Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the moredifficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in spacetime appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).

Canonical quantization is often used to suggest new effects in quantum gravity, in the dynamics as well as the structure of space-time. Usually, possible phenomena are first seen in a modified version of the classical dynamics, for instance in an effective Friedmann equation, but there should also be implications for a modified space-time structure. Quantum space-time effects, however, are often ignored in this setting because they are not obvious: they require a careful analysis of gauge transformations and the anomaly problem. It is shown here how modified space-time structures and effective line elements can be derived unambiguously, provided an offshell anomaly-free system of modified constraints exists. The resulting effective line elements reveal signature change as an inescapable consequence of non-classical gauge transformations in the presence of holonomy modifications. The general framework is then specialized to black-hole models in loop quantum gravity. In contrast to previous studies, a self-consistent space-time structure is taken into account, leading to a new picture of black-hole interiors.

No abstract

We show that the entropy of cosmological perturbations originating as quantum vacuum fluctuations in the very early universe, including the contribution of the leading nonlinear interactions, can be viewed as momentum space entanglement entropy between sub-and super-Hubble modes. The interactions between these modes cause decoherence of the super-Hubble fluctuations which, in turn, leads to a nonvanishing entropy of the reduced density matrix corresponding to the super-Hubble inhomogeneities. In particular, applying this to inflationary cosmology reveals that the entanglement entropy produced by leading order nonlinearities dominates over that coming from the squeezing of the vacuum state unless inflation lasts for a very short period. Furthermore, demanding that this entanglement entropy be smaller than the thermal entropy at the beginning of the radiation phase of standard cosmology leads to an upper bound on the duration of inflation which is similar to what is obtained from the trans-Planckian censorship conjecture.

Recent results in the construction of anomaly-free models of loop quantum gravity have shown obstacles when local physical degrees of freedom are present. Here, a set of no-go properties is derived in polarized Gowdy models, raising the question whether these systems can be covariant beyond a background treatment. As a side product, it is shown that normal deformations in classical polarized Gowdy models can be Abelianized.Comment: 20 page