Canonical transformations and squeezing formalism in cosmology

Understand

Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system.

• In the first part of this work we study the symplectic structure associated with linear canonical transformations.
• After reviewing salient mathematical properties of the symplectic group in a pedagogical way, we introduce the squeezing formalism, and show how any linear dynamics can be cast in terms of an invariant representation.
• In the second part, we apply these results to the case of cosmological perturbations, and focus on scalar field fluctuations during inflation.