Semiclassical gravity: conceptual and mathematical foundations

Fundamental physics currently describes nature using two distinct theories. Large-scale gravitational phenomena are described by general relativity. This theory makes astounding --but experimentally corroborated-- predictions such as the existence of black holes and gravitational waves and describes the large-scale structure of the universe. Meanwhile, quantum theory extremely accurately describes the microscopic world, including the laws of the fundamental quantum fields, which describe the subatomic particles that are the building blocks of the matter we know in our universe.

Enormous scientific efforts have been made to unify these two theories into a single 'quantum gravity theory', and important advances have been achieved. However, despite undeniable progress, a fully-workable and complete theory of quantum gravity is still beyond our reach. Nevertheless, we think that --whatever the details-- there should be a mesoscopic regime where quantum gravity is approximated by a theory called semiclassical gravity, which describes the effective interactions of quantum matter with classical gravity.

Semiclassical gravity has offered us fascinating insights on quantum gravity. A notable example is the prediction that black holes evaporate, highlighting important tensions in the gravity-quantum unification, collectively known as the 'information loss puzzle': if black holes evaporate leaving just thermal radiation behind, what happens to all the information that went inside them in the first place? The formation of structure in our universe is also understood by appealing to semiclassical gravity, where quantum field fluctuations in the early universe eventually evolve into a rich universe populated with galaxies, stars, dust and all of the matter we see around us.

Unfortunately, the conceptual and mathematical foundations of semiclassical gravity are not established rigorously. This is very problematic if we wish to have confidence in its predictions. For example, we know that there are some 'highly quantum' states of matter that lie outside the scope of applicability of semiclassical gravity. More generally it is unknown what class of quantum states of matter are admissible in the framework of the theory. Furthermore, the complicated form of the system of mathematical equations defining the evolution laws of semiclassical gravity prevents us from inferring whether the theory is, in all mathematical rigour, predictive.

My project addresses these problems. We carry out, for the first time, a thorough study of the mathematical and conceptual foundations of semiclassical gravity, using state-of-the-art mathematical techniques in quantum physics and gravity, and characterising precisely semiclassical gravity's regime of applicability with full precision. This is of utmost importance not only because it puts our semiclassical insight on solid theoretical ground, but because it allows us to seek for new exciting physical predictions beyond general relativity, for example, in the study of black holes or cosmology. One fertile arena for new physics is gravitational-wave astronomy, where it is imperative to determine whether semiclassical gravity's predictions for gravitational wave signals deviate from general relativity in an observable way.

The goals of this project also bring us closer to resolving fundamental questions in physics, such as the information loss puzzle: Understanding semiclassical gravity in detail will allow us to better characterise the late stages of black hole evaporation, which is crucial to resolving the puzzle in a rigorous fashion.

This project will thus substantially advance our understanding of quantum gravity in its semiclassical regime, while also contributing to the resolution of current important open questions in fundamental physics. It will furthermore make new physical predictions beyond general relativity, leading potentially to transformative advances in our understanding of nature.