The bispectrum of axion perturbations

Inflation traces the wealth of structures in the Universe back to quantum fluctuations of the inflaton, the scalar field driving the accelerated expansion during inflation. Compelling as this may be, cosmological data are just as consistent with classical primordial fluctuations. This might be explained by the inflationary mechanism itself: the rapid expansion of the Universe squeezed the inflaton fluctuations. At the level of free fields, squeezed quantum states are observationally indistinguishable from classical probability distributions, so whether interactions remove the ambiguity is a question worth exploring. An ideal setup for this purpose is that of axion-like particles in the early Universe. In this thesis, we consider axions from the misalignment mechanism and explore the possibility that the bispectrum of axion fluctuations may encode information about their quantum nature. We find that the quantum bispectrum is enhanced in the squeezed configuration and always larger near the axion potential maximum, regardless of the geometry of the wave vectors. We also find that the classical bispectrum does not differ from the quantum one due to the absence of time derivatives in the axion self-interactions.