Seminarium Teorii Względności i Grawitacji

I will apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner Hamiltonian formalism linearized around the Friedmann-Lemaitre universe. I will explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions, reduced phase space, physical Hamiltonian and physical dynamics. In particular, I will use the key concept which is the canonical isomorphism between different gauge-fixed surfaces. The formalism is first developed for the universe with a single fluid and then extended to the multi-fluid case. I will apply the formalism to describe the reduced phase space of cosmological perturbations in some gauges that are popular in the cosmological literature.