Cosmology with Nonminimal Derivative Couplings

Luca Amendola (Rome Astronomical Observatory)

REVIEW

Cosmology with Nonminimal Derivative Couplings

Luca Amendola (Rome Astronomical Observatory)

General Relativity and Quantum Cosmology · Submitted 10 Feb 1993 · 25 references

Pith's verdict: A real, checkable extension of the nonminimal-coupling program — the widened M range is the paper's genuine contribution, but the attractor claim rests on the truncated equation it was derived from.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 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 →

· 5 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDgr-qc/9302010 (version 1)

Pith IDEJL7UBJE, Pith's permanent record of this paper and its review

CitationLuca Amendola (Rome Astronomical Observatory). "Cosmology with Nonminimal Derivative Couplings." arXiv:gr-qc/9302010 (1993). https://pith.science/paper/EJL7UBJE

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

The thing to know: Amendola adds a derivative coupling μ φ;αφ;α R on top of the usual ξf(φ)R and argues the inflationary window widens from 2 ≤ M < 2+√3 to M ≥ 2 with no ceiling. That widening is the paper. It's a modest but real result, and it's derived here rather than quoted, so it's worth your time if you work on scalar-tensor inflation at all. This is an early entry in what became the Horndeski lineage, and it reads that way — a first step, not a finished theory. The Lagrangian reduction in Sect. 2 is tidy: he lists the six four-derivative terms, uses the three total-divergence identities to cut to one, and keeps L1 because it's what falls out of a TR coupling. The effective-potential argument at Eq. (20) — U(φ) = ξ(M−2)(4μ)⁻¹f(φ), positive-definite slope for M > 2 when ξ/μ > 0 — is short and correct as far as it goes. The three-epoch picture (NMDC quasi-de Sitter, then NMC power law, then minimal coupling) is a nice structural observation, and the double/triple inflation remark follows from it without extra fields. Where it's soft: the attractor status of Eq. (23) is asserted — 'can be easily proved' — and never proved. The phase-space portraits integrate Eq. (17), the truncated equation, so they confirm the truncation is self-consistent, not that it tracks the full fourth-order Eq. (6). He does check ẍ ≪ 3Hẋ along the solution, which is the right kind of check, but it lives inside the approximation. The conformal-transformation section is a sketch: he tries the standard factor, shows residual second derivatives of f1 survive, and concludes no rescaling works. Suggestive, not a no-go theorem. The abstract's non-scale-invariant spectrum claim is 'may display' — no spectrum is computed. The bubble section is qualitative, no numbers. The baseline 2 ≤ M < 2+√3 comes from Ref. 18, listed as in preparation, so you can't check it yet; that's a minor annoyance, not a flaw. I'd not weight the missing figures — the captions are there and this looks like a scan artifact. Verdict: send it out. The central claim is specific and falsifiable, the gaps are closable by a follow-up, and the paper is honest about the approximation it uses.

Referee report

Significance

If the attractor survives beyond the truncation, the result is a genuinely useful extension of the NMC literature: it removes the upper bound on M that constrained earlier models and it offers a single-field route to a non-scale-invariant fluctuation spectrum, which is a real economy over two-field double-inflation scenarios. The analytic chain from Eq. (4) through Eq. (21) is checkable and I did check it: the reduction of Eq. (20) to Eq. (21) with N = m(M-2) is correct, and the effective-potential sign argument for M > 2 is clean. The paper is also candid that the numerics are performed in the second-order approximation (abstract, sentence s3). The value of the work therefore turns on whether the truncated attractor is representative of the full fourth-order system, which is exactly where the manuscript is thinnest.

Major objections (5)

[§4, Eq. (23) and Figs. 1-2] The attractor status of Eq. (23) is asserted rather than shown: 'It can be easily proved that this really is an attractor; a graphic evidence is provided by our phase-space portraits, Figs (1,2).' No proof is given, and the figures are explicitly 'obtained integrating Eq. (17)' — the truncated second-order equation, not the full fourth-order Eq. (6). The self-consistency check that ẍ is negligible along the solution establishes only that the solution is consistent within the truncation, not that the truncation faithfully represents the full dynamics. Since the abstract (s2) and §5 state the M ≥ 2 result without the second-order qualifier, the headline claim is stronger than the evidence supports. Either add the qualifier to the abstract and conclusions, or supply a stability argument for the full system (for example, an expansion of Eq. (6) about the solution of Eq. (23) showing that the neglected third- and fourth-order pieces are damped), or integrate Eq. (6) directly for at least one parameter set.
[§1 and §4, baseline range 2 ≤ M < 2+√3] The entire 'greatly expanded' claim is measured against the range 2 ≤ M < 2+√3 and the power-law exponent of Eq. (1), both attributed to Ref. (18), which is listed as 'in preparation' by the same author. An unpublished comparison baseline cannot carry the central quantitative claim of a published Letter. Either summarize in this manuscript the derivation of the NMC bound and of Eq. (1) in enough detail to be checked, or point to a published source containing them.
[§5 versus §3] There is an internal tension between sections. Section 3 concludes that a conformal rescaling cannot recast the theory in Einstein form (Eq. 12 and the surrounding discussion), yet §5 states that the false-vacuum probability p_FV 'should be calculated in an Einstein frame; for what concerns the following discussion this precisation is of secundary importance.' If no Einstein frame exists for this theory, the parenthetical needs justification rather than dismissal, since the whole graceful-exit argument rests on comparing the nucleation integral Eq. (30) with the expansion history of Eqs. (26) and (1). Please reconcile the two statements or restrict the §5 discussion explicitly to the NMC epoch, where an Einstein frame does exist.
[§2-§3, Eqs. (5)-(9)] The theory is fourth order in φ and the author counts five degrees of freedom (H, φ, φ̇, φ̈, φ''' ), but the manuscript nowhere discusses the stability of the extra degree of freedom. Lagrangians with four-derivative terms of the form φ;αφ;αR generically propagate an additional mode whose Hamiltonian is unbounded below (Ostrogradski), and this is the standard viability question for such terms. At minimum the paper should state whether the truncated system evades this, and whether the attractor of Eq. (23) survives when the extra mode is excited. Without that, the reader cannot judge whether the expanded M range describes a physically viable cosmology or an unstable sector of the theory.
[§4, Eqs. (22), (23), (27)] Several constants in the quoted solution do not reproduce from the preceding equations as printed, and since they feed the e-folding estimate E and the de Sitter limit they should be re-derived and checked. (i) Combining Eq. (9) with R(0) = 4V/(ξf) from Eq. (14) gives a coefficient 4μ/ξ for the ẋ² term in Eq. (22), not the printed 3μ/ξ. (ii) Using Eq. (25) and ẋ = bx^p in Eq. (21) gives b = -N(ξ/μ)(|ξ|/λ)^{1/2}/√3, whereas Eq. (23) states b = -N√3(ξ³/λμ)^{1/2}; these differ by a factor of 3. (iii) As printed, k = 2(N+1)² + N - m in Eq. (27) is dimensionally inconsistent with the exponent structure of Eq. (26); direct integration of H ∝ x^{(N+m)/2} with x ∝ (1+t/τ)^{1/(1-p)} gives k = 2(N+1)/(N-m+2), which for the paper's own example (m=1, M=3, N=1) gives k=2 rather than the printed k=8. Some of this may be typesetting, but the numbers propagate into E and into the claim that φ0 of order unity suffices for E > 60, so they should be verified explicitly.

Minor objections (8)

[Figs. 1-2] The figure captions are present but the figures themselves are not included in the version under review. Since the phase-space portraits are offered as the graphic evidence for the attractor claim, they need to be supplied and should be legible enough to identify the attractor trajectories and the stability point at φ̇ = φ = 0.
[§3, Eq. (6)] The notation is ambiguous: f′ in Eq. (6) denotes the derivative of f(φ) with respect to φ, but the Lagrangian is written in terms of f1(φ, φ;α), which also depends on derivatives. Please state explicitly that f′ means ∂f/∂φ and distinguish f from f1 throughout.
[§4, sign assumptions] The paper adopts ξ, μ ≤ 0 as 'a sufficient condition, although not a necessary one' and then derives the M ≥ 2 result under that choice (the effective potential of Eq. 20 requires ξ/μ > 0). The abstract and conclusions should state that the expanded range is established for ξ/μ > 0, and the paper should say whether the result survives ξ/μ < 0.
[§4, Eq. (28) and the worked example] With ξ < 0 as adopted, the expression x1 = [3ξ²m²/(2|μ|λ)]^{1/(N+1)} is positive but the text then writes 'x1 = ξ', which is negative and inconsistent with x ≥ 0; presumably |ξ| is meant. In the same example (|μ|λ = 3/2, M = 3, m = 1) one finds x1 = x2 = 1, so the statement 'If x2 > x1 the NMC phase disappears' is degenerate for the very parameters used in Fig. 1 and should be illustrated with a case where x1 ≠ x2.
[§1, Eq. (1)] As printed, Eq. (1) reduces to p = 3 + (M-2)/(M-1), which gives p = 3 at M = 2, whereas the following sentence states that M = 2 yields de Sitter exponential inflation. Please check the formula or state the M = 2 limit explicitly.
[§2, Eq. (2)] The text states that L1 'turns out to be the simplest one' and that the terms studied 'are those appearing in the simplest natural coupling, namely TR.' Since TR is a combination of L1, L2 and L3 rather than L1 alone, please state which linear combination is being retained and why the others are dropped beyond convenience.
[§5, abstract s4] The claim that the model 'may display different inflationary epochs, generating a non-scale-invariant fluctuation spectrum' is qualitative; no spectrum is computed. This is appropriately hedged with 'may', but the conclusions should say plainly that the spectral index is not calculated here and that the statement is an expectation rather than a result.
[typography] There are numerous typographical errors that should be corrected: 'trasforms' and 'trasformed' (§3), 'explicitely' (§4), 'd'Alambertian' (§4), 'It rises natural the question' (§1), 'It worths remarking' (§4), 'secundary' (§5), 'thermalizes' (§5), and stray spacing in the abstract ('matte r', 'ne w', 'paramete rs').

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

The paper

The paper claims

Adding a derivative coupling to gravity widens the range of scalar-field models that can inflate, from a narrow band of one parameter to everything above a threshold.

The reading

Amendola asks whether a scalar field can drive inflation in a much wider class of gravity theories if the field is allowed to couple to curvature through its derivatives and not only through its value. The proposed extra term is $L_1 = 3.5$

What carries the argument

The load-bearing device is a bookkeeping scheme rather than a new symmetry: expand the field equation and the Friedmann equation and keep only terms up to second order in time derivatives, then read off which power of $f( 3.5$

Extended reading notes

Core claim

The paper's central claim is that adding the nonminimal derivative coupling $L_1 = 3.5$

Load-bearing premise

The claim rests on truncating the field equations at second order in time derivatives and assuming that the attractor found there survives in the full fourth-order system; the paper asserts this attractor property is easily proved and points to phase-space figures that are not reproduced in the text.

Editorial extensions

If this is right

The viable range of the exponent $M$ in $V=\lambda f^{M}$ grows from the narrow strip $2\le M<2+\sqrt{3}$ to all $M\ge 2$, so a model such as $M=4$ that fails as an ordinary nonminimal theory still inflates here.
A single field can pass through three successive inflationary stages (quasi-de Sitter, power-law, quasi-de Sitter), which breaks scale invariance of the primordial spectrum without a second scalar field.
A first-order phase transition in a second field can complete its graceful exit during the power-law stage, giving a bubble spectrum that ranges from harmlessly small to large enough to seed large-scale structure, depending on how the e-foldings are split.
The effective potential $U(\phi)=\xi(M-2)(4\mu)^{-1}f(\phi)$ makes the coupling function itself the inflaton potential, so the shape of the nonminimal coupling, not a separately chosen $V(\phi)$, controls the expansion history.
A conformal rescaling cannot put this theory into Einstein form; the author argues a Legendre-type transformation would be needed, which introduces tensor rather than scalar auxiliary fields.

Reading between the lines

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

Because the expanded $M$ range comes entirely from the $mu$-term dominating the coefficient $A$ of $\Box\phi$ at large $f$, the result should be sensitive to the sign condition $\xi,\mu\le 0$ that the paper adopts for regularity; relaxing it is the obvious next stress test.
The three-epoch structure suggests a calculable signature: a step-like or bent spectrum with a characteristic wavenumber set by $x_1$ in Eq. (28), the field value where the derivative coupling hands over to the ordinary nonminimal one.
If the effective potential picture survives beyond second order, the same mechanism could drive late-time acceleration with a coupling function rather than a tuned quintessence potential, though the paper does not pursue this.
The bubble-spectrum discussion is qualitative; a useful extension would compute the percolation condition from Eqs. (29)-(30) using the explicit scale factor of Eq. (26) and state which split of e-foldings is excluded by microwave-background limits.

Original abstract

We study a theory which generalizes the nonminimal coupling of matter to gravity by including derivative couplings. This leads to several interesting new dynamical phenomena in cosmology. In particular, the range of parameters in which inflationary attractors exist is greatly expanded. We also numerically integrate the field equations and draw the phase space of the model in second order approximation. The model introduced here may display different inflationary epochs, generating a non-scale-invariant fluctuation spectrum without the need of two or more fields. Finally, we comment on the bubble spectrum arising during a first-order phase transition occurring 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, 4,770 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.34 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We study a theory which generalizes the nonminimal coupling of matter to gravity by including derivative couplings. This leads to several interesting new dynamical phenomena in cosmology. In particular, the range of parameters in which inflationary attractors exist is greatly expanded. We also numerically integrate the field equations and draw the phase space of the model in second order approximation. The model introduced here may display different inflationary epochs, generating a non-scale-invariant fluctuation spectrum without the need of two or more fields. Finally, we comment on the bubble spectrum arising during a first-order phase transition occurring 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 study a theory which generalizes the nonminimal coupling of matter to gravity by including derivative couplings.	contribution 0.99	0.86	0.06	asserted 0.96
s1	This leads to several interesting new dynamical phenomena in cosmology.	interpretation 0.46	0.55	0.13	asserted 0.99
s2	In particular, the range of parameters in which inflationary attractors exist is greatly expanded.	result 1.00	0.80	0.28	asserted 1.00
s3	We also numerically integrate the field equations and draw the phase space of the model in second order approximation.	method 0.93	0.96	0.05	asserted 0.98
s4	The model introduced here may display different inflationary epochs, generating a non-scale-invariant fluctuation spectrum without the need of two or more fields.	result 0.85	0.65	0.31	hedged possibility 1.00
s5	Finally, we comment on the bubble spectrum arising during a first-order phase transition occurring in our model.	contribution 0.70	0.64	0.06	unclear 0.60

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from simulation or computation 0.95.

What was examined, and what was not

sources read

arXiv listing abstract v1

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

References

Works cited (25)

[1]

A. Linde, Phys. Lett. 129B (1983) 177; Nucl. Phys. B216 (1983 ) 421 (1983)

View on Pith 1983
[2]

F. Lucchin and S. Matarrese, Phys. Rev. D32 (1985) 1316

View on Pith 1985
[3]

R. Wald, Phys. Rev. D28 (1983) 2118; K.-I. Maeda, Phys. Rev. D 37 (1988) 858

View on Pith 1983
[4]

U. Kasper, Nuovo Cim. B103 (1989) 291; T. Futamase and K. Mae da, Phys. Rev. D39 (1989) 399; L. Amendola, M. Litterio and F. Occhionero, Int. J. Mo d. Phys. A 5 (1990) 3861

View on Pith 1989
[5]

P. A. M. Dirac, Proc. R. Soc. A338 (1974) 439; P. Jordan, Schw erkraft und Weltall (Wieweg, Braunschweig, 1955); C. Brans and R. H. Dicke Phys. Rev . , 124 (1961) 925

View on Pith 1974
[6]

N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Spaces ( Cambridge Univ. Press, Cambridge, 1982)

View on Pith 1982
[7]

A. Zee, Phys. Rev. Lett. , 42 (1979) 417; F. S. Accetta, D. J. Zoller and M. S. Turner, Phys. Rev. D31 (1985) 3046

View on Pith 1979
[8]

E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Menlo Park, CA, 1990)

View on Pith 1990
[9]

S. Randjbar-Daemi, A. Salam, and J. Strathdee, Phys. Lett. B 135 (1984) 388; K. Maeda, Class. Quantum Gravit. 3 (1986) 233; T. Applequist and A. C hodos, Phys. Rev. Lett. 50 (1983) 141

View on Pith 1984
[10]

M. Morikawa, Ap. J. Lett. , 362 (1990) L37

View on Pith 1990
[11]

J. Yokohama, Phys. Lett. , B212 (1988) 273

View on Pith 1988
[12]

J. Bekenstein and M. Milgrom, Ap. J. , 286 (1984) 7. 11

View on Pith 1984
[13]

D. La and P. J. Steinhardt, Phys. Rev. Lett. , 62 (1989) 376; D. La and P. J. Steinhardt, Phys. Lett. B220 (1989) 375; F. S. Accetta and J. J. Trester, P hys. Rev. D 39 (1989) 2854; A. Linde, CERN-TH-5806/90 preprint (1990)

View on Pith 1989
[14]

P. J. Steinhardt and F. S. Accetta, Phys. Rev. Lett. 64 (199 0) 2740

View on Pith
[15]

R. Holman, E. W. Kolb, and Y. Wang, Phys. Rev. Lett. 65 (1990) 17; R. Holman, E. W. Kolb, S. L. Vadas and Y. Wang, Phys. Rev. D43 (1991) 995; D43 ( 1991) 3833; Y. Wang, Phys. Rev. D 42 (1990) 2541

View on Pith 1990
[16]

Y. Wang, Phys. Rev. D42 (1990) 2541; D. La, Phys. Rev. D44 ( 1991) 1680; L. Amendola, S. Capozziello, M. Litterio and F. Occhionero, Phys. Rev. D45 (1992) 417

View on Pith 1990
[17]

T. Damour, G. W. Gibbons and C. Gundlach, Phys. Rev. Lett. 64 (1990) 123; G. Piccinelli, F. Lucchin and S. Matarrese, Phys. Lett. B277 (1992) 58

View on Pith 1990
[18]

L. Amendola, D. Bellisai and F. Occhionero, in preparation

View on Pith
[19]

B. Whitt, Phys. Lett. 145B (1984) 176; J. D. Barrow and Cots akis S., Phys. Lett. , 214B (1988) 515; K.-I. Maeda, Phys. Rev. D39 (1989) 3159; H.-J. Schmidt, Class. Q. Grav. 7 (1990) 1023

View on Pith 1984
[20]

G. Magnano, M. Ferraris and M. Francaviglia, Gen. Relativ. Grav it. , 19 (1987) 465

View on Pith 1987
[21]

L. A. Kofman, A. Linde and A. Starobinsky, Phys. Lett. B157 ( 1985) 361; L. Amendola, F. Occhionero and D. Saez, Ap. J. 349 (1990) 399

View on Pith 1990
[22]

A. H. Guth and E. J. Weinberg, Phys. Rev. D23 (1981) 876; Nuc l. Phys. B212 (1983) 321

View on Pith 1981
[23]

M. S. Turner and F. Wilczek Phys. Rev. Lett. 66 (1991) 5

View on Pith 1991
[24]

M. S. Turner, Fermilab-Conf-91/220-A, preprint (1991); M. S. Turner, E. J. Weinberg and L. M. Widrow, Fermilab-Pub-91/334-A, preprint (1992)

View on Pith 1991
[25]

D. La, Phys. Lett. B265 (1991) 232. 12

View on Pith 1991

Forward citations

Cited by 22 Pith papers

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

Black Holes in Bi-scalar Extensions of Horndeski Theories
gr-qc 2014-04 conditional novelty 6.0 of 10

A two-scalar Horndeski theory admits asymptotically flat black holes with a regular conformally coupled scalar and an independent scalar charge.
Fab 5: Noncanonical Kinetic Gravity, Self Tuning, and Cosmic Acceleration
astro-ph.CO 2012-08 conditional novelty 6.0 of 10

A nonlinear combination of purely kinetic gravity terms can produce cosmic acceleration and self-tune away a large cosmological constant on a Friedmann background without introducing extra propagating degrees of freedom.
Linear perturbations in Galileon gravity models
astro-ph.CO 2012-08 conditional novelty 6.0 of 10

Full linear perturbation equations for covariant Galileon gravity, solved in a modified CAMB, predict strong Galileon clustering, a deepening Weyl potential, enhanced matter growth, and excess low-l CMB power.
New Model of Inflation with Non-minimal Derivative Coupling of Standard Model Higgs Boson to Gravity
hep-ph 2010-03 conditional novelty 6.0 of 10

A derivative coupling of the Higgs boson to the Einstein tensor yields slow-roll inflation with Standard Model parameters and no tree-level unitarity violation.
Observational constraints on inflationary models with non-minimally derivative coupling by ACT
gr-qc 2025-06 conditional novelty 5.0 of 10

Inflationary potentials with non-minimally derivative coupling can produce larger scalar spectral tilts and lower tensor-to-scalar ratios, allowing them to fit ACT data, though the exponential attractor constraints co...

Show 17 more citing papers

Beyond generalized Proca theories
hep-th 2016-05 conditional novelty 5.0 of 10

New beyond-Proca vector interactions are shown to keep the same propagating degrees of freedom as generalized Proca theories on a flat cosmological background, with a modified scalar sound speed.
Scalar-Fluid theories: cosmological perturbations and large-scale structure
astro-ph.CO 2015-05 conditional novelty 5.0 of 10

Linear perturbation equations for algebraically and derivatively coupled scalar-fluid dark sector models are derived, and requiring zero effective sound speed in the coupled dark matter restricts the fluid Lagrangian ...
$f(T,\mathcal{T})$ gravity and cosmology
gr-qc 2014-05 conditional novelty 5.0 of 10

A new modified gravity theory, f(T,T), couples torsion to the matter energy-momentum trace and yields parameter-dependent cosmic acceleration, quintessence or phantom dark energy, and a claimed stability window.
Solutions in the scalar-tensor theory with nonminimal derivative coupling
gr-qc 2013-12 accept novelty 5.0 of 10

Exact static black hole solutions are found for a scalar-tensor theory with derivative coupling to the Einstein tensor, showing that the asymptotic geometry is set by the coupling constant, not the cosmological constant.
Scaling attractors in interacting teleparallel dark energy
gr-qc 2013-05 conditional novelty 5.0 of 10

A teleparallel dark energy model with a coupling function engineered so that alpha vanishes at the fixed point admits a stable scaling attractor with accelerated expansion, whereas constant coupling does not.
Scalar Hair from a Derivative Coupling of a Scalar Field to the Einstein Tensor
gr-qc 2011-11 conditional novelty 5.0 of 10

A scalar field kinetically coupled to the Einstein tensor produces a regular, anisotropic hairy black hole that is thermodynamically favored over the Reissner-Nordstrom solution near a computed critical temperature.
UV-protected (Natural) Inflation: Primordial Fluctuations and non-Gaussian Features
astro-ph.CO 2011-06 accept novelty 5.0 of 10

Gravitationally enhanced friction inflation reduces to single-field inflation with standard consistency relations, and its local non-Gaussianity is dominated by the gauge transformation from flat to uniform-field slicing.
Disformal Scalar Fields and the Dark Sector of the Universe
astro-ph.CO 2010-04 conditional novelty 5.0 of 10

Disformal quintessence, a canonical scalar field coupled to a disformal metric, remains compatible with WMAP7, Union SNe and SDSS data provided the potential slope alpha is above about 8.5 and the disformal slope rati...
Exact cosmological solutions with nonminimal derivative coupling
gr-qc 2009-10 conditional novelty 5.0 of 10

For the nonminimal derivative coupling κGμν φ,μ φ,ν with positive κ, the flat FRW equations have an early quasi-de Sitter attractor and a late-time power-law exit, without a scalar potential.
Palatini-Higgs inflation with non-minimal derivative coupling
gr-qc 2020-08 conditional novelty 4.0 of 10

A non-minimal derivative coupling in Palatini Higgs inflation can raise the tensor-to-scalar ratio to the 10^-4 range, making the model accessible to future CMB experiments.
Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor
hep-th 2016-07 conditional novelty 4.0 of 10

A Horndeski-type kinetic coupling of the bulk scalar to the Einstein tensor suppresses the holographic condensate and breaks the usual gap-to-condensate relation, which the authors read as an impurity analogue.
Effective field theory approach to modified gravity including Horndeski theory and Ho\v{r}ava-Lifshitz gravity
hep-th 2014-09 accept novelty 4.0 of 10

A general 3+1 effective action, expanded to second order in scalar perturbations on a flat FLRW background, yields a single quadratic Lagrangian covering Horndeski, GLPV and Horava-Lifshitz gravity and reproduces thei...
Four-Dimensional Asymptotically AdS Black Holes with Scalar Hair
gr-qc 2013-09 conditional novelty 4.0 of 10

A new closed-form family of asymptotically AdS black holes with scalar hair is derived by potential reconstruction, and a low-temperature thermal phase transition to the hairy configuration is reported.
Phase Transition to a Hairy Black Hole in Asymptotically Flat Spacetime
hep-th 2013-08 conditional novelty 4.0 of 10

A derivative coupling of a charged scalar to the Einstein tensor lets an asymptotically flat Reissner-Nordström black hole grow spherically symmetric scalar hair below a critical temperature, with the hair concentrate...
Non-minimal Kinetic coupling to gravity and accelerated expansion
hep-th 2009-11 conditional novelty 4.0 of 10

A non-minimally kinetic-coupled scalar field can drive accelerated expansion and mimic a cosmological constant, but only for specific parameter choices and without matter.
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.
The effective field theory of inflation/dark energy and the Horndeski theory
gr-qc 2014-04 accept novelty 3.0 of 10

Horndeski scalar-tensor gravity is a sub-class of the effective field theory of cosmological perturbations, with its background dynamics fixed by three time-dependent functions, and this review derives the resulting i...

How the literature uses it

58 arXiv papers cite this in 76 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 · 46 sentences without a confident label

Cites it as background 29 papers

In 1993, Amendola [ref] has been considered the most general gravity Lagrangian linear in the curvature scalar $R$, quadratic in $ϕ$, and containing terms with four derivatives including all of the following terms (see also [ref] for details): L_1=κ_1 Rϕ_,μϕ^,μ; L_2=κ_2 R_μνϕ^,μϕ^,ν; L_3=κ_3 R ϕ□ϕ; L_4=κ_4 R_μν ϕϕ^;μν ; L_5=κ_5 R_;μ ϕϕ^,μ ; L_6=κ_6 □R ϕ^2, where coefficients $κ_1,…,κ_6$ are coupling parameters with dimensions of length-squared.

Exact cosmological solutions with nonminimal derivative coupling · Introduction · 0.88
Such are couplings of the scalar field to the Ricci scalar curvature $∼f(ϕ)R$ [ref] or derivative couplings to the Ricci tensor $∼(∂_ μϕ∂_ νϕ)R^ μν$ [ref] .

Inflation and reheating in quadratic metric-affine gravity with derivative couplings · Introduction · 0.89
The most general gravity Lagrangian linear in the curvature scalar R, quadratic in the scalar field $ϕ$, and containing terms with four derivatives was considered in [ref] .

Scalar Hair from a Derivative Coupling of a Scalar Field to the Einstein Tensor · Introduction · 0.99

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]

A. Linde, Phys. Lett. 129B (1983) 177; Nucl. Phys. B216 (1983 ) 421 (1983)

View on Pith 1983

[2] [2]

F. Lucchin and S. Matarrese, Phys. Rev. D32 (1985) 1316

View on Pith 1985

[3] [3]

R. Wald, Phys. Rev. D28 (1983) 2118; K.-I. Maeda, Phys. Rev. D 37 (1988) 858

View on Pith 1983

[4] [4]

U. Kasper, Nuovo Cim. B103 (1989) 291; T. Futamase and K. Mae da, Phys. Rev. D39 (1989) 399; L. Amendola, M. Litterio and F. Occhionero, Int. J. Mo d. Phys. A 5 (1990) 3861

View on Pith 1989

[5] [5]

P. A. M. Dirac, Proc. R. Soc. A338 (1974) 439; P. Jordan, Schw erkraft und Weltall (Wieweg, Braunschweig, 1955); C. Brans and R. H. Dicke Phys. Rev . , 124 (1961) 925

View on Pith 1974

[6] [6]

N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Spaces ( Cambridge Univ. Press, Cambridge, 1982)

View on Pith 1982

[7] [7]

A. Zee, Phys. Rev. Lett. , 42 (1979) 417; F. S. Accetta, D. J. Zoller and M. S. Turner, Phys. Rev. D31 (1985) 3046

View on Pith 1979

[8] [8]

E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Menlo Park, CA, 1990)

View on Pith 1990

[9] [9]

S. Randjbar-Daemi, A. Salam, and J. Strathdee, Phys. Lett. B 135 (1984) 388; K. Maeda, Class. Quantum Gravit. 3 (1986) 233; T. Applequist and A. C hodos, Phys. Rev. Lett. 50 (1983) 141

View on Pith 1984

[10] [10]

M. Morikawa, Ap. J. Lett. , 362 (1990) L37

View on Pith 1990

[11] [11]

J. Yokohama, Phys. Lett. , B212 (1988) 273

View on Pith 1988

[12] [12]

J. Bekenstein and M. Milgrom, Ap. J. , 286 (1984) 7. 11

View on Pith 1984

[13] [13]

D. La and P. J. Steinhardt, Phys. Rev. Lett. , 62 (1989) 376; D. La and P. J. Steinhardt, Phys. Lett. B220 (1989) 375; F. S. Accetta and J. J. Trester, P hys. Rev. D 39 (1989) 2854; A. Linde, CERN-TH-5806/90 preprint (1990)

View on Pith 1989

[14] [14]

P. J. Steinhardt and F. S. Accetta, Phys. Rev. Lett. 64 (199 0) 2740

View on Pith

[15] [15]

R. Holman, E. W. Kolb, and Y. Wang, Phys. Rev. Lett. 65 (1990) 17; R. Holman, E. W. Kolb, S. L. Vadas and Y. Wang, Phys. Rev. D43 (1991) 995; D43 ( 1991) 3833; Y. Wang, Phys. Rev. D 42 (1990) 2541

View on Pith 1990

[16] [16]

Y. Wang, Phys. Rev. D42 (1990) 2541; D. La, Phys. Rev. D44 ( 1991) 1680; L. Amendola, S. Capozziello, M. Litterio and F. Occhionero, Phys. Rev. D45 (1992) 417

View on Pith 1990

[17] [17]

T. Damour, G. W. Gibbons and C. Gundlach, Phys. Rev. Lett. 64 (1990) 123; G. Piccinelli, F. Lucchin and S. Matarrese, Phys. Lett. B277 (1992) 58

View on Pith 1990

[18] [18]

L. Amendola, D. Bellisai and F. Occhionero, in preparation

View on Pith

[19] [19]

B. Whitt, Phys. Lett. 145B (1984) 176; J. D. Barrow and Cots akis S., Phys. Lett. , 214B (1988) 515; K.-I. Maeda, Phys. Rev. D39 (1989) 3159; H.-J. Schmidt, Class. Q. Grav. 7 (1990) 1023

View on Pith 1984

[20] [20]

G. Magnano, M. Ferraris and M. Francaviglia, Gen. Relativ. Grav it. , 19 (1987) 465

View on Pith 1987

[21] [21]

L. A. Kofman, A. Linde and A. Starobinsky, Phys. Lett. B157 ( 1985) 361; L. Amendola, F. Occhionero and D. Saez, Ap. J. 349 (1990) 399

View on Pith 1990

[22] [22]

A. H. Guth and E. J. Weinberg, Phys. Rev. D23 (1981) 876; Nuc l. Phys. B212 (1983) 321

View on Pith 1981

[23] [23]

M. S. Turner and F. Wilczek Phys. Rev. Lett. 66 (1991) 5

View on Pith 1991

[24] [24]

M. S. Turner, Fermilab-Conf-91/220-A, preprint (1991); M. S. Turner, E. J. Weinberg and L. M. Widrow, Fermilab-Pub-91/334-A, preprint (1992)

View on Pith 1991

[25] [25]

D. La, Phys. Lett. B265 (1991) 232. 12

View on Pith 1991