Since the beginning of the project, I conducted 7 studies, with various collaborators, each leading to a publication.
1) I developed new tools to study particle production in cosmology when the universe undergoes a bounce, that is, a transition from a contracting to an expanding phase. In these types of problem, the dynamics of space-time is implemented using semiclassical solutions. Unfortunately, these are singular on a bounce (it is a turning point). To avoid this problem, we constructed semiclassical solutions in momentum representation, which are now regular. Essentially, this amounts to using (extrinsic) curvature instead of volume as a degree of freedom of the universe. We show what is the domain of validity of these solutions, under what conditions it becomes equivalent to the usual ones, and how to exploit them to describe particle production near a bounce. This has lead to the single authored publication A. Coutant, Phys. Rev. D 93 (2016) 043520.
2) We studied the general mechanism of appearance of unstable mode in the presence of superradiance. We detailed this mechanism in both explicit and abstract general examples. We also established a clear link between these modes and, quasi-normal modes, which are essential in black hole physics. The link was established by a careful study of the analytic properties of the resolvent. We therefore clarified the relation between the mathematical spectral theory and stability analysis of black holes. This has lead to the publication A. Coutant, F. Michel, and R. Parentani, Class. Quant. Grav. 33 (2016) 125032.
3) We studied the modification of the Hawking effect in fluids whose velocity do not surpasses the speed of sound, i.e. without a horizon. Naively, the effect should be entirely absent. However, due to dispersive effects, it is not, and the Hawking effect leaves an imprint. Characterising this imprint was an open question so far. To proceed, we developed a new mathematical tool to study the scattering in such flows (a generalization of the Bremmer series). This lead to the publication A. Coutant and S. Weinfurtner, Phys. Rev. D 94 (2016) 064026.
4) We studied (theoretically) a new possible experimental setup for detecting superradiance in fluids. The model is based on the study of wave scattering on a rotating cylinder immersed in the fluid. In close analogy to the Zeldovich' cylinder, low frequency waves shows superradiance. We analyzed in detail this model, its stability, and how the value of the cylinder's impedance affects superradiance. The results are presented in the publication V. Cardoso, A. Coutant, M. Richartz, S. Weinfurtner, Phys. Rev. Lett. 117 (2016) 271101.
5) We performed an experimental verification of black hole superradiance in a water wave analogue of a rotating black hole. For this we image and analyze both the flow of a draining bathtub vortex, and waves propagating on it. We show that in some cases, the energy carried by the waves is amplified, showing that these waves have extracted energy from the vortex. We show that this process satisfies the superradiant condition of black holes. We study how the amplification or absorption varies with the frequency and angular momentum of the wave. These results have been published in T. Torres, S. Patrick, A. Coutant, M. Richartz, E. W. Tedford, and S. Weinfurtner, Nature Phys., 13 no. 9, 833836 (2017).
6 and 7) We analyzed the analogue of the Hawking effect in the regime of low frequencies where it is the most visible. In this regime, side effects are also significant, and the properties of the Hawking radiation are significantly altered by dispersion, greybody factors, or non-zero temperatures. We obtained exact mathematical results, that allows us to describe these side effects, and how they affect the observables. We conducted the analysis in two important models: the Korteweg-de Vries model describing water waves, and the Bogoliubov-de Gennes model describing sound in Bose-Einstein condensates. These two works have been submitted as independent publications in Physical Review D, and uploaded on arxiv: arXiv:1707.09651 [gr-qc], and arXiv:1707.09664 [gr-qc].
To disseminate the results, and exchange with the community, we organized a workshop at the University of Nottingham in April 2017. I was the main organiser of the workshop, helped by S. Weinfurtner and V. Cardoso. This workshop, called ``Fluids and gravity: superradiance and analogue black holes,'' gathered physicists from various fields, such as gravity, mathematics, quantum optics, hydrodynamics, quantum fluids, around a common problematic. The event was partially funded by my Marie Sklodowska-Curie fellowship.
To promote fundamental sciences and research, I also co-organised, with M. Cianciaruso and P. Knott an outreach event at the University of Nottingham. The event gathered about 20 high school students and 2 teachers. We showed a live experiment of a cloud chamber, that allowed us to observe cosmic particles. The aim was both to show that fundamental physics is accessible and to promote the work of researchers. The event was awarded a Widening Participation Scheme from the University of Nottingham.
