# Microscopic Quantum Structure and Dynamics of Spacetime

The research of the group aims at constructing a complete theory of quantum gravity, valid at all scales of distances and energies.

The research of the group focuses on Quantum Gravity, that is the construction of a theory of space, time and geometry in terms of fundamentally quantum degrees of freedom, valid at all scales of distances and energies, but reducing to General Relativity at large distances and in a semi-classical approximation. A theory of Quantum Gravity is also needed to describe the universe as a whole, including its beginning and possible end, and to shed light on cosmological puzzles like the nature of dark energy, and on the fate of Lorentz and Poincare' symmetry at higher energies.

The main, foundational questions at the root of quantum gravity research are the most fundamental of all: what is space? what is time? what is the fundamental structure of the universe and the physical reason for its very existence?

Our group works in the context of several recent approaches to this problem. In particular, we focus on Group Field Theories, Tensor Models, Loop Quantum Gravity, Spin Foam Models, Simplicial Quantum Gravity, all closely related to each other. These approaches are all background independent, in the sense that they do not assume a fixed background spacetime structure, but deal with how spacetime itself (in both its geometric and topological properties) is dynamically generated from some basic building blocks, and thus describe it as fundamentally discrete. Starting from different assumptions and using different techniques, all have achieved important results concerning both the kinematical description of quantum space, and the tentative description of its dynamics. Many formal aspects of such dynamics are still to be understood, however, as is the mutual relations between these approaches. One of our main lines of research concerns precisely the formal development of all of them. Also, we aim at clarifying the links between them, and try to merge the different insights that each of them provides about space and time at the Planck scale.

The main questions that all these approaches to quantum gravity have to answer, before being considered as successful, are: If spacetime is fundamentally discrete, where does the continuum spacetime we experience at low energies and macroscopic scales come from? How does such a continuum spacetime emerge from its fundamentally discrete building blocks, and end up being described by General Relativity? And in this macroscopic regime, what are the phenomenological and experimental implications of the fundamental quantum discrete structure of spacetime and of their microscopic dynamics?

It is our main research objective to answer these questions in a rigorous way. In doing so, we also aim at producing effective descriptions of the fundamental quantum dynamics of space and matter, which could be used to predict new phenomena and quantum gravity corrections to the cosmological dynamics, of the early universe in particular.

We use also mathematical tools and physical insights coming from other areas of theoretical physics, for example condensed matter theory and statistical field theory. In particular, we look at analog gravity models in condensed matter physics, as instances of the transition between discrete microscopic and continuum macroscopic realms, and of the emergence of gravity (and matter) from non-gravitational systems.

Bridging the gap between our (tentative) descriptions of quantum spacetime at the Planck scale and the world as we see it also means constructing effective models of a quantum spacetime and making contact with quantum gravity phenomenology. To this aim, we study the relation between the above-mentioned approaches and effective non-commutative models of spacetime and matter in the near flat regime, and with non-commutative geometry in general. Indeed, they form the basis of much of current quantum gravity phenomenology, focusing on the possibility of quantum gravity-induced deformation of relativistic dispersion relations and scattering thresholds. Finally, as mentioned, an important part of the group's research is concerned with (quantum) cosmology. We work on the extraction, from fundamental theories, of simplified quantum gravity models suitable for the description of the universe at large scales. Using them, we aim at obtaining new insights on the role that quantum gravity effects play in the early phases of the evolution of the universe, close to the big bang, and in the formation of large scale structures (including the universe itself).

People working on this topic:

*Junior scientists:*

Joseph Bengeloun

Lorenzo Sindoni

Casey Tomlin

Edward Wilson-Ewing

**PhD students:**

Marco Finocchiaro

Alexander Kegeles

Johannes Thürigen

**Master/Diploma students:**

Nicolai Friedhoff

**Long-term visitors:**

Stefano Bianco