Informal Pizza Seminar

Manifestly Gauge-Invariant General Relativistic Perturbation Theory

Kristina Giesel

Max Planck Institute

Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e.g. by cosmic microwave anisotropy probes. A key issue in this theory is to extract the gauge invariant degrees of freedom which allow unambiguous comparison between theory and experiment. In this talk we will present a manifeslty gauge invariant formulation of general relativistic perturbation theory. This can be achieved by starting with Einstein's equations and combining the relational formalism, which was introduced to circumvent the problem of time in General Relativity, with the Brown-Kuchar-Mechanism. One can derive the algebra of (manifestly) gauge invariant observables togehter with a so called physical Hamiltonian, which generates the (physical) time evolution of these observables. We will compare the results of the linear perturbations for this approach with the one of standard cosmological perturbation theory as for instance obtained by Mukhanov, Feldmann and Brandenberger. Finally we will comment on why such a manifestly gauge invariant framework might have advantages when considering perturbations beyond linear order and the quantisation of the perturbed physical degrees of freedom.