Week 25.04.2022 – 01.05.2022

I can formulate the purpose of my research as an attempt to look to the quantum gravity through both the theoretical and observational windows. My previous research was mainly dedicated to obtaining both observational predictions and theoretical constraints for the models of inflation which can be stated as 'minimal'. They contain only the fields which are proved to exist: Higgs field and gravity. As the results of this work, we proved the self-consistency and investigated the reheating mechanism in a model describing inflation driven by the interplay of Higgs and gravity. My recent research is more focused on the theoretical window to the nature of quantum gravity based on the scattering amplitudes and dispersive relations. The scattering amplitudes through the graviton exchange contain the IR singularities in forward limit. The divergences at $t\rightarrow 0$ can be cancelled in the dispersive relation only if the UV limit of the amplitude is tuned in a specific way which establishes the non-trivial connection between UV and IR forms of the amplitude. We show that this connection can be expressed in terms of the Laplace transform and it can give an information about the UV amplitude in the limit $t \log{s}\rightarrow 0$. We discuss the implications of this approach for QED with gravity.

Recent works in quantum gravity, motivated by the factorization problem and baby universes, have considered sums over bordisms with fixed boundaries in topological quantum field theory. I will discuss this construction, its scope and its limitations, and describe the total amplitude in this class of theories in terms of a curious splitting formula; Part of the London TQFT Journal Club; it will be possible to follow this talk online (please register at https://london-tqft.co.uk)

Quantum mechanical theories describing large N by N matrices of oscillators can lead to an emergent space as N -> infinity. In the most fully fledged version, the emergent space is dynamical and gravitating. However, there are also simpler, lower dimensional versions of this phenomenon. One of the simplest occurs in the so-called quantum Hall matrix model, in which a 2 dimensional space emerges and supports Chern-Simons dynamics. I will describe how this solvable model leads to insights about the emergence of space from matrices. In particular, I will describe how the emergent spatial locality is reflected in the entanglement structure of the ground state of theory.