are investigating limitations within QFT itself, deeply connected to the uncertainty principle, that prevent the energy density being too negative on average. These limitations are expressed mathematically by Quantum Energy Inequalities (QEIs).

### QFT in de Sitter space

QFT in cosmological spacetimes is an important subject because experimental data in cosmology are becoming more and more accurate. We study aspects of QFT in de Sitter space, which approximates the very early universe in inflationary cosmology, such as the infrared properties of the gravitational perturbations and the so-called partially-massless fields.

### Quantum fields on discrete spacetime backgrounds

Several approaches to quantum gravity assume spacetime to be discrete at small scales. It is important to be able to construct quantum fields on such structures and to understand how they relate to the theory of QFT on continuum spacetimes.