Quantum Cosmology with Third Quantisation

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler–DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1 + 5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe–antiuniverse pairs.

Conceptual Challenges on the Road to the Multiverse

The current debate about a possible change of paradigm from a single universe to a multiverse scenario could have deep implications on our view of cosmology and of science in general. These implications therefore deserve to be analyzed from a fundamental conceptual level. We briefly review the different multiverse ideas, both historically and within contemporary physics. We then discuss several positions within philosophy of science with regard to scientific progress, and apply these to the multiverse debate. Finally, we construct some key concepts for a physical multiverse scenario and discuss the challenges this scenario has to deal with in order to provide a solid, testable theory.

A Universe that Does Not Know the Time

In this paper, we propose that cosmological time is a quantum observable that does not commute with other quantum operators essential for the definition of cosmological states, notably the cosmological constant. This is inspired by properties of a measure of time—the Chern–Simons time—and the fact that in some theories it appears as a conjugate to the cosmological constant, with the two promoted to non-commuting quantum operators. Thus, the Universe may be “delocalised” in time: it does not know the time, a property which opens up new cosmological scenarios, as well as invalidating several paradoxes, such as the timelike tower of turtles associated with an omnipresent time line. Alternatively, a Universe with a sharply defined clock time must have an indeterminate cosmological constant. The challenge then is to explain how islands of localized time may emerge, and give rise to localized histories. In some scenarios, this is achieved by backward transitions in quantum time, cycling the Universe in something akin to a time machine cycle, with classical flow and quantum ebbing. The emergence of matter in a sea of Lambda probably provides the ballast behind classical behaviour.

Achronal cosmic future

The spherically symmetric accretion of dark and phantom energy onto Morris-Thorne wormholes is considered. It is obtained that the accretion of phantom energy leads to a gradual increase of the wormhole throat radius which eventually overtakes the superaccelerated expansion of the Universe and becomes infinite at a time in the future before the occurrence of the big rip singularity. After that time, as it continues accreting phantom energy, the wormhole becomes an Einstein-Rosen bridge whose corresponding mass decreases rapidly and vanishes at the big rip.

Measuring spacetime: from the big bang to black holes

Space is not a boring static stage on which events unfold over time, but a dynamic entity with curvature, fluctuations, and a rich life of its own. Spectacular measurements of the cosmic microwave background, gravitational lensing, type Ia supernovae, large-scale structure, spectra of the Lyman alpha forest, stellar dynamics, and x-ray binaries are probing the properties of spacetime over 22 orders of magnitude in scale. Current measurements are consistent with an infinite flat everlasting universe containing about 30% cold dark matter, 65% dark energy, and at least two distinct populations of black holes.