Arnold Sommerfeld Center for Theoretical Physics
Quantum gravity manifests to the highest degree all that I find exciting in scientific research in general: to be at the frontier of knowledge, questioning even the most basic elements of our understanding of natural phenomena; to navigate through uncertainty and intellectual surprises, finding a new question behind any new answer; to be constantly amazed by the complexity, richness and beauty of the natural world.
Main research focus: Quantum Gravity and emergence of spacetime, quantum information techniques in quantum gravity, fundamental cosmology, foundations of quantum mechanics
The problem of the quantum nature of spacetime and geometry, and its cosmological implications, is the focus of my research. Many results in semi-classical physics (e.g. black hole and spacetime thermodynamics) strongly suggest an underlying discrete, non- spatiotemporal microstructure, not corresponding to straightforwardly quantized continuum fields, and several quantum gravity formalisms provide concrete proposals. Therefore, at the fundamental level, spacetime `dissolves' into new quantum entities (“atoms of space”), of no direct gravitational or spatiotemporal interpretation, from which it emerges in suitable approximations.
We work on several quantum gravity formalisms, with a special focus on tensorial group field theories (TGFTs). TGFTs are field theories for fundamental building blocks of space, pictured as polyhedra, such that: a) their discrete geometry is encoded in group-theoretic data, b) many-body states correspond to polyhedral complexes, c) interaction processes produce cellular complexes of one dimension higher. TGFTs tackle problems in quantum gravity using ideas from condensed matter physics and quantum information in a very direct way, since they describe spacetime as a (peculiar) quantum many-body system.
Our research within MQC/MCQST is organized mainly along two directions.
- Foundations of quantum spacetime: quantum geometry, causality and entanglement
Focus: construct compelling models of quantum spacetime, and clarify its quantum information foundations, in particular how entanglement grounds its topological, geometrical and causal aspects
Most TGFT models for 4d quantum gravity are based on simplicial geometry and spin foam techniques. In the Lorentzian setting, though, work has been limited. In order to boost modelbuilding, we have developed a formulation based on flux variables (conjugate to the discrete gravity connection), using tools from non- commutative geometry, notably the non-commutative Fourier transform for Lie groups, in the Riemannian setting. Now the focus is on developing Lorentzian TGFT models, based on the same non-commutative tools, and analyze in detail how the incorporate the discrete and quantum seeds of continuum causal structures. The growing conviction that spacetime emerges from purely quantum non-geometric entities has spurred a lot of activities at the interface of quantum information and geometry in several quantum gravity formalisms. Tensor networks techniques play a powerful role in these activities, as computational tools, and as encoding structural properties of entangled quantum systems. We have recently defined a dictionary between TGFT states and generalised tensor networks, with applications to holography and new derivations of the Ryu-Takayanagi area-entropy relation in quantum gravity. Future research will focus on the quantum information- theoretic characterisation of quantum gravity states, with special attention to entanglement properties, and tensor networks techniques in the analysis of their dynamics, coarse-graining and emergent geometry.
- Emergent cosmology from quantum gravity: the universe as a quantum fluid
Focus: extract effective cosmological dynamics from quantum gravity and make contact with observations
All current semiclassical cosmological scenarios for the early universe are fundamentally incomplete, since they make assumptions, about the initial state of the universe, or the resolution of the big bang singularity, that semi-classical physics cannot control. Quantum gravity can complement such cosmological scenarios or suggest new ones. Moreover, in emergent spacetime scenarios, also largescale features of cosmological dynamics (e.g. dark energy), can be of direct quantum gravity origin.The issues faced by quantum gravity approaches in this context are analogous to those faced by condensed matter theorists (the extraction of macroscopic dynamics from the atomic description of a system). Inspired by this analogy, we have explored the idea of quantum spacetime as a condensate of TGFT building blocks, and of cosmological dynamics as its hydrodynamic regime. We have studied the effective dynamics of TGFT condensate states, showing that: 1) they can describe homogeneous geometries, apt to describe the universe at cosmological scales; 2) for such states, an effective cosmological dynamics can be extracted as the TGFT hydrodynamics, and it reproduces a modified Friedmann equation; 3) quantum gravity corrections may replace the big bang singularity with a quantum bounce; 4) the emergent cosmological dynamics allows for a late-time accelerated expansion of purely quantum gravity origin, analogous to phantom dark energy. The next steps are: a)to extend this framework to include further aspects of the microscopic theory (e.g. entanglement among spacetime constituents, anisotropies); b) analyse the cosmological interpretation of quasiparticles and depletion terms in the quantum gravity condensate; b) to derive a complete theory of cosmological perturbations from first quantum gravity principles, and connect quantum gravity models in a solid manner to CMB and other cosmological observations.
- Other research directions of our group include the foundations of physical theories, with specific interest in conceptual issues of emergent spacetime scenarios, and in the foundations and interpretations of quantum mechanics. In this latter context, we focus on epistemic interpretations, based on quantum information and on a relational or agent-based perspective of quantum states.