Cosmological research is entering a new phase. Data probing the distribution of matter and energy in our universe are unveiling its anatomy on the largest observable scales, with an unprecedented accuracy. The recent WMAP and Planck satellite missions, in combination with small-scale ground-based experiments, have provided us with extremely high-quality measurements of the Cosmic Microwave Background (CMB) anisotropies, shedding new light on the physical processes that took place in the early universe. In the near future, several major experiments aiming at measuring the CMB polarisation or the distribution or various astrophysical objects, should further improve the precision of this picture by orders of magnitude.
These observations constitute a fantastic opportunity to constrain the physical conditions that prevailed at early times, where inflation is believed to have taken place. Inflation is a phase of accelerated expansion that occurred at very high energy and that was first introduced 35 years ago as a possible solution to the hot Big Bang model problems. During inflation, vacuum quantum fluctuations are stretched to astrophysical scales and parametrically amplified. This gives rise to primordial cosmological perturbations, probed in the CMB and in the large scale structure (LSS) of the universe. Inflation predicts that these perturbations should be almost Gaussian, close to scale invariance and phase coherent, predictions that have been remarkably well confirmed. Further, their detailed statistics allow one to constrain the microphysics of inflation and its dynamics. Inflation has thus become a very active field of research, since the energy scales involved during this early epoch are many orders of magnitude greater than those accessible in particle physics experiments. Therefore, the early universe is certainly the most promising probe, and possibly the only one, to test far beyond standard model physics.
Single-field models are the simplest inflationary scenarios compatible with observations. However, when embedded in high-energy frameworks, these single-field models often come with additional scalar degrees of freedom. Reheating is also a key aspect of the inflationary scenario. It explains how inflation is connected to the subsequent radiation era, and is driven by the interactions between the inflaton and the other fundamental fields. A first objective was therefore, in preparation of future missions, to develop new tools and systematic techniques to identify those models favoured by observations, in the unavoidable presence of multiple fields and taking reheating into account.
Inflation is also one of the only places in physics where an effect based on General Relativity and Quantum Mechanics leads to predictions that can be tested experimentally. This makes it an ideal playground to discuss fundamental questions related to the interplay between these two theories. For example, while it has been shown that some CMB observables can be reproduced by classical states, it is still not clear whether a genuinely quantum signal can be seen in the CMB. Thanks to recent developments in Quantum Information Theory, tools are now available that characterise the presence of quantum correlations in a given state and provide techniques to detect them. A second objective was therefore to apply the newly developed tools of quantum information theory to cosmological perturbations, to better understand the quantum nature of cosmological perturbations and its potential detectability.
Another tool to address these questions is the stochastic inflation formalism, which is well behaved even in the regimes where quantum corrections are large, which is where primordial black holes are expected to be seeded. A third objective was thus to study the production of primordial black holes in regimes dominated by quantum diffusion, and extend the stochastic inflation formalism to non slow-roll dynamics.
