Tuesday, May 1, 2018

Cosmological perturbations in terms of observables and physical clocks

Tuesday, Apr 17th

Kristina Giesel, FAU Erlangen-Nürnberg
Title: Gauge invariant observables for cosmological perturbations 
PDF of the talk (8M)
Audio+Slides of the talk (15M)

By Jorge Pullin, LSU

When one sets up to quantize general relativity something unusual happens. When one constructs a key quantity for describing the evolution called the Hamiltonian, it turns out it vanishes. What the framework is telling us is that since in general relativity one can choose arbitrary coordinates, the coordinate t that one normally associated with time is arbitrary. That means that the evolution described in terms of it is arbitrary.

Of course this does not mean that the evolution predicted by general relativity is arbitrary. It is just that one is choosing to describe it in terms of a coordinate that is arbitrary. So how can one get to the invariant part of the evolution? Basically one needs to construct a clock out of physical quantities. Then one asks how other variables evolve in terms of the variable of the clock. The relational information between such variables is coordinate independent and therefore characterizes the evolution in an invariant way.

Cosmological perturbation theory is an approximation in which one assumes that the universe at large scales is homogeneous and isotropic plus small perturbations. One can then expand the Einstein equations keeping only the lower order terms in the small perturbations. That makes the equations much more manageable. Up to now most studies of cosmological perturbations were done in coordinate dependent fashion, in particular the evolution was described in terms of a coordinate t. This talk discusses how to formulate cosmological perturbation theory in terms of physical clocks and physically observable quantities. Several choices of clocks are discussed.

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