Talks

In the context of loop quantum gravity and spin foam models, the simplicity constraints are essential in that they allow to write general relativity as a constrained topological theory. I will first recall the spin foam quantization procedure and focus more particularly on the step consisting in implementing the simplicity constraints. Then, I will present the U(N) framework initially developed for SU(2) intertwiners. Finally, I will show how we can apply this new framework to impose the simplicity constraints in the context of 4d Euclidean gravity and present new solutions defined in term of U(N) coherent states.

The gravitational observatory LISA will detect radiation from massive black hole sources at cosmological distances, accurately measure their luminosity distance and help identify the electromagnetic counterparts that such sources may generate. I will describe various astrophysical scenarios for the generation of electromagnetic counterparts and discuss observational strategies aimed at identifying them. Successful identifications will enable novel studies of black hole astrophysics and cosmological physics.

We propose one way to regularize the fluctuations generated during inflation. We show that, as long as we consider the case that the non-linear interaction acts for a finite duration, observable fluctuations are free from IR divergences not only in the single field models but also in the multi field model. In contrast to the single field model, to discuss observables, we need to take into account the effects of quantum decoherence which pick up a unique history of the universe from various possibilities contained in initial quantum state set naturally in the early stage of the universe.

De Sitter space is a maximally symmetric space, and any (time dependent) backreaction necessarily breaks the symmetry. On the other hand, the backreaction in FLRW spaces (which, from the cosmological perspective, are more realistic spaces) respects the symmetries of the background space. One could therefore argue that it is more natural to study the backreaction on quasi-de Sitter spaces, and more generally on FLRW spaces. As examples, I will present our results on the one loop (Hubble) effective potential calculation, and the one loop stress energy calculation. We find that the backreaction from infrared modes can be important if a massless scalar couples nonminimally to the Ricci with a negative coupling, and if the Universe expands faster than exponentially.

A method is developed for dealing with ultraviolet divergences in calculations of cosmological correlations, which does not depend on dimensional regularization. An extended version of the WKB approximation is used to analyze the divergences in these calculations, and these divergences are controlled by the introduction of Pauli--Villars regulator fields. This approach is illustrated in the theory of a scalar field with arbitrary self-interactions in a fixed flat-space Robertson--Walker metric with arbitrary scale factor $a(t)$. Explicit formulas are given for the counterterms needed to cancel all dependence on the regulator properties, and an explicit prescription is given for calculating finite correlation functions.