Resolution of type IV singularities in quantum cosmology

Claus Kiefer; Manuel Kraemer; Mariam Bouhmadi-Lopez

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Resolution of type IV singularities in quantum cosmology

Mariam Bouhmadi-Lopez, Claus Kiefer, Manuel Kraemer

General Relativity and Quantum Cosmology · Submitted 20 Dec 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.86 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.97 · mentions code or data availability 0.01.

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss the fate of classical type IV singularities in quantum cosmology.	contribution 0.74	0.72	0.03	unclear 0.86
s1	The framework is Wheeler-DeWitt quantization applied to homogeneous and isotropic universes with a perfect fluid described by a generalized Chaplygin gas.	method 0.99	0.56	0.02	asserted 0.99
s2	Such a fluid can be dynamically realized by a scalar field.	background 0.59	0.14	0.02	hedged possibility 0.56
s3	We treat the cases of a standard scalar field with positive kinetic energy and of a scalar field with negative energy (phantom field).	method 0.74	0.57	0.02	asserted 0.93
s4	We first present the classical solutions.	method 0.69	0.83	0.01	asserted 0.74
s5	We then discuss in detail the Wheeler-DeWitt equation for these models.	method 0.83	0.86	0.02	asserted 0.77
s6	We are able to give analytic solutions for a special case and to draw conclusions for the general case.	method 0.66	0.95	0.06	asserted 0.99
s7	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.	result 1.00	0.96	0.89	asserted 1.00
s8	We compare this result with earlier results found for other types of singularities.	contribution 0.45	0.79	0.04	unclear 0.57

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

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.

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References

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8 arXiv papers cite this in 9 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Cites it as support 1 paper

Indeed, it has been shown that in some specific models, most DE related singularities can be avoided in the analogous quantum version [ref] .

Quantisation of the holographic Ricci dark energy model · Introduction · 0.98

Cites it as background 4 papers

Some works have applied the methods of quantum cosmology to the classical models leading to these DE related singularities [ref] .

The quantum realm of the "Little Sibling" of the Big Rip singularity · Introduction · 0.84
For works on this type of singularity, see Refs. [ref] . * Type II (“sudden”): This type of singularity is milder than the Big Rip scenario, and it is also known as a pressure singularity, firstly studied in Refs. [ref] , and later developed in [ref] , see also [ref] .

The dark universe future and singularities: the account of thermal and quantum effects · Finite-time future singularities in the dark universe: the account of thermal effects · 0.96
The first concrete classification of finite-time future cosmological singularities was done in Ref. [ref] and for an important stream of articles on finite-time cosmological singularities, see Refs. [ref] and the references therein.

Finite-time Cosmological Singularities and the Possible Fate of the Universe · Introduction · 0.95

What it cites · 31 sentences without a confident label

Uses the method or tool of 3 papers

In treating the Wheeler–DeWitt equation, we apply the methods used in the earlier papers [ref] .

Quantum phantom cosmology · Quantum analysis · 1.00
In treating the Wheeler–DeWitt equation, we apply the methods used in the earlier papers [ref] .

Quantum cosmology with big-brake singularity · Quantum analysis · 1.00
In treating the Wheeler–DeWitt equation, we apply the methods used in the earlier papers [ref] .

On the quantum fate of singularities in a dark-energy dominated universe · Quantum analysis · 1.00

Compares with 6 papers

Notice that near $a_min$ ($ϕ=0$), the potential is positive and finite, in contrast to the cases discussed in [ref] .

On the quantum fate of singularities in a dark-energy dominated universe · Phantom GCG and type IV singularity · 0.96
This is in stark contrast to the cases discussed in [ref] and is connected with the soft nature of the type IV singularity.

Quantum cosmology with big-brake singularity · Standard GCG and type IV singularity · 1.00
This is in stark contrast to the cases discussed in [ref] and is connected with the soft nature of the type IV singularity.

Quantum phantom cosmology · Standard GCG and type IV singularity · 1.00

Cites as background 22 papers

Depending on the variables that become divergent, they are called type I (big rip) [ref] , type II (big brake, sudden or big démarrage) [ref] , type III (big freeze) [ref] and type IV [ref] .

Sudden Future Singularities · Introduction · 0.94
Depending on the variables that become divergent, they are called type I (big rip) [ref] , type II (big brake, sudden or big démarrage) [ref] , type III (big freeze) [ref] and type IV [ref] .

Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity · Introduction · 0.94
Depending on the variables that become divergent, they are called type I (big rip) [ref] , type II (big brake, sudden or big démarrage) [ref] , type III (big freeze) [ref] and type IV [ref] .

Phantom Energy and Cosmic Doomsday · Introduction · 0.94

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