The quantum realm of the "Little Sibling" of the Big Rip singularity

Francisco Cabral; Imanol Albarran; Mariam Bouhmadi-L\'opez; Prado Mart\'in-Moruno

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The quantum realm of the "Little Sibling" of the Big Rip singularity

Imanol Albarran, Mariam Bouhmadi-López, Francisco Cabral, Prado Martín-Moruno

General Relativity and Quantum Cosmology · Submitted 24 Sep 2015

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

The authors' main claim We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.

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arXiv ID1509.07398 (version 1)

Pith IDDJIJCHTJ, Pith's permanent record of this paper and its review

CitationFrancisco Cabral, Imanol Albarran, Mariam Bouhmadi-L\'opez, Prado Mart\'in-Moruno. "The quantum realm of the "Little Sibling" of the Big Rip singularity." arXiv:1509.07398 (2015). https://pith.science/paper/DJIJCHTJ

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We analyse the quantum behaviour of the "Little Sibling" of the Big Rip singularity (LSBR) [1]. The quantisation is carried within the geometrodynamical approach given by the Wheeler--DeWitt (WDW) equation. The classical model is based on a Friedmann--Lema\^{i}tre--Robertson--Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character. We analyse the WDW equation in two setups. In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid. We then solve the WDW equation within a WKB approximation, for two factor ordering choices. On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field. We solve the WDW equation, with the Laplace--Beltrami factor-ordering, using a Born--Oppenheimer approximation. In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance. We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We analyse the quantum behaviour of the "Little Sibling" of the Big Rip singularity (LSBR) [1].	contribution 0.99	0.92	0.02	asserted 0.86
s1	The quantisation is carried within the geometrodynamical approach given by the Wheeler--DeWitt (WDW) equation.	method 0.99	0.75	0.02	asserted 1.00
s2	The classical model is based on a Friedmann--Lema\^{i}tre--Robertson--Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character.	method 0.90	0.29	0.02	asserted 1.00
s3	We analyse the WDW equation in two setups.	method 0.91	0.88	0.01	asserted 0.89
s4	In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid.	method 0.99	0.48	0.01	asserted 1.00
s5	We then solve the WDW equation within a WKB approximation, for two factor ordering choices.	method 0.99	0.96	0.02	asserted 0.99
s6	On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field.	method 0.96	0.85	0.02	asserted 0.97
s7	We solve the WDW equation, with the Laplace--Beltrami factor-ordering, using a Born--Oppenheimer approximation.	method 0.99	0.95	0.02	asserted 1.00
s8	In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance.	method 0.98	0.94	0.04	asserted 0.73
s9	We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.	interpretation 0.74	0.93	0.97	hedged possibility 0.63

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 analyse the quantum behaviour of the "Little Sibling" of the Big Rip singularity (LSBR) [1]. The quantisation is carried within the geometrodynamical approach given by the Wheeler--DeWitt (WDW) equation. The classical model is based on a Friedmann--Lema\^{i}tre--Robertson--Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character. We analyse the WDW equation in two setups. In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid. We then solve the WDW equation within a WKB approximation, for two factor ordering choices. On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field. We solve the WDW equation, with the Laplace--Beltrami factor-ordering, using a Born--Oppenheimer approximation. In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance. We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Reconstructing sign-switching dark energy histories: Scalar-field regularity, conditional potential comparison, and representative dynamics
gr-qc 2026-09 accept novelty 6.0 of 10

The error-function, smooth-step, and ladder dark energy histories have fundamentally different scalar-field realizations: regular, non-Lipschitz, and nonexistent, respectively, within the minimal single-field action.
Observational constraints on 3-forms dark energy
astro-ph.CO 2025-12 conditional novelty 6.0 of 10

Fitting a Gaussian-potential 3-form dark-energy model to Planck, DESI, Pantheon+, Cepheid and DES data shifts H0 up by only ~0.4 km/s/Mpc and yields a weak statistical preference over ΛCDM.
Classical and semi-classical energy conditions
gr-qc 2017-02 accept novelty 2.0 of 10

The chapter surveys classical and semiclassical energy conditions, showing that nonlinear and quantum variants remain better behaved than the standard pointwise conditions under quantum vacuum effects.

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12 arXiv papers cite this in 21 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 · 18 sentences without a confident label

Compares with it 1 paper

This is in strike difference to what happens in GR in presence of a BR singularity induced by a phantom minimally coupled scalar field where $G^AB$ has a positive signature [ref] .

$f(R)$ quantum cosmology: avoiding the Big Rip · Modified Wheeler–DeWitt equation · 1.00

Cites it as background 2 papers

Examples of these models can be found, for instance, in references [ref] .

Classical and quantum $f(R)$ cosmology: The big rip, the little rip and the little sibling of the big rip · Modified Wheeler-DeWitt · 0.81
This abrupt event has been well studied in [ref] and dubbed as Little Sibling of the Big Rip since it smooths the big rip singularity in the future.

Smoothing the $H_0$ tension with a dynamical dark energy model · introduction · 0.93

What it cites · 25 sentences without a confident label

Uses the method or tool of 1 paper

Using the WKB (Wentzel, Kramers, Brillouin) approximation method at first order, which is enough to ensure that the DW condition is satisfied; i.e. $Ψ(u)$ vanishes for $u→∞$, the wave function of the universe can be described by [ref]

Quantisation of the holographic Ricci dark energy model · First quantisation procedure ($aĤ(a,π̂_a)ψ(a)=0$) · 0.87

Cites as background 13 papers

This future event is what we refer as “Little Sibling” of the Big Rip singularity [ref] .

The little sibling of the big rip singularity · The Little Sibling of the Big Rip event: review · 0.80
This second case, it what we named the Big Démarrage, it results from a phantom fluid leading to a cosmic expansion that starts with infinite acceleration [ref] .].

On the quantum fate of singularities in a dark-energy dominated universe · Introduction · 0.83
Some works have applied the methods of quantum cosmology to the classical models leading to these DE related singularities [ref] .

Does loop quantum cosmology replace the big rip singularity by a non-singular bounce? · Introduction · 0.84

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