Switching internal times and a new perspective on the 'wave function of the universe'

Despite its importance in general relativity, a quantum notion of general covariance has not yet been established in quantum gravity and cosmology, where, given the a priori absence of coordinates, it is necessary to replace classical frames with dynamical quantum reference systems. As such, quantum general covariance bears on the ability to consistently switch between the descriptions of the same physics relative to arbitrary choices of quantum reference system. Recently, a systematic approach for such switches has been developed (arXiv:1809.00556, 1809.05093, 1810.04153). It links the descriptions relative to different choices of quantum reference system, identified as the correspondingly reduced quantum theories, via the reference-system-neutral Dirac quantization, in analogy to coordinate changes on a manifold. In this work, we apply this method to a simple cosmological model to demonstrate how to consistently switch between different internal time choices in quantum cosmology. We substantiate the argument that the conjunction of Dirac and reduced quantized versions of the theory defines a complete relational quantum theory that not only admits a quantum general covariance, but, we argue, also suggests a new perspective on the 'wave function of the universe'. It assumes the role of a perspective-neutral global state, without immediate physical interpretation, that, however, encodes all the descriptions of the universe relative to all possible choices of reference system at once and constitutes the crucial link between these internal perspectives. While, for simplicity, we use the Wheeler-DeWitt formulation, the method and arguments might be also adaptable to loop quantum cosmology.Comment: 14+7 pages. Invited contribution to the special issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms", Eds. S. Carrozza, S. Gielen and D. Oriti. Minor clarifications, updated references, matches published versio

BKL oscillations in 2+1 space-time dimensions

We investigate the question whether there are cosmological models in 2+1 space-time dimensions which exhibit dynamics similar to BKL oscillations, as the cosmological singularity is approached. Based on intuition, we conceive a toy model which displays such oscillatory dynamics. We show that in the phase space of this model, the cosmological singularity is represented by a separatrix curve and discuss the model's dynamics within the cosmological billiards picture. Finally, we offer a physical interpretation for a family of similar cosmological models in terms of the topological degrees of freedom of gravity in 2+1 dimensions.Comment: 22 pages, 4 figure