Cosmological dynamics from full loop quantum gravity

Tuesday, Sept 26th
Andrea Dapor and Klaus Liegener, FAU Erlangen
Title: Cosmological Effective Hamiltonian from full Loop Quantum Gravity 
PDF of the talk (2.2M)
Audio+Slides [.mp4 13MB]

By Jorge Pullin, LSU

Due to the complexity of theories like general relativity, a common line of attack to understand the theory is to consider situations with high symmetry. In them, one freezes almost all degrees of freedom but a few and studies them. Examples are the studies of homogeneous cosmologies, where the only degrees of freedom left are the volume of the universe and perhaps variables characterizing its anisotropy. In some cases people choose to freeze most of the degrees of freedom and then quantize the remaining ones. This is called "minisuperspace" quantization. In the case of cosmologies that means that one is left with just a handful of degrees of freedom, turning a field theory with infinitely many degrees of freedom like general relativity into a "mechanical system" in the sense of having only a finite number of degrees of freedom. The resulting quantization is therefore much simplified and a lot of progress can be made. The field of study of these quantizations is known as "loop quantum cosmology". The hope is that the resulting theories resemble what happens when one follows the evolution of a highly symmetric state in the full theory. This is, however, not guaranteed. There are known examples where "reducing then quantizing" does not yield the same result as "quantizing then reducing".

The seminar dealt with an attempt to "quantize then reduce" loop quantum gravity and see if the results of loop quantum cosmology follow for such an approach. This requires choosing quantum states in the full theory whose probabilities are "peaked" around homogeneous geometries and that evolve maintaining the homogeneity. States that are peaked around certain classical solutions and follow their evolution in quantum theory are known as "coherent states". In this talk such states for loop quantum gravity based on cubic lattices were constructed and their evolution was studied. It was noted that the resulting evolution does not coincide with the one usually chosen in loop quantum cosmology. When one quantizes theories there are ambiguities in how one proceeds and choices need to be made in how one write certain classical equations as quantum operators. It turns out that one of the choices usually made in loop quantum cosmology does not match with what one gets in the "quantize then reduce" approach. This suggests novel dynamics to study in the context of loop quantum cosmology that may affect the emerging picture of how our universe's Big Bang got replaced by a Big Bounce. In the traditional loop quantum cosmology approach the bounce is preceded by a large classical universe like ours. In the new dynamics suggested in this talk the bounce is preceded by a large but very quantum universe with a large Planck-scale cosmological constant. In the distant past our universe asymptotes to a very symmetrical universe known as De Sitter space. Further studies need to be done to check the consistency of the approach.