Periodic Reporting for period 1 - TESTINF (Testing Cosmic Inflation and Reheating in the Very Early Universe) Reporting period: 2017-06-07 to 2019-06-06 Summary of the context and overall objectives of the project 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. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far BAYESIAN APPROACH TO INFLATIONARY MODELS TESTING:I have studied the fine tuning problem of initial conditions for inflation, and the associated issue of defining a phase-space measure. The consequences of the latest Planck data, which has been released during the course of the fellowship, for inflation in general and inflationary model selection in particular, have also been studied. The Bayesian program was also applied to multiple-field setups such as geometrical destabilization; curvaton scenarios and measurements of the total duration of inflation; the feebly interacting massive particle model of dark matter and measurements of the energy scale at which inflation takes.Finally, design optimisation for future missions has been studied, where a new tool for design optimisation, that we dubbed “decisiveness”, has been developed, and applied to the case study of inflation and CMB missions. UNVEILING QUANTUM SIGNALS IN INFLATIONARY OBSERVABLES:Since inflationary perturbations must generically couple to all degrees of freedom present in the early Universe, it is more realistic to view these fluctuations as an open quantum system interacting with an environment. These interactions lead to quantum decoherence, which is often thought to play a role in the quantum-to-classical transition of cosmological perturbations. I have studied this mechanism in the context of Lindblad equations, and shown that it is also associated to modification of the power spectrum, which allowed me to identify which scenarios of quantum decoherence are in agreement with the CMB data. The inclusion of the constraints from non-Gaussianities was also performed.The possibility to carry out Bell inequality violation experiments, that would prove the quantum origin of cosmological perturbations, have been studied from different perspectives. Finally, the Continuous Spontaneous Localisation model solves the measurement problem of standard quantum mechanics, by coupling the mass density of a quantum system to a white-noise field. I have derived the first calculation of primordial cosmological inhomogeneities in this model. This allowed me to constrain the parameters of the theory in a regime that had never been accessed before, and to show that measurements of the cosmic microwave background are already incompatible with other laboratory experiments.PRIMORDIAL BLACK HOLES FROM QUANTUM DIFFUSION IN THE EARLY UNIVERSE:Since the first detection of gravitational waves associated to black-hole mergers by the LIGO collaboration in 2015, the interest in the physics of primordial black holes (PBHs) has kept increasing. They may indeed explain the existence of progenitors for these events, and possibly play a role in the dark matter.PBHs are expected to form from large density perturbations produced during inflation. I have included the back reaction of these inhomogeneities during inflation, with the formalism of “stochastic inflation”. I have also studied PBHs production from preheating parametric instabilities, and used stochastic inflation to study quantum tunnelling in the early universe. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) The work summarised above gave rise to 14 scientific publications, and 23 scientific talks including 13 in international conferences. All projects went beyond the state of the art and a substantial amount of publications is in preparation, that further investigate the directions highlighted in the overall objectives.