General Relativity & Quantum Cosmology

Observers in a typical gravitational or cosmological setting only have access to part of the spacetime and the degrees of freedom in it. The observer sees an open quantum system, and the complete dynamics of all degrees of freedom can be reconstructed by gluing together the (possibly overlapping) open systems associated with each observer. I will discuss what can be learned from treating familiar laboratory closed systems as ensembles of open systems, and how we can begin to extrapolate from there to systems relevant for cosmology.

I will discuss aspects of  the path sum of causal set theory, in which the continuum is replaced by a sample space of locally finite partially ordered sets.  This sample space not only contains continuumlike causals of different dimensions, but an entire zoo of non-continuumlike ones.  An open question is whether this path sum can be treated as a UV regularisation of the continuum path integral, as  the number of elements increases. I will discuss some results as well as  challenges in answering this question.

While a complete theory of quantum gravity remains elusive, several alternative approaches are being explored. Which ones are the most promising, and whether they are connected or fundamentally distinct, remain outstanding open questions. I will argue that looking at quantum gravity through the lens of effective field theory offers a promising path to test the internal consistency of different theories and systematically compare their low-energy manifestations. I will illustrate this perspective using asymptotically safe quantum gravity as a case study, discussing its interface with positivity bounds and swampland conjectures. Finally, I will outline how a similar strategy can be utilized to chart the landscape of quantum spacetimes stemming from an asymptotically safe ultraviolet completion.

Many researchers in quantum gravity favour the notion of a quantum foam, coined by Wheeler 70 years ago to capture "whatever becomes of spacetime at the Planck scale". The underlying idea is that the quantum fluctuations of spacetime are so large that a description based on smooth metrics is no longer adequate. Equally popular is the notion that spacetime as we know it should "emerge" from this primordial quantum foam, alongside interesting quantum-gravitational effects. These ideas are enticing, but remain speculative unless backed up by quantitative analysis and modelling within a coherent, nonperturbative formulation of quantum gravity. Fully nonperturbative computational tools are available in the form of 'lattice quantum gravity 2.0', based on causal dynamical triangulations. The power and beauty of this methodology lies in its use of curved, dynamical lattices, incorporating the principles of quantum field theory and general relativity from the outset. This has produced quantitative blueprints of both quantum foam and spacetime emergence, and a concrete perspective on what it means to “solve" quantum gravity. [arXiv:2501.17972]