Quantum aspects of two-field cosmology

In single-field inflation, cosmological perturbations are placed in a two-mode squeezed state from which cosmological structures later form. The generalization to two-field cosmology naturally leads to the concept of four-mode squeezed states. In this talk, I will introduce these states, show how they can be understood as two two-mode squeezed state exchanging quanta and discuss the case where one of the fields is unobserved. In this situation, environmental effects such as quantum decoherence take place and modify the observables of the system. A comparison between the exact results we obtained and effective approaches of decoherence provide a benchmark of these techniques that I will illustrate in the case of the cosmological master equation.