Singularities In Quantum Cosmology Research Articles

Elimination of cosmological singularities in quantum cosmology by suitable operator orderings

Canonical quantization of general relativity does not yield a unique quantum theory for gravity. This is in part due to operator ordering ambiguities. In this paper, we investigate the role of different operator orderings on the question of whether a big bang or big crunch singularity occurs. We do this in the context of the minisuperspace model of a Friedmann-Lemaitre-Robertson-Walker universe with Brown-Kuchar dust. We find that for a certain class of operator orderings such a singularity is eliminated without having to impose boundary conditions.

The evolution of modern cosmology as seen through a personal walk across six decades

This highly personal account of evolution of cosmology spans a period of approximately six decades 1959–2017. It begins when in 1959 the author, as an undergraduate at Cambridge, was attracted to the subject by the thought provoking lectures by Fred Hoyle as well as by his popular books The Nature of Universe and The Frontiers of Astronomy. The result was that after a successful performance at the Mathematical Tripos (Part III) examination, he enrolled as a research student of Hoyle. In this article the author describes the interesting works in cosmology that kept him busy both in Cambridge and in India. The issues pertinent to cosmological research in the 1960s and 1970s included the Mach’s principle, the Wheeler-Feynman theory relating the local electromagnetic arrow of time to the cosmological one, the observational tests of specific expanding universe models, and issues like singularity in quantum cosmology. However, post-1965, the nature of cosmological research changed dramatically with the discovery of the cosmic microwave background radiation (CMBR). Given the assumption that the CMBR is a relic of big bang there has been a host of papers on the early universe, going as close to the big bang as the very early universe would permit: around just 10−36 s. The author argues that despite the popularity of the standard hot big bang cosmology (SBBC) it rests on rather shaky foundations. On the theoretical side there is no well established physical framework to support the SBBC; nor is there independent observational support for its assumptions like the nonbaryonic dark matter, inflation and dark energy. While technological progress has made it possible to explore the universe in greater detail with open mind, today’s cosmologists seem caught in a range of speculations in support of the big bang dogma. Thus, in modern times cosmology appears to have lost the Camelot spirit encouraging adventurous studies of the unknown. A spirit of openness is advocated to restore cosmology to its rightful position as the flagship of astronomy.

Resolution of type IV singularities in quantum cosmology

We discuss the fate of classical type IV singularities in quantum cosmology. The framework is Wheeler-DeWitt quantization applied to homogeneous and isotropic universes with a perfect fluid described by a generalized Chaplygin gas. Such a fluid can be dynamically realized by a scalar field. We treat the cases of a standard scalar field with positive kinetic energy and of a scalar field with negative energy (phantom field). We first present the classical solutions. We then discuss in detail the Wheeler-DeWitt equation for these models. We are able to give analytic solutions for a special case and to draw conclusions for the general case. Adopting the criterion that singularities are avoided if the wave function vanishes in the region of the classical singularity, we find that type IV singularities are avoided only for particular solutions of the Wheeler-DeWitt equation. We compare this result with earlier results found for other types of singularities.

On the avoidance of classical singularities in quantum cosmology

Many cosmological models based on general relativity contain singularities. I address here the question whether consistent models without singularities can exist in quantum cosmology. The discussion is based on the Wheeler-DeWitt equation of quantum geometrodynamics. The models under consideration are partly motivated by recent discussions of dark energy. Natural criteria of singularity avoidance in the quantum theory are the vanishing of the wave function at the classical singularity or the breakdown of the semiclassical approximation upon approaching the region of the singularity. I show that singularity avoidance in this sense can happen in the models under consideration.

Probing singularities in quantum cosmology with curvature scalars

We provide further evidence that the canonical quantization of cosmological models eliminates the classical Big Bang singularity, using the de Broglie–Bohm interpretation of quantum mechanics. We compute the ‘local expectation value’ of the Ricci and Kretschmann scalars, for some quantum FRW models. We show that they are finite for all time.

Some remarks on singularities in quantum cosmology

We discuss to what extent classical singularities persist upon quantization in two simple cosmological models.

The singularities in quantum cosmology

A cosmological model is proposed, in which quantum effects lead to infinitely many terms nonlinear in curvature, and these terms lead to the following conclusion: the physical singularity (i.e., a state with infinite matter densityp) occurs int≃10−43 s, when the curvature is finite. An attempt is made to give physical interpretation of this model from the viewpoint of the ‘foam-like’ model of space-time.