A New Cosmological Model of Quintessence and Dark Matter

Limin Wang; Varun Sahni

REVIEW

A New Cosmological Model of Quintessence and Dark Matter

Varun Sahni, Limin Wang

Astrophysics · Submitted 5 Oct 1999 · 23 references

Pith's verdict: The oscillatory route to w < −1/3 is real and worth knowing; the FCDM half is a tuned plausibility argument, not a demonstrated result.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 4 major objections · 6 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDastro-ph/9910097 (version 3)

Pith IDZSLR46OB, Pith's permanent record of this paper and its review

CitationLimin Wang, Varun Sahni. "A New Cosmological Model of Quintessence and Dark Matter." arXiv:astro-ph/9910097 (1999). https://pith.science/paper/ZSLR46OB

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Two things to take away. First, the mechanism is genuinely new relative to the tracker literature the authors cite: instead of slow-rolling down a flat exponential, the field oscillates about φ = 0 in the small-field branch of V = V0(cosh λφ − 1)^p, and the virial theorem gives ⟨w⟩ = (p−1)/(p+1). For p < 1/2 that sits below −1/3, so acceleration comes from oscillation rather than slow roll, and the field ends up at small values instead of super-Planckian ones. The algebra is right: V ∝ φ^{2p} gives the quoted average, and the Damour–Mukhanov condition ⟨V − φV′⟩ = (1−2p)V is positive for p < 1/2, so the worry that the virial average fails exactly where they need it does not land. The tracking branch (Eq. 5) is standard and correctly used. The axion-motivated potential in Eq. 11 is a nice touch, though undeveloped. Second, the FCDM half is where I would push. The Jeans length lands at ~1 kpc only because V0ψ and λψ in Fig. 3 were chosen to put it there; the 'natural resolution' of the core problem is arranged, not predicted. The estimate also uses a fluid sound speed v_s² = dp/dρ for what is a canonical scalar field, where the high-k propagation speed is c; the real suppression scale needs the Klein–Gordon perturbation equation in an expanding background, not a Jeans formula. And their λ_J expression differs by a factor of a few from the standard one, so the quoted kpc could move. None of this is dishonest — they say 'could provide' — but it is a plausibility argument presented as a resolution. Fig. 2 is a parameter choice, not a fit: no residuals, no χ². Fine for a workshop letter, thin for a claim about matching supernovae. They flag their own weak points — the weak-coupling assumption needed to dodge preheating, and V″ < 0 during oscillation for p < 1/2 possibly affecting long-wavelength modes. Both are honest and I would leave them alone. Who should read it: anyone working on oscillatory or axion-like dark energy, and anyone thinking about small-scale suppression from ultralight fields — the FCDM idea anticipated a lot of later work. Worth a serious referee, mainly to force the perturbation calculation.

Referee report

Significance

If the mechanism holds, it is a genuinely different route to quintessence: acceleration arises from oscillation rather than from a flat, slowly rolling potential, so the field remains sub-Planckian and the standard slow-roll constraints are evaded, while the exponential branch retains the tracker behaviour that suppresses initial-condition fine tuning. The derivation of Eq. (6) is analytic and requires no new parameters beyond V0, λ and p, the tracker solution Eq. (5) is exhibited explicitly, and the model makes contact with data in Fig. 2. The FCDM extension, if substantiated, would connect dark energy and dark matter within one potential family and would yield a falsifiable clustering scale of order a kiloparsec. These are real strengths and are the reason the paper merits review rather than dismissal.

Major objections (4)

[Eq. (10) and the FCDM paragraph] The Jeans length is estimated as λJ ≃ sqrt(v_s²/(2πGρψ)) and evaluated to about 1 kpc for the parameters of Fig. 3. Two issues need to be addressed before this number can carry the FCDM claim. First, the normalization differs from the standard fluid Jeans length λJ = c_s sqrt(π/(Gρ)) by a factor of about 4.4, so with the conventional convention the quoted scale becomes several kpc rather than 1 kpc; since the argument is that λJ is comparable to the core radii of low surface brightness halos, the convention must be stated explicitly and the number given in it. Second, v_s² = dpψ/dρψ is a property of the homogeneous oscillating condensate, whereas the suppression of growth at wavenumber k requires solving the Klein-Gordon perturbation equation in an expanding background with the effective mass m_eff² = V''; for a canonical scalar field the high-k propagation speed is c, not v_s. The authors should either derive the growth suppression scale from the perturbation equation or state clearly that Eq. (10) is a fluid estimate whose coefficient is uncertain at the factor-of-several level.
[Fig. 3 and abstract] The parameters of the ψ field (pψ = 1, Ṽψ = 3 × 10⁵ m_Pl² Mpc⁻², λψ = 8 m_Pl⁻¹) are chosen so that λJ lands at a kiloparsec, and the abstract then describes FCDM as providing 'a natural resolution to the core density problem'. As presented, the resolution is arranged by parameter choice rather than predicted. The paper should either show that a range of (Ṽψ, λψ) consistent with the observed ΩCDM and with the oscillation epoch gives λJ in the astrophysically interesting range, or soften the abstract to describe FCDM as a plausibility argument contingent on that choice. The same applies to the statement that the two-field model 'ameliorates' the coincidence problem, which is asserted without quantification of the improvement over single-field tracker models.
[Paragraph following Eq. (11)] The negative equation of state for p < 1/2 follows from the small-field form V ∝ |φ|^{2p}, which is non-analytic at φ = 0. The authors propose regulating it by φ → (φ² + φ_c²)^{1/2} with φ_c → 0 and assert that this 'will not affect our results in any significant way'. That assertion is load-bearing: a regulated potential has a different virial relation near the origin, and since the field spends a substantial fraction of each oscillation at small |φ|, the time-averaged ⟨w⟩ could shift appreciably. A numerical integration of the oscillating solution with the regulated potential, showing that ⟨w⟩ remains below −1/3 for p < 1/2, would settle the point.
[Paragraph before the acknowledgements] The authors acknowledge that V'' < 0 during the oscillatory stage for p < 1/2 and that this 'is likely to affect very long wavelength fluctuations in φ'. Because this is precisely the parameter regime on which the quintessence claim rests, the acknowledgement should be followed by an estimate: the tachyonic growth rate of long-wavelength φ perturbations, the scales affected, and whether the growth leads to observable consequences or to backreaction on the homogeneous solution. As it stands the reader cannot judge whether the instability is a curiosity or a threat to the model.

Minor objections (6)

[Eq. (5) and Fig. 1] The tracker solution gives Ωφ/ΩB of order 0.1 during radiation domination for the quoted parameters, and the text states only that Ωφ/ΩB < 0.2 is required by nucleosynthesis. It would help to translate this into an effective ΔN_ν at BBN so the reader can see how close the model sits to the constraint.
[Eq. (10)] The condition λJ > m⁻¹ is stated as λ > m_Pl⁻¹; with λJ = m_Pl/sqrt(2V0) and m = sqrt(V0)λ the condition is λ > sqrt(2)/m_Pl. The numerical factor should be corrected or the derivation shown.
[Eq. (6)] The equation of state quoted is a time average, while the instantaneous wφ oscillates and repeatedly crosses −1/3. It should be stated explicitly that the acceleration in Eq. (1) is driven by the averaged quantity and over what averaging time relative to H⁻¹ this is valid.
[Fig. 2] The caption should state the cosmological parameters used for the solid curve and identify what the dashed 'standard CDM' curve assumes (Ωm = 1?), since the comparison is only meaningful with those values given.
[References] Reference [13] (Branchina, hep-ph/0002013) is a preprint and is cited in support of the claim that exponential potentials arise from non-perturbative renormalization group equations; a published reference or a brief indication of the result would be preferable.
[Text] There are several typographical errors, including 'constraind' in the penultimate paragraph, 'discrepency' and 'accomodate' in the FCDM paragraph, and stray spacing in the author addresses. These should be corrected in the final version.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

A scalar field that oscillates instead of rolling could produce cosmic acceleration, and the same potential can supply a new kind of dark matter.

The reading

The paper asks whether the accelerated expansion of the universe can come from a scalar field that is *oscillating* at late times rather than slowly rolling down a flat potential. The authors take a single potential, $V(φ) = V_0(cosh λφ − 1)^p$, and exploit a split personality: at large field values it is an exponential that lets the field track radiation and matter without fine tuning, while at small field values it becomes a power law and the field oscillates about $φ = 0$. Applying the virial theorem to those oscillations gives a time-averaged equation of state $⟨w_φ⟩ = (p−1)/(p+1)$, so any $p < 1/2$ gives $⟨w_φ⟩ < −1/3$ and late-time acceleration. Because the field ends up near zero rather than at super-Planckian values, the usual complaints about slow-roll quintessence — flat potentials and trans-Planckian excursions — do not apply. The same construction, run with $p = 1$, gives a dust-like condensate of ultra-light particles whose Compton wavelength can be of order a kiloparsec, which the authors call Frustrated Cold Dark Matter and propose as a cure for the cuspy-halo and missing-dwarf problems.

What carries the argument

The load-bearing device is the potential $V(φ) = V_0(cosh λφ − 1)^p$, whose two asymptotic regimes do two different jobs. The exponential regime $V ≃ Ṽ_0 e^{-pλφ}$ supplies the tracker behaviour that keeps $ρ_φ$ subdominant through radiation and matter domination; the power-law regime $V ≃ Ṽ_0 (λφ)^{2p}$ supplies the oscillations whose virial average sets the late-time equation of state. The averaging itself is the second piece of machinery: for an oscillating field the virial theorem replaces the instantaneous $w_φ$ with $⟨w_φ⟩ = (p−1)/(p+1)$, so the sign of the effective pressure is a property of the shape of the potential near its minimum rather than of how slowly the field moves. The authors extend this to a two-field version, $V(φ,ψ) = V_φ(cosh λ_φ φ − 1)^{p_φ} + V_ψ(cosh λ_ψ ψ − 1)^{p_ψ}$ with $p_ψ = 1$ and $p_φ ≲ 0.5$, so that one field is the dark matter and the other the dark energy. For the $ψ$ field they derive a Jeans length $λ_J ≃ √(m_Pl²/2V_0) = (λ/√2)(m_Pl/m)$, which exceeds the Compton wavelength when $λ > m_Pl^{-1}$; with the parameters of their figure this comes out around 1 kpc, so clustering below that scale is suppressed.

Extended reading notes

Core claim

The central claim is that the equation of state of an oscillating scalar field is controlled by the exponent of its potential near the minimum, and that this gives a working quintessence model. For $V(φ) = V_0(cosh λφ − 1)^p$ the large-$|φ|$ branch is exponential and drives a tracker solution with $ρ_φ/(ρ_B + ρ_φ) = 3(1+w_B)/(p^2 λ^2)$, keeping the field a fixed small fraction of the background until late times. When the field reaches the power-law branch it oscillates, and the virial theorem gives $⟨w_φ⟩ = (p−1)/(p+1)$ with $ρ_φ ∝ a^{-3(1+⟨w_φ⟩)}$ and $a ∝ t^c$, $c = 2/[3(1+⟨w_φ⟩)]$. The cases the authors single out are $p = 1$ (pressureless, behaves as cold dark matter), $p = 1/2$ ($⟨w_φ⟩ = −1/3$, $ρ_φ ∝ a^{-2}$, a coasting $a ∝ t$ expansion that mimics an open universe without the omega problem), and $p < 1/2$ ($⟨w_φ⟩ < −1/3$, accelerated expansion beginning at $1 + z_* = (Ω_φ/Ω_m)^{-1/3⟨w_φ⟩}$). A worked example with $p = 0.2$ is shown to track the background and then rise to $Ω_φ ≃ 0.7$ today, and its luminosity distance is compared against the high-redshift supernova data.

Load-bearing premise

The whole construction rests on treating the virial-theorem average $⟨w_φ⟩ = (p−1)/(p+1)$ as the actual cosmological equation of state in the regime $p < 1/2$, where the authors themselves note that $V'' < 0$ during oscillation, that $V'(φ)$ is weakly singular at $φ = 0$, and that the averaging assumes oscillations fast compared with the expansion rate, spatial homogeneity, and negligible gradient energy.

Editorial extensions

If this is right

Acceleration at late times can be produced without slow roll, so quintessence model building is freed from the requirement of an extremely flat potential and from field values above the Planck mass.
The choice $p = 1/2$ gives an exactly coasting expansion, $a(t) ∝ t$, reproducing the expansion history of an open universe in a spatially flat model.
A second field with $p = 1$ acts as cold dark matter made of ultra-light particles, with mass set by the epoch at which it starts oscillating; in the worked example $m^{-1} ≃ 228$ pc.
Suppressing clustering below a kiloparsec-scale Jeans length would give shallower halo cores and fewer dwarf galaxies than standard cold dark matter predicts.
The same oscillation mechanism can be embedded in an axion-like potential, $V(φ) = λ(|φ|^2 − f^2/2)^2 + m^2 f^2 (1 − cos θ)^p$, giving $⟨w_θ⟩ ≤ −1/3$ for $p ≤ 1/2$.
Because the field oscillates about a small value, the model also narrows the coincidence problem and the gap between the present matter-to-radiation ratio and its value at the end of inflation.

Reading between the lines

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

If the oscillating-field equation of state is right, then the dark energy is not slowly rolling today, which changes what a measurement of $dw/dz$ would look for: the prediction is a step-like transition at $z_*$ rather than a gentle drift.
The FCDM cutoff scale is set by when the $ψ$ field starts to oscillate, so the model ties a galactic-scale observable — the core radius of a dark matter halo — to a cosmological epoch, which is a checkable relation rather than a free parameter.
A natural follow-up the paper does not do is a linear perturbation calculation for $p < 1/2$: since $V'' < 0$ during oscillation, the growth of $φ$ fluctuations on horizon-scale wavelengths may differ from the homogeneous equation of state, and that difference is where the model is most likely to be tested by CMB and large-scale structure data.
The two-field version suggests a joint fit in which the same potential shape parameter controls both the small-scale clustering cutoff and the late-time equation of state, so a single set of cosmological data could in principle over-determine the model.

Original abstract

We propose a new class of quintessence models in which late times oscillations of a scalar field give rise to an effective equation of state which can be negative and hence drive the observed acceleration of the universe. Our ansatz provides a unified picture of quintessence and a new form of dark matter we call "Frustrated Cold Dark Matter" (FCDM). FCDM inhibits gravitational clustering on small scales and could provide a natural resolution to the core density problem for disc galaxy halos. Since the quintessence field rolls towards a small value, constraints on slow-roll quintessence models are safely circumvented in our model.

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, 3,632 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.14 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.31 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We propose a new class of quintessence models in which late times oscillations of a scalar field give rise to an effective equation of state which can be negative and hence drive the observed acceleration of the universe. Our ansatz provides a unified picture of quintessence and a new form of dark matter we call "Frustrated Cold Dark Matter" (FCDM). FCDM inhibits gravitational clustering on small scales and could provide a natural resolution to the core density problem for disc galaxy halos. Since the quintessence field rolls towards a small value, constraints on slow-roll quintessence models are safely circumvented in our model.

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	We propose a new class of quintessence models in which late times oscillations of a scalar field give rise to an effective equation of state which can be negative and hence drive the observed acceleration of the universe.	contribution 0.98	0.66	0.47	asserted 0.53
s1	Our ansatz provides a unified picture of quintessence and a new form of dark matter we call "Frustrated Cold Dark Matter" (FCDM).	contribution 0.96	0.81	0.35	asserted 1.00
s2	FCDM inhibits gravitational clustering on small scales and could provide a natural resolution to the core density problem for disc galaxy halos.	interpretation 0.83	0.29	0.16	hedged possibility 0.97
s3	Since the quintessence field rolls towards a small value, constraints on slow-roll quintessence models are safely circumvented in our model.	interpretation 0.77	0.54	0.08	asserted 0.93

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from argument 0.89.

What was examined, and what was not

sources read

arXiv listing abstract v3

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
R cross-paper relations

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 evolution of the dimensionless density pa

Showing 1 of the paper's 3 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:astro-ph/9910097 by the authors.

References

Works cited (23)

[1]

S.J. Perlmutter, et al., Nature 391, 51 (1998). S.J. Perl- mutter, et al., Ap J. 517, 565 (1999)

View on Pith 1998
[2]

A.G. Riess, et al., Astron. J. 116, 1009 (1998)

View on Pith 1998
[3]

L. Wang, R.R. Caldwell, J.P. Ostriker and P.J. Stein- hardt, astro-ph/9901388 (1998)

View on Pith Pith review arXiv 1998
[4]

V. Sahni and A.A. Starobinsky, astro-ph/9904398 (1999)

View on Pith Pith review arXiv 1999
[5]

J. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995)

View on Pith 1995
[6]

I. Zlatev, L. Wang and P.J. Steinhardt, Phys. Rev. Lett., 82 896 (1999); P.J. Steinhardt, L. Wang, and I. Zlatev, Phys.Rev. D 59 123504 (1999)

View on Pith 1999
[7]

B. Ratra, and P.J.E. Peebles, Phys. Rev. D, 37, 3406 (1988); C. Wetterich, Nuclear Physics B 302, 668 (1988); P.G. Ferreira, and M. Joyce, Phys. Rev. Lett. 79, 4740 (1997)

View on Pith 1988
[8]

M.S. Turner, Phys. Rev. D, 28 1243 (1983)

View on Pith 1983
[9]

M. Kamionkowski and N. Toumbas, Phys. Rev. Lett. 77, 587 (1996); D. Spergel and U.-L. Pen, Astrophys. J. 491, L67 (1997)

View on Pith 1996
[10]

T. Damour and V.F. Mukhanov, Phys. Rev. Lett. 80, 3440 (1998)

View on Pith 1998
[11]

see P.G. Ferreira and M. Joyce, Phys. Rev. D 58 , 023503 (1998) and references therein

View on Pith 1998
[12]

A. Khare, S. Habib and A. Saxena, Phys. Rev. Lett. 79 3797 (1997)

View on Pith 1997
[13]

V. Branchina, hep-ph/0002013

View on Pith Pith review arXiv
[14]

I. Zlatev and P.J. Steinhardt, astro-ph/9906481 (1999 )

View on Pith Pith review arXiv 1999
[15]

B. Moore, et al. Astrophys. J. 524, L19 (1999)

View on Pith 1999
[16]

B. Moore, et al. astro-ph/9903164

View on Pith Pith review arXiv
[17]

J.F. Navarro and M. Steinmetz, astro-ph/9908114

View on Pith Pith review arXiv
[18]

S. Ghigna et al., astro-ph/9910166

View on Pith Pith review arXiv
[19]

D.N. Spergel and P.J. Steinhardt, astro-ph/9909386 (1999)

View on Pith Pith review arXiv 1999
[20]

M. Kamionkowski and A. R. Liddle, astro-ph/9911103 (1999)

View on Pith Pith review arXiv 1999
[21]

P.J.E. Peebles and A. Vilenkin, Phys. Rev. D60, 103506 (1999)

View on Pith 1999
[22]

We beneﬁtted from discussions with Jim Peebles and Alexei Starobinsky on this issue

View on Pith
[23]

C. Kolda and D.H. Lyth, Phys. Lett. B 458 , 197 (1999). 4

View on Pith 1999

Forward citations

Cited by 31 Pith papers

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

Black hole formation from axion stars
astro-ph.CO 2016-09 conditional novelty 7.0 of 10

Full numerical-relativity simulations of axion stars with the nonperturbative cosine potential map a three-region stability diagram and locate a triple point at f_a about 0.3 M_pl, below which black hole formation is ...
Neutrino Oscillations as a Probe of Light Scalar Dark Matter
hep-ph 2016-08 conditional novelty 7.0 of 10

Null searches for periodic modulations in the solar neutrino flux constrain the coupling between ultralight scalar dark matter and neutrinos to gφ ≲ 4×10⁻²⁵ (mφ/10⁻²² eV), far below CMB bounds.
Two new diagnostics of dark energy
astro-ph 2008-07 conditional novelty 6.5 of 10

A new statistic, Om(z), built from the Hubble parameter, is constant if and only if dark energy is a cosmological constant, giving a null test that does not require knowing the matter density.
Binary-lens amplification of starlight: from magnification flares to quasi-periodic tracking of orbital evolution
astro-ph.GA 2026-10 conditional novelty 6.0 of 10

Gravitational lensing by supermassive black hole binaries produces a zoo of stellar flares and quasi-periodic signals whose peak shapes, spacings, and Fourier spectra encode the binary's period, eccentricity, inclinat...
Learning Boson Star Solution Families with Physics-Informed Neural Networks
gr-qc 2026-08 conditional novelty 6.0 of 10

A physics-informed neural network trained on 20% of reference solutions reconstructs complete boson star families, including the hard-to-reach inner spiral branches, in a single forward pass.

Show 26 more citing papers

Automatic detection of fast oscillations of dark matter scalar field and updated cosmological constraints on QCDM
astro-ph.CO 2026-08 conditional novelty 6.0 of 10

An automatic algorithm in the CLASS Boltzmann code detects the onset of rapid oscillations in scalar-field dark matter and enables accurate averaging even with dark matter-dark energy interactions; updated QCDM constr...
General parametrization for energy density of quintessence field
astro-ph.CO 2024-11 conditional novelty 6.0 of 10

A step-like parametrization of quintessence energy density reproduces all three known dark energy dynamics across redshifts, but cosmological data still prefer ΛCDM except in the CPL model.
New insights into the formation and growth of boson stars in dark matter halos
astro-ph.CO 2020-11 conditional novelty 6.0 of 10

Simulations confirm that boson star growth saturates at late times, and show that attractive self-interactions cause collapse or fragmentation while repulsive ones promote larger, Thomas-Fermi-like stars.
Dark Matter Direct Detection with Accelerometers
hep-ph 2015-12 conditional novelty 6.0 of 10

Ultralight dark matter coupled to B-L or the Higgs portal would drive an oscillating equivalence-principle-violating acceleration that existing torsion balances, atom interferometers, and pulsar timing arrays can alre...
Numerical simulations of single and binary black holes in scalar-tensor theories: circumventing the no-hair theorem
gr-qc 2013-04 conditional novelty 6.0 of 10

A black hole binary immersed in a constant scalar-field gradient emits dipole scalar radiation dominantly at twice the orbital frequency, confirmed by numerical relativity and a slow-motion analytical model.
Refining inflation using non-canonical scalars
astro-ph.CO 2012-05 conditional novelty 6.0 of 10

Non-canonical scalar fields with a power-law kinetic term can rescue quartic and exponential inflationary potentials by lowering the tensor-to-scalar ratio and raising the scalar spectral index.
Cold and Fuzzy Dark Matter
astro-ph 2000-03 conditional novelty 6.0 of 10

Ultra-light scalar dark matter at m ~ 10^-22 eV, behaving as a coherent wave, suppresses small-scale structure and forms kpc-scale cores, potentially solving the cusp-core and missing-satellite problems of cold dark matter.
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.
Quantum corrections as a Bound for Detecting Self-Interacting Ultralight Dark Matter
hep-ph 2026-07 conditional novelty 5.0 of 10

Radiative stability of the SIULDM potential under Yukawa couplings to SM fermions yields upper bounds on y that already intersect the projected reach of optical and nuclear clocks.
Ultralight dark matter search in a large liquid scintillator detector
hep-ph 2025-12 conditional novelty 5.0 of 10

A JUNO-like detector could constrain the neutrino–ultralight-dark-matter oscillation-modulation parameters to ηΔ21 < 2.5×10^-2 and ηΔ31 < 5×10^-3 at 90% CL.
Quantifying Scalar Field Dynamics with DESI 2024 Y1 BAO measurements
astro-ph.CO 2024-04 conditional novelty 5.0 of 10

Canonical quintessence with a linear or quadratic potential fits DESI BAO plus CMB and supernovae about as well as a cosmological constant, with a 2 to 4 percent kinetic energy preference that reaches 95% confidence o...
Quintessential Inflation for Exponential Type Potentials: Scaling and Tracker Behavior
gr-qc 2020-09 conditional novelty 5.0 of 10

Slow-roll initial conditions for exponential-type quintessential inflation potentials with large n do not enter the scaling attractor during radiation, so the potential must be supplemented to fit current cosmic acceleration.
Towards accurate cosmological predictions for rapidly oscillating scalar fields as dark matter
astro-ph.CO 2015-11 conditional novelty 5.0 of 10

A change of variables turns the stiff equations of oscillating scalar field dark matter into a small dynamical system that CLASS can integrate accurately, confirming that kJ = a sqrt(mH) sets the small-scale suppression.
Observational Constraints on Teleparallel Dark Energy
astro-ph.CO 2011-10 conditional novelty 5.0 of 10

Teleparallel dark energy with a nonminimal torsion-scalar coupling is compatible with SNIa, BAO, and CMB data, and the fits mildly prefer a nonzero coupling.
The oscillating dark energy: future singularity and coincidence problem
hep-th 2006-03 conditional novelty 5.0 of 10

Oscillating dark energy models can produce alternating acceleration phases, a bounded dark-energy to matter ratio, and future singularities of all four known types.
Gravitational probes of dark matter physics
astro-ph.CO 2017-12 accept novelty 4.0 of 10

The authors propose a two-dimensional parameter space, interaction strength versus characteristic halo mass, to organize dark matter models and locate where astrophysical anomalies might reveal new dark-sector physics.
Dynamical age of the universe as a constraint on the parametrization of dark energy equation of state
astro-ph 2006-03 conditional novelty 4.0 of 10

Using the CMB-measured cosmic age, the paper rejects most popular time-varying dark energy parameterizations as predicting a universe younger than observed, with only Lee's parameterization surviving.
Theory and Cosmology of Biverse Volume-Normalized Gravity
hep-th 2026-10 conditional novelty 3.0 of 10

A 'biverse' volume-normalized gravity framework claims to cancel the cosmological constant, source dark energy from massive gravity, and predict an exactly zero tensor-to-scalar ratio.
Dark energy in Horndeski theories after GW170817: A review
gr-qc 2018-09 accept novelty 3.0 of 10

After GW170817, dark energy in Horndeski theories is restricted to four classes of models with distinct growth and lensing signatures.
Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (I) Inspiral-Merger
gr-qc 2018-01 accept novelty 3.0 of 10

Gravitational-wave observations of merging compact objects already constrain several modified gravity theories, and the paper adds a new all-orders-in-spin derivation of the black hole scalar charge in decoupled dynam...
Reconstructing Dark Energy
astro-ph 2006-10 accept novelty 3.0 of 10

Model-independent reconstruction of the cosmic expansion history from 2006-era data is consistent across parametric and non-parametric methods, and a plain cosmological constant still fits as well as any evolving dark energy.
Small-scale structure of fuzzy and axion-like dark matter
astro-ph.CO 2019-12 accept novelty 2.0 of 10

Axion-like dark matter produces distinctive small-scale structure (solitonic cores, suppressed small-scale power, miniclusters, axion stars), and current observations push the fuzzy dark matter mass above roughly 10^-21 eV.
Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
gr-qc 2017-05 accept novelty 2.0 of 10

Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.
Axion Cosmology
astro-ph.CO 2015-10 accept novelty 2.0 of 10

Axions can act as dark matter, dark energy, or dark radiation depending on mass, and existing cosmological data already exclude a single ultralight axion species below about 10^-24 eV from composing all of the dark matter.
The Cosmological Constant
astro-ph 2000-04 accept novelty 2.0 of 10

Independent supernova, microwave-background, and cluster-mass measurements converge on a flat universe with about 30% matter and 70% vacuum energy, leaving the origin of that vacuum energy unexplained.
The Case for a Positive Cosmological Lambda-term
astro-ph 1999-04 accept novelty 1.0 of 10

Observations of distant supernovae and the cosmic microwave background favor a flat universe whose energy budget is about 70 percent cosmological constant and 30 percent matter.

How later papers used it

109 later papers cite it

Evidence: some. 107 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 7 of the 136 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

1 later paper by other authors is listed below: 1 compared its own results with it.

Compares with it 1 of 2 papers with this label

Said that, differently from this paper, its minimum is non-zero.

Affine equation of state from quintessence and k-essence fields (2007) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

83 arXiv papers cite this in 107 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 · 50 sentences without a confident label

Uses its data or values 1 paper

For instance, QCD axions have masses in the range $10^-11-10^-2$ eV [ref] , while the ultralight boson particles have masses as low as $10^-22-10^-19$ eV [ref] .

New insights into the formation and growth of boson stars in dark matter halos · Introduction · 0.80

Compares with it 2 papers

However, differently from Ref. [ref] , here the minimum is non-zero.

Affine equation of state from quintessence and k-essence fields · Quintessence · 0.93
This hence gives: [equation] One sees that ([ref]) is of the same form as the potential proposed in [ref] : [equation] for cold dark matter!

"Finite" Non-Gaussianities and Tensor-Scalar Ratio in Large Volume Swiss-Cheese Compactifications · Conclusion and Discussion · 0.97

Cites it as support 2 papers

According to previous studies, the regime of fast oscillations must be present already before the time of radiation-matter equality for a good consistency with cosmological observations [ref] .

Non-relativistic approach for cosmological Scalar Field Dark Matter · Introduction · 0.97
This expectation has also been confirmed by accurate numerical simulations [ref] (see also Fig. [ref] in the Appendix [ref]), and then we can safely take for granted that the SFDM background density will evolve as a matter component, $ρ_ϕ∝a^-3$, irrespectively of the presence of other fluid components.

Towards accurate cosmological predictions for rapidly oscillating scalar fields as dark matter · Early, intermediate, and late time behaviors · 0.99

Cites it as background 46 papers

Many DDE models are designed to solve the coincidence problem by having $ρ_de(t) ∼ρ_m(t)$ for a large fraction of the history/future of the universe [ref] .

Dark-Energy Dynamics Required to Solve the Cosmic Coincidence · Introduction · 0.83
This was a central assumption in most of previous references about scalar field dark matter models [ref] .

Bosonic gas as a Galactic Dark Matter Halo · Rotation Curves in scalar field galaxy halos · 0.83
The SFDM hypothesis has been investigated for a number of self-interaction potentials like the cosh-like [ref] , and the quadratic ones [ref] , with the consequent discovery of several exact solutions of cosmological interest.

Dynamics of Scalar Field Dark Matter With a Cosh-like Potential · Introduction · 0.83

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.

[1] [1]

S.J. Perlmutter, et al., Nature 391, 51 (1998). S.J. Perl- mutter, et al., Ap J. 517, 565 (1999)

View on Pith 1998

[2] [2]

A.G. Riess, et al., Astron. J. 116, 1009 (1998)

View on Pith 1998

[3] [3]

L. Wang, R.R. Caldwell, J.P. Ostriker and P.J. Stein- hardt, astro-ph/9901388 (1998)

View on Pith Pith review arXiv 1998

[4] [4]

V. Sahni and A.A. Starobinsky, astro-ph/9904398 (1999)

View on Pith Pith review arXiv 1999

[5] [5]

J. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995)

View on Pith 1995

[6] [6]

I. Zlatev, L. Wang and P.J. Steinhardt, Phys. Rev. Lett., 82 896 (1999); P.J. Steinhardt, L. Wang, and I. Zlatev, Phys.Rev. D 59 123504 (1999)

View on Pith 1999

[7] [7]

B. Ratra, and P.J.E. Peebles, Phys. Rev. D, 37, 3406 (1988); C. Wetterich, Nuclear Physics B 302, 668 (1988); P.G. Ferreira, and M. Joyce, Phys. Rev. Lett. 79, 4740 (1997)

View on Pith 1988

[8] [8]

M.S. Turner, Phys. Rev. D, 28 1243 (1983)

View on Pith 1983

[9] [9]

M. Kamionkowski and N. Toumbas, Phys. Rev. Lett. 77, 587 (1996); D. Spergel and U.-L. Pen, Astrophys. J. 491, L67 (1997)

View on Pith 1996

[10] [10]

T. Damour and V.F. Mukhanov, Phys. Rev. Lett. 80, 3440 (1998)

View on Pith 1998

[11] [11]

see P.G. Ferreira and M. Joyce, Phys. Rev. D 58 , 023503 (1998) and references therein

View on Pith 1998

[12] [12]

A. Khare, S. Habib and A. Saxena, Phys. Rev. Lett. 79 3797 (1997)

View on Pith 1997

[13] [13]

V. Branchina, hep-ph/0002013

View on Pith Pith review arXiv

[14] [14]

I. Zlatev and P.J. Steinhardt, astro-ph/9906481 (1999 )

View on Pith Pith review arXiv 1999

[15] [15]

B. Moore, et al. Astrophys. J. 524, L19 (1999)

View on Pith 1999

[16] [16]

B. Moore, et al. astro-ph/9903164

View on Pith Pith review arXiv

[17] [17]

J.F. Navarro and M. Steinmetz, astro-ph/9908114

View on Pith Pith review arXiv

[18] [18]

S. Ghigna et al., astro-ph/9910166

View on Pith Pith review arXiv

[19] [19]

D.N. Spergel and P.J. Steinhardt, astro-ph/9909386 (1999)

View on Pith Pith review arXiv 1999

[20] [20]

M. Kamionkowski and A. R. Liddle, astro-ph/9911103 (1999)

View on Pith Pith review arXiv 1999

[21] [21]

P.J.E. Peebles and A. Vilenkin, Phys. Rev. D60, 103506 (1999)

View on Pith 1999

[22] [22]

We beneﬁtted from discussions with Jim Peebles and Alexei Starobinsky on this issue

View on Pith

[23] [23]

C. Kolda and D.H. Lyth, Phys. Lett. B 458 , 197 (1999). 4

View on Pith 1999