A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state

R.R. Caldwell (Dartmouth)

REVIEW

A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state

R.R. Caldwell (Dartmouth)

Astrophysics · Submitted 16 Aug 1999 · 20 references

Pith's verdict: The paper that opened the w < -1 parameter space, with a clean background analysis and a perturbation section that is sketched rather than derived.

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arXiv IDastro-ph/9908168 (version 2)

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CitationR.R. Caldwell (Dartmouth). "A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state." arXiv:astro-ph/9908168 (1999). https://pith.science/paper/VVNEIMBP

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Editor's note

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This is the paper that made w < -1 a legitimate thing to think about, and it did so with a toy model that is honest about being a toy. The background cosmology is the solid part: the flipped-sign kinetic term gives w <= -1, the energy density grows with the scale factor, and the scale factor diverges in finite time. That last point is a real result and it is worked out correctly. The paper also does the standard observational tests in the new regime and shows the models sit inside the current data. Credit where it is due: nobody had done this systematically before, and the closing warning against a w >= -1 prior is well taken and still worth repeating. The paper is also candid that the supernova evidence could be dust or evolution, which is more than most papers in this area say out loud. The classifier's note that the authors state no limitations is wrong; they state several, including that a more careful analysis is needed to quantify the status of w < -1. The soft spots are real but modest. The perturbation section is the weak one. Figures 5 and 7 rest on constant w and c_p = 1, and the paper says the observational differences from varying these are 'not expected to be very large' without showing it. The stress-test note is right that c_p = 1, not a separate no-clustering postulate, is the operative premise, and right that the k-essence references the paper itself cites allow c_s well below 1. That matters for sigma_8 and for the acoustic peaks, but the phantom only dominates at very low redshift, so the effect is likely small. It is a gap to be filled, not a hole in the argument. Second, the SNe and cluster comparisons are graphical, with no chi-squared or error bars, so 'compatible' is not quantified anywhere. Again, the paper says as much. Who should read it: anyone working on dark energy, and anyone who wants to see how a new region of parameter space gets opened responsibly. It deserves referees, and it got them. My recommendation is to engage with it directly rather than cite it as background.

Referee report

Major objections (3)

[Figures 3, 4, and 7] The abstract's claim that phantom models are ``compatible with most classical tests'' is supported only graphically. The Figure 3 caption says the models provide ``low χ²/d.o.f.'' but gives no value; the Figure 4 contours carry no stated confidence level; and the Figure 7 shaded regions are 2σ but the cluster abundance extension to w < -1 is not described. For a paper whose central claim is compatibility rather than detection, this is load-bearing. Please provide a table of χ²/d.o.f. for the models shown in Figure 3 and state the Δχ² level of the Figure 4 contours.
[Paragraph beginning ``Turning this around, one may instead dictate the histories''] The paper fixes constant w_p and c_p = 1, concedes that this is ``not a generic prediction of the dynamical models described above,'' and then asserts that ``the observational differences are not expected to be very large'' without demonstration. That assertion is load-bearing for Figures 5 and 7. For the k-essence models the paper itself cites ([6,9]), the sound speed need not be 1 and can be substantially smaller, which would permit sub-horizon phantom clustering and shift both the growth factor g (hence σ8 in Figure 7) and the late ISW and acoustic-peak positions (Figure 5). Please either demonstrate the insensitivity with a c_p < 1 run or soften the claim to an explicit caveat.
[Paragraph beginning ``We describe the system of gravitation, normal matter, and phantom energy''] The Lagrangian L_p = -dφdφ/2 - V has a wrong-sign kinetic term, i.e., a ghost with negative-norm states and a quantum instability. The paper calls the construction ``unorthodox'' but does not name the instability. Since the paper presents this as a ``microphysical model,'' it should state explicitly that the simple model is a ghost and that the k-essence route is the intended viable alternative. This is a correctness-risk concern about the model-building section, not a demand to solve the UV completion.

Minor objections (6)

[Paragraph beginning ``Next, we consider the behavior of the mass power spectrum''] The quoted ``up to 20%'' does not follow from g_Λ = 0.8 and g_P <= 1, which gives up to 25%; please reconcile this with the subsequent ``20 + 5%'' total.
[Figure 4 caption] ``prefering'' should be ``preferring'' and ``contraint'' should be ``constraint''; in the Figure 3 caption, ``deSitter'' should be ``de Sitter.''
[Paragraph beginning ``The expansion scale factor grows rapidly''] The finite-time divergence of a(t) is noted but its implications (the future singularity, the effect on the age bound, and the horizon) are not discussed; a sentence would help the reader place the result.
[Paragraph beginning ``We begin by constructing a classical cosmology''] The statement that it is ``no fatal flaw'' to violate the dominant energy condition, citing bulk viscous stress [2], conflates DEC violation with sustained w < -1; please clarify that the cited mechanism is illustrative and does not by itself produce a phantom.
[Paragraph beginning ``The phantom-dominated background evolution''] The paper says the phantom ``does not fluctuate on scales well below the Hubble horizon''; the preceding V,φφ analysis supports this for constant w, but the connection should be made explicit so the assumption does not read as independent.
[Figure 5 caption] The caption says the peaks ``shift to smaller angular scales'' while the text says ``higher multipole moments''; these are consistent, but using the same language in both places would avoid confusion.

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The paper

The paper claims

Caldwell argues that dark energy with an equation of state below $-1$ — 'phantom' energy — is not ruled out by current cosmological data, and that the $w=-1$ cosmological-constant boundary is a theoretical habit rather than an observational

The reading

Nearly every explanation of the accelerating universe assumes that the dark energy's equation of state $w = p/ρ$ sits at or above the cosmological-constant value $w = -1$. Caldwell asks what lies on the other side of that line and constructs a toy 'phantom' component with $w < -1$, meaning its pressure is more negative than its energy density is positive, so that $ρ + p < 0$. He then runs the standard cosmological tests — the type Ia supernova magnitude–redshift relation, the cosmic microwave background anisotropy spectrum, and the matter power spectrum normalized against cluster abundances — and finds that phantom models fit about as well as $Λ$ or quintessence. The claim is not that the phantom is likely, but that the data do not by themselves exclude it, so analyses that impose $w ≥ -1$ as a prior may misread the evidence. The paper closes by noting that if the accelerating expansion turns out to be dust or supernova evolution instead, the phantom may be literally that — an apparition.

What carries the argument

The mechanism is a sign flip in the kinetic term of a scalar field Lagrangian, $L_p = -∂_μφ ∂^μφ/2 - V(φ)$, so that $ρ_p = -φ̇^2/2 + V$ and $p_p = -φ̇^2/2 - V$, which yields $w ≤ -1$ and forces the field to run up, not down, its potential toward larger energy. Caldwell notes this cannot be done with a free canonical scalar field, and points to non-canonical kinetic terms of the kind appearing in supergravity and higher-derivative gravity, and to the $k$-essence constructions that were already shown to give stable super-negative equations of state. The perturbation equation $δ̈φ + 3H δ̇φ + (k^2 - V_{,φφ})δφ = -ḣ φ̇/2$ carries the argument: for constant $w$ the effective mass stays real over the relevant range, so there is no tachyon instability. The rest of the machinery is the very late onset of phantom domination, which is what licenses treating the mass power spectrum shape as standard and shifting only its normalization.

Extended reading notes

Core claim

The paper's central claim is that a dark energy component with super-negative equation of state, $w < -1$, is compatible with most classical tests of cosmology based on the data available at the time: type Ia supernovae, CMB anisotropy, and the mass power spectrum. Caldwell makes the case by building an explicit toy model and following its consequences. Because $ρ_p ∝ a^{-3(1+w)}$ grows with time when $w < -1$, the phantom must come to dominate very late — for $w = -3$ and $Ω_m ∼ 0.3$, the universe was still 90% cold dark matter at $z ∼ 0.4$, against $z ∼ 1.8$ in a $Λ$ cosmology. That lateness is what makes the model hard to distinguish: growth suppression is weaker, the late integrated Sachs–Wolfe effect is smaller, and the acoustic peaks shift to higher multipoles because the distance to last scattering increases. The age in units of the Hubble time can rise by up to about 30% over the $w = -1$ case, the volume–redshift relation predicts more strongly lensed quasars, and high-redshift supernovae are dimmer. The most striking consequence is stated almost in passing: the scale factor diverges in finite time, at $t = 3t_m/2$ for $w = -3$, though for $Ω_m$ not much below 1 that limit lies well after the present day.

Load-bearing premise

The compatibility claim rests on treating the phantom as a smooth fluid with constant $w$ and sound speed $c_p = 1$ that does not cluster on scales well below the Hubble horizon, so that the mass power spectrum keeps its standard shape and only its normalization moves.

Editorial extensions

If this is right

If $w < -1$ is real, the cosmic expansion ends in a finite-time divergence of the scale factor rather than asymptotically approaching a de Sitter state.
The distance to last scattering grows as $w$ becomes more negative, so the acoustic peaks move to higher multipoles — a shift that later CMB data could confirm or exclude.
Phantom models predict more strong gravitational lensing per redshift interval than quintessence or $Λ$, and dimmer high-redshift supernovae, giving independent handles beyond the magnitude–redshift fit.
The CMB-normalized amplitude $σ_8$ comes out up to roughly 20–25% higher than in the comparable $Λ$ model, which cluster-abundance counts can test.
Because $w < -1$ cannot be achieved with Einstein gravity and a canonical Lagrangian, a confirmed detection would require new gravitational physics or a non-canonical field sector.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's finite-time blow-up is the feature most likely to be decisive in the long run: a future measurement of the equation of state drifting below $-1$ would turn a fit to present data into a prediction of a specific cosmic endpoint, with a date set by $w$ and $Ω_m$.
The compatibility argument is weakest exactly where it is most convenient — the phantom is assumed smooth below the horizon, so the analysis never has to say what the phantom would look like if it clustered; a detection of clustering in the dark energy would reopen the whole fit.
The paper's own hedge, that the signal could be dust or supernova evolution, suggests a concrete near-term test: the same distance–redshift data reanalyzed with independent systematics controls should either pull the preferred $w$ back above $-1$ or leave it below.
Because the phantom dominates so late, its imprint on the growth rate is small, which means the strongest near-term discriminator is likely the distance ladder and the acoustic-peak positions rather than cluster counts.

Original abstract

It is extraordinary that a number of observations indicate that we live in a spatially flat, low matter density Universe, which is currently undergoing a period of accelerating expansion. The effort to explain this current state has focused attention on cosmological models in which the dominant component of the cosmic energy density has negative pressure, with an equation of state $w \ge -1$. Remarking that most observations are consistent with models right up to the $w=-1$ or cosmological constant ($\Lambda$) limit, it is natural to ask what lies on the other side, at $w<-1$. In this regard, we construct a toy model of a ``phantom'' energy component which possesses an equation of state $w<-1$. Such a component is found to be compatible with most classical tests of cosmology based on current data, including the recent type 1a SNe data as well as the cosmic microwave background anisotropy and mass power spectrum. If the future observations continue to allow $w<-1$, then barring unanticipated systematic effects, the dominant component of the cosmic energy density may be stranger than anything expected.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,084 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.74 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.32 · compares with prior results 0.51 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

It is extraordinary that a number of observations indicate that we live in a spatially flat, low matter density Universe, which is currently undergoing a period of accelerating expansion. The effort to explain this current state has focused attention on cosmological models in which the dominant component of the cosmic energy density has negative pressure, with an equation of state $w \ge -1$. Remarking that most observations are consistent with models right up to the $w=-1$ or cosmological constant ($\Lambda$) limit, it is natural to ask what lies on the other side, at $w<-1$. In this regard, we construct a toy model of a ``phantom'' energy component which possesses an equation of state $w<-1$. Such a component is found to be compatible with most classical tests of cosmology based on current data, including the recent type 1a SNe data as well as the cosmic microwave background anisotropy and mass power spectrum. If the future observations continue to allow $w<-1$, then barring unanticipated systematic effects, the dominant component of the cosmic energy density may be stranger than anything expected.

background contribution method result interpretation main claim

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	It is extraordinary that a number of observations indicate that we live in a spatially flat, low matter density Universe, which is currently undergoing a period of accelerating expansion.	background 1.00	0.05	0.03	hedged possibility 0.78
s1	The effort to explain this current state has focused attention on cosmological models in which the dominant component of the cosmic energy density has negative pressure, with an equation of state $w \ge -1$.	background 1.00	0.05	0.04	asserted 0.96
s2	Remarking that most observations are consistent with models right up to the $w=-1$ or cosmological constant ($\Lambda$) limit, it is natural to ask what lies on the other side, at $w<-1$.	gap 0.53	0.09	0.04	asserted 0.44
s3	In this regard, we construct a toy model of a ``phantom'' energy component which possesses an equation of state $w<-1$.	contribution 0.79	0.93	0.09	asserted 0.85
s4	Such a component is found to be compatible with most classical tests of cosmology based on current data, including the recent type 1a SNe data as well as the cosmic microwave background anisotropy and mass power spectrum.	result 1.00	0.90	0.23	asserted 0.93
s5	If the future observations continue to allow $w<-1$, then barring unanticipated systematic effects, the dominant component of the cosmic energy density may be stranger than anything expected.	interpretation 0.94	0.15	0.53	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from analysis of existing data 0.76.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1. The age in units of the Hubble time is plotted versus Ω

**Figure 2.** FIG. 2. The volume - red shift relationship is shown for phant

**Figure 3.** FIG. 3. The magnitude - red shift relationship is shown for th

**Figure 4.** FIG. 4. The contraint on the allowed values of Ω

**Figure 5.** FIG. 5. The CMB anisotropy spectra are shown for various cosm

**Figure 6.** FIG. 6. The amplitude of the growth suppression factor

**Figure 7.** FIG. 7. The cluster abundance constraint is shown for a seque

Figures reproduced from arXiv:astro-ph/9908168 by the authors.

References

Works cited (20)

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[20]

Wang, X., Tegmark, M., & Zaldarriaga, M., astro-ph/010 5091 (2001). 10 FIGURES 0.0 0.2 0.4 0.6 0.8 1.0 Ωm 0.5 1.0 1.5 2.0 2.5H0t0 P: w << -1 P: w=-3 P: w=-3/2 Λ: w=-1 Q: w=-1/2 FIG. 1. The age in units of the Hubble time is plotted versus Ω m for a series of cosmological models containing dark energy with diﬀerent values of w. 11 0 1 10 red shift: z 0.0 0...

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Interacting Vector-like Dark Energy, the First and Second Cosmological Coincidence Problems
astro-ph 2006-03 conditional novelty 6.0 of 10

Interacting vector-like dark energy has stable late-time attractors with comparable dark energy and matter densities and with wA < -1, offered as a simultaneous alleviation of two cosmological coincidence problems.
Black Holes and Generalized Scalar Field
gr-qc 2006-02 conditional novelty 6.0 of 10

A tachyon field with positive potential cannot form scalar hair on an asymptotically flat static black hole with a regular horizon.
Gauss-Bonnet dark energy
hep-th 2005-04 conditional novelty 6.0 of 10

Adding a scalar-Gauss-Bonnet coupling to gravity yields exact power-law cosmologies with effective phantom or quintessence behavior, and the coupling can act against the Big Rip.
Could dark energy be vector-like?
astro-ph 2004-05 conditional novelty 6.0 of 10

A set of three orthogonal vector fields with a tachyonic self-interaction can act as dark energy, reaching an equation of state below minus one with a conventional kinetic term, and it violates the scalar/vector/tenso...
Late-time cosmology in (phantom) scalar-tensor theory: dark energy and the cosmic speed-up
hep-th 2004-05 conditional novelty 6.0 of 10

Exact flat-FRW phantom scalar-tensor cosmologies with exponential potentials are constructed, and one-loop quantum corrections are argued to replace the finite-time Big Rip with an asymptotically de Sitter phase.
The phantom menaced: constraints on low-energy effective ghosts
hep-ph 2003-11 conditional novelty 6.0 of 10

Gravitational vacuum decay of ghost fields, compared with the EGRET diffuse gamma-ray flux, requires a Lorentz-violating cutoff below about 3 MeV, and a Lorentz-invariant cutoff is excluded outright.
Super-Acceleration from Massless, Minimally Coupled $\phi^4$
gr-qc 2002-04 conditional novelty 6.0 of 10

A massless, minimally coupled quartic scalar in de Sitter space develops a two-loop stress tensor with negative energy density plus pressure, providing a renormalizable mechanism for cosmological super-acceleration.
Braneworld models of dark energy
astro-ph 2002-02 conditional novelty 6.0 of 10

Adding brane and bulk cosmological constants to a braneworld with an induced curvature term yields a cosmology that can mimic phantom dark energy without phantom pathologies, and can make the current acceleration transient.
Scalar-tensor gravity in an accelerating universe
gr-qc 2000-09 accept novelty 6.0 of 10

Given a Hubble expansion history matching general relativity plus a cosmological constant, scalar-tensor theories without a potential or with a massless scalar remain physically consistent only out to redshifts of rou...
Accelerating Universes with Scaling Dark Matter
gr-qc 2000-09 conditional novelty 6.0 of 10

A two-parameter time-varying dark energy equation of state is introduced and shown to be nearly indistinguishable from a constant one in luminosity-distance data at redshifts below 1.
Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
gr-qc 2000-01 conditional novelty 6.0 of 10

Two cosmological observables, luminosity distance and matter clustering, can in principle fix both unknown functions of a scalar-tensor gravity theory and the present matter density, to first order in the inverse Bran...
Kinetically Driven Quintessence
astro-ph 1999-12 accept novelty 6.0 of 10

Non-canonical kinetic terms alone, with no potential, produce a quintessence field whose constant equation of state is a late-time attractor, and an eighth-order kinetic function yields a stable phantom with w < -1.
Quintessence arising from exponential potentials
astro-ph 1999-10 conditional novelty 6.0 of 10

Two exponential terms with different slopes let a quintessence field scale with radiation and matter and then dominate today with w about -0.8, provided slopes that current particle physics models do not supply.
Are Dynamical Dark-Energy Cosmologies Old Enough?
astro-ph.CO 2026-10 accept novelty 5.0 of 10

Imposing a lower bound on the cosmic age, motivated by the oldest globular clusters, reduces the statistical preference for dynamical dark energy in DESI data from 2.56 to 1.72 sigma.
Observational constraints on scalar-vector-tensor dark energy with phantom-divide crossing
astro-ph.CO 2026-09 conditional novelty 5.0 of 10

Current supernova, BAO, compressed CMB, and growth data are consistent with a stable phantom-divide crossing in a scalar-vector-tensor dark-energy model, with Bayes factors of 2 to 13 over flat LambdaCDM depending on ...
Effective Field Theory for Freezing Gravity with Minimally Coupled Matter
gr-qc 2026-08 conditional novelty 5.0 of 10

Adding a perfect fluid to freezing gravity preserves linear stability, lowers the stability cutoff, and yields new quasi-static gravitational coupling and slip formulas.
Organizing transitions and their cascades: Generalized symmetry enforcement in massless flows or Higgs transitions
hep-th 2026-08 conditional novelty 5.0 of 10

The unbroken fusion ring symmetry FR(SU(2)_{p-2}) stabilizes the massless RG flow M(p,p+1)->M(p-1,p) by making every invariant IR primary field irrelevant.
Cosmological dynamics based on Lovelock's gravity. Qualitative analysis
gr-qc 2026-08 conditional novelty 5.0 of 10

For flat FRW universes in Lovelock gravity, the dynamics reduces to a single first-order ODE whose fixed and singular points classify all evolutions, including a new 'Big Shock' initial state for N>4 with negative couplings.
A Friendly Phantom: Late-time AdS-to-dS transition and cosmological tensions
gr-qc 2026-06 unverdicted novelty 5.0 of 10

Ph-Λ_sCDM realizes sign-switching dark energy via a phantom scalar on a tanh potential, enabling controlled AdS-to-dS transition without Big Rip.
Endpoint Logarithms in the NLO Mueller-Navelet Jet Vertex: Threshold Matching and BLM/MOM Prescription Sensitivity
hep-ph 2026-06 unverdicted novelty 5.0 of 10

A conservative BFKL-aware threshold matching scheme is constructed for the NLO forward jet vertex that resums ordinary endpoint logs, preserves NLO accuracy, and is tested against CMS azimuthal observables, showing in...
Exploring the Dark Sector: Interacting Radiation in Light of Modern Cosmological Probes
astro-ph.CO 2026-05 unverdicted novelty 5.0 of 10

New constraints on dark radiation parameters from recent cosmological datasets show the model alleviates the Hubble tension with SH0ES inclusion while remaining consistent with standard expectations without it.
Hubble Tension as an Effect of Horizon Entanglement Nonequilibrium
astro-ph.CO 2026-01 reject novelty 5.0 of 10

A phenomenological 'horizon entanglement deficit' with the form ρ ∝ H² is fit to low-z data under a forced H0=73 prior; the nonzero amplitude is a restatement of that prior.
Reanalyzing DESI DR1: 2. Constraints on Dark Energy, Spatial Curvature, and Neutrino Masses
astro-ph.CO 2025-11 unverdicted novelty 5.0 of 10

Reanalysis of DESI full-shape clustering data tightens constraints on neutrino mass, spatial curvature, and dark energy equation-of-state parameters relative to BAO-only results.
Cosmological constraints on Galileon dark energy with broken shift symmetry
astro-ph.CO 2025-09 conditional novelty 5.0 of 10

A broken shift symmetric cubic Galileon with a quadratic potential, fitted to DESI DR2, supernova and CMB data, is strongly favored over ΛCDM for DESY5/Union3 supernovae and reproduces the phantom-crossing equation of...
Kalb-Ramond Black Holes Sourced by ModMax Electrodynamics: Some Perturbative Properties in the Phantom Sector
gr-qc 2025-07 reject novelty 5.0 of 10

A new analytical black hole solution in Kalb-Ramond gravity with ModMax electrodynamics is presented, and its perturbative properties (QNMs, greybody factors, Hawking sparsity) are computed in both ordinary and phanto...
Is Dark Energy an Effective Manifestation of Non-equilibrium Thermodynamics? -- Insights from DESI
astro-ph.CO 2025-07 conditional novelty 5.0 of 10

Two phenomenological dark matter creation rates can reproduce the accelerated expansion of the universe and fit current background data as well as or slightly better than LambdaCDM for some DESI-based data combinations.
About electroweak domain walls in Majoron models
hep-ph 2025-06 conditional novelty 5.0 of 10

Electroweak instantons alone do not produce Majoron domain walls; a tiny instanton mass from B+L breaking is cosmologically negligible and can act as a bias or dark energy.

See all 118 Pith citations

How later papers used it

404 later papers cite it

Evidence: substantial. 403 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 485 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 2 compared their own results with it.

Compares with it 2 of 7 papers with this label

Said that, by analogy between its braneworld warp factor and the scale factor, its singularity bears many similarities to the one studied in this paper, since all quantities a, a', ρ and consequently P become asymptotically divergent.

Brane singularities and their avoidance (2010) · 1.00 · paraphrased: the licence does not allow quoting
Said that, by analogy between its braneworld warp factor and the scale factor, its singularity bears many similarities to the one studied in this paper, since all quantities a, a', ρ and consequently P become asymptotically divergent.

Brane singularities and their avoidance in a fluid bulk (2010) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

333 arXiv papers cite this in 403 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 · 176 sentences without a confident label

Uses its data or values 2 papers

Using Planck CMB data [ref] , Planck SZ data [ref] , and the recent $H_0$ measurement [ref] , we find that resolving the $H_0$ and $S_8$ tensions simultaneously require phantom-like DE [ref] and $∑m_ν∼0.4$.

The implications of an extended dark energy cosmology with massive neutrinos for cosmological tensions · Introduction · 0.95
In Ref. [ref] they are taken to be uniform in the ranges $[-3,1]$ and $[-3,2]$ respectively, with the additional condition $w_0 + w_a <0$ to allow early matter domination.[In practice the data go nowhere near this last condition, which would be entirely off the top of the constraint plot shown later.] The cosmological constant, or $Λ$CDM, model corresponds to $w_0=-1$ and $w_a = 0$, and a regime in which $w(a)<-1$ is called a `phantom' regime [ref] .

Interpreting DESI's evidence for evolving dark energy · Models, priors, and pivots · 0.87

Compares with it 7 papers

This new type of singularity is perceived by infalling observers in a similar way as the future singularity of the Big Rip cosmological scenario [ref] , with the expansion scalar of congruences of geodesics going to an infinite positive value in a finite amount of proper time.

Non-symmetric wormholes and localized Big Rip singularities in Einstein-Weyl gravity · Introduction · 0.87
This can be easily proven by noticing that the asymptotic behaviour of the Hubble parameter at large value of the scale factor is [equation] Consequently, the Hubble rate does not grow as fast as in phantom energy models with a constant equation of state where a big rip singularity takes place on the future evolution of a homogeneous and isotropic universe [ref] .

Exploring the dark side of the Universe in a dilatonic brane-world scenario · The self-accelerating branch · 0.93
For the case of non-relativistic matter ([ref]) reduces to [equation] The big rip singularity is approached after a time span $t̃_br$ [equation] Notice that this big rip solution is different from Caldwell's solution in GR [ref] .

Power-law solutions for TeVeS · Dynamics in the physical frame · 1.00

Cites it as support 4 papers

Surprisingly, and even though they violate the null energy condition, these models are the most supported by cosmological observations [ref] rather than being ruled out as it was expected.

Cosmological constraints of interacting phantom dark energy models · INTRODUCTION · 0.97
Therefore, the universe would avoid a big rip singularity [ref] , even if it is filled with phantom energy [ref] .

On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity? · PGCG I · 0.96
Surprisingly, phantom models are not excluded, but even seem to be favoured by observations [ref] .

Cosmological constraints of phantom dark energy models · introduction · 0.99

Cites it as background 199 papers

5D standing wave braneworld [ref] is generated by gravity coupled to a non-self-interacting scalar phantom-like field (different brane models with phantom fields can be found in [ref] ), which depends on time and propagates in the bulk.

Localization Problem in the 5D Standing Wave Braneworld · Background solution · 0.96
Finally, in the finite time, the Big Rip singularity is reached, and all bounded objects in the universe are torn apart [ref] .

Dark Energy Accretion onto a Black Hole in an Expanding Universe · Introduction · 0.81
The simplest model for phantom energy involves a scalar field with a negative kinetic energy term [ref] [equation] The negative sign in front of the kinetic energy term makes this an unusual field theory.

A Unified Model of Phantom Energy and Dark Matter · Introduction · 0.86

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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Wang, X., Tegmark, M., & Zaldarriaga, M., astro-ph/010 5091 (2001). 10 FIGURES 0.0 0.2 0.4 0.6 0.8 1.0 Ωm 0.5 1.0 1.5 2.0 2.5H0t0 P: w << -1 P: w=-3 P: w=-3/2 Λ: w=-1 Q: w=-1/2 FIG. 1. The age in units of the Hubble time is plotted versus Ω m for a series of cosmological models containing dark energy with diﬀerent values of w. 11 0 1 10 red shift: z 0.0 0...

View on Pith 2001