Cuscuton and low energy limit of Horava-Lifshitz gravity

Niayesh Afshordi (Perimeter Institute)

REVIEW

Cuscuton and low energy limit of Horava-Lifshitz gravity

High Energy Physics - Theory · Submitted 30 Jul 2009 · 21 references

Pith's verdict: The action-level match to cuscuton is exact and worth knowing; the solution-level equivalence is conditional, and the abstract's 'uniquely' is a step ahead of §II.

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CitationNiayesh Afshordi (Perimeter Institute). "Cuscuton and low energy limit of Horava-Lifshitz gravity." arXiv:0907.5201 (2009). https://pith.science/paper/NT3NTGWG

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Editor's note

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The thing to take away: the low-energy non-projectible Horava-Lifshitz action, Einstein-Hilbert plus (1-lambda)K^2/(16 pi G_N), is algebraically the quadratic cuscuton action with mu^2 = -m^2 = -(1-lambda)/(8 pi G_N). That matching (Eqs 1-7) is short, clean, and checkable in ten minutes, and it is why people cite this paper. If you accept it, the scalar that drove the 2009 ghost and instability arguments is a constrained field, not a propagating mode, and the whole debate looks different. That is a real organizing result, and it is delivered in five pages without padding. The geometric symmetry argument in §IV (Eqs 16-22, the soap-film analogy, decoupling of constant-phi surfaces) is the part I find most interesting and it is also the most compressed; it deserves a longer treatment than it gets here, but the idea is sound and it is the seed of a lot of later cuscuton work. The lambda bound is quoted from [6], which is published and data-based, so I would not hold that against the paper; the new content is the mapping, not the constraint. Where I would push: the abstract says 'uniquely given' and 'non-dynamical to all orders,' and §II is more careful than that. The paper itself says extremizing S_qc is 'sufficient (but not necessary)' for extremizing S_lambda, and the gap is closed by a maximum-principle argument in the uniform-psi, g0i = 0 gauge with uniform phi at spatial infinity. That argument is reasonable and probably right for FRW asymptotics, but it is conditional, and the paper knows it. The 'all orders' claim is really about perturbation theory around uniform backgrounds, which is defensible; the abstract just does not say so. The acknowledged breakdown near black hole horizons and at caustics is honestly flagged, and the lambda < 1 instability note is a genuine caveat rather than a hedge. So: a good, honest short note whose body is more careful than its abstract. Anyone working on modified gravity, cuscuton, or the HL literature should read it. I would send it out; the referees will mostly argue about the boundary-condition step, which is exactly the argument worth having.

Referee report

Significance

If the mapping holds, it materially reframes the 2009 discussion of the extra scalar in Hořava–Lifshitz gravity: the mode that motivated much of the ghost/instability literature would be a constrained field rather than a propagating degree of freedom. The core of the argument is short, algebraic, and checkable, which is a genuine virtue; I verified that Eq. (13) follows from Eq. (6) by direct substitution, and the auxiliary-field manipulation of Eqs. (3)–(5) is correct. The λ bound is a quantitative, falsifiable statement linking a UV parameter to a cosmological observable, and the soap-film/CMC interpretation of Eq. (22) is a clean geometric observation that earns its place. The paper is also commendably explicit about where its own equivalence argument is conditional.

Major objections (3)

[Abstract (s2, s3) versus §II, Eqs. (7)–(11)] The abstract states that the low-energy limit is 'uniquely given' by the quadratic cuscuton and that the extra scalar is 'non-dynamical to all orders in perturbation theory', but §II concedes that extremizing S_qc is 'a sufficient (but not necessary) condition' to extremize S_λ, and that equivalence requires uniform-ϕ boundary conditions at spatial infinity together with the g⁰ⁱ = 0 gauge. The closing step is a maximum-principle argument on Eq. (10), which additionally requires M^{ij} in Eq. (11) to be elliptic; §IV itself notes a possible breakdown near black hole horizons. The body is honest about this, so the fix is local, but the abstract and the Conclusions should carry the same qualification, and §II should add one explicit sentence on the conditions under which M^{ij} fails to be elliptic and what happens to the equivalence there.
[§IV, paragraph beginning 'We should point out that neglecting this non-local constraint...'] The paper dismisses a body of work ([9]–[14]) in a single sentence, asserting that others inferred instabilities or ghosts by neglecting the non-local constraint. Since this is the manuscript's principal point of contact with the existing literature and a large part of why the result matters, the rebuttal should be made checkable: name the specific calculation in, say, [10] or [13], identify the specific step that is invalid, and state why the flat-foliation Minkowski background those works perturb around is not an admissible background for λ ≠ 1. The observation that flat foliation is not a solution is made later in the same section and is the right argument; it should be connected explicitly to the cited papers rather than left as a general remark.
[§II, Eq. (1) and the sentence introducing it] The sentence introducing Eq. (1) is grammatically incomplete ('the most general low-energy limit of (non-projectible) Hořava-Lifshitz gravity action is particularly interesting'), and the claim that this is the most general low-energy limit is not argued in the text. Footnote [20] points to [19] for a systematic covariant derivation, but not for the generality claim, and a cosmological constant term is nowhere written. Because the word 'uniquely' in the abstract rests entirely on Eq. (1) being the complete low-energy action within the reduced symmetry class, a short justification — or an explicit statement of what has been dropped and why — is needed here.

Minor objections (8)

[Abstract versus Eq. (14)] Eq. (14) reports λ − 1 = 0.003 ± 0.014 at 95% CL, which implies λ − 1 ∈ [−0.011, 0.017], whereas the abstract quotes |λ − 1| < 0.014. The two should be reconciled, either by quoting the asymmetric interval or by stating that the central value is being neglected.
[§III, Eq. (13)] The step from Eq. (6) to Eq. (13) is correct but compressed; inserting the intermediate substitution μ⁴/m² = −(1−λ)/(8πG_N) and defining M_{p,IR} and M_{p,UV} at the point of use would let the reader verify the factor of 3/2 without leaving the page.
[§III, Eq. (6)] For λ < 1 the relation μ² = −m² = −(1−λ)/(8πG_N) makes m² negative, i.e. the potential is inverted. One sentence explaining why this is not a tachyonic instability in the usual sense — because ϕ carries no propagating degree of freedom — would preempt an obvious misreading, especially given the instability discussion in §IV.
[§IV, Eq. (23)] The Hamiltonian is written after setting g⁰ⁱ = 0, and the claim that short-wavelength perturbations can have arbitrarily negative energies for λ < 1 depends on whether the gradient is spacelike or timelike (the denominator √(∂_μϕ∂^μϕ) behaves differently in the two cases). State the gauge choice and the regime explicitly.
[§IV, Eqs. (16)–(19)] The statement that the cuscuton action is invariant under (16) for any f(ϕ) and a large class of a^μ is plausible given Eq. (17), but the text does not say whether the transformations close into an algebra or whether they are the only such symmetries. A brief remark on closure would clarify what 'can protect the low energy theory' is meant to guarantee.
[§III, Eq. (14) and reference [6]] The λ bound is a translation of the constraint obtained in [6], not a new data analysis. Saying so explicitly at the point where Eq. (14) is quoted would make the provenance of the headline number transparent to a reader who does not know the earlier cuscuton papers.
[Figure 1] The figure is described as a cartoon, but the caption does not identify the dashed line, the numbered surfaces, or the two spatial-infinity markers. A one-line legend would make it usable independently of the text.
[Terminology] The manuscript uses 'non-projectible' throughout; the standard spelling in this literature is 'non-projectable'. This is cosmetic but appears in the abstract.

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The paper

The paper claims

The extra scalar in Horava-Lifshitz gravity may be a constrained field rather than a propagating particle, since the low-energy limit of the theory is exactly the quadratic cuscuton model.

The reading

Horava-Lifshitz gravity was proposed as a power-counting renormalizable theory of quantum gravity that gives up Lorentz invariance at high energies. Dropping that symmetry introduces an apparent extra scalar degree of freedom, and much of the early follow-up literature read that scalar as a ghost, a tachyon, or an instability. This paper argues that at low energies the theory is not merely similar to but identical with the quadratic cuscuton: a scalar with infinite speed of sound and a quadratic potential, minimally coupled to Einstein gravity, whose field is fixed by a spatial constraint rather than by initial data. If that identification holds, the extra scalar never propagates, and the standard cosmological bounds on the cuscuton translate directly into a bound on the one Lorentz-breaking parameter that survives at low energies.

What carries the argument

The load-bearing device is an auxiliary-field rewriting. Introducing a Lagrange multiplier $^2$ and a unit-norm vector $v_$, the cuscuton action becomes linear in $v_$ and in $^2$, so varying $v_$ forces $v_$ to be the normalized gradient of the field. The Horava-Lifshitz correction $(1-2)K^2/(16G_N)$, with $K=_u^$, is rewritten the same way, and the two actions coincide once $^2=-m^2=-(1-2)/(8G_N)$. The gap between them is that Horava-Lifshitz imposes the gradient condition at the level of the action, while the cuscuton imposes it only through its equations of motion. The paper closes that gap by going to the preferred frame with $g_{0i}=0$, where the residual equation for the field becomes an elliptic spatial equation, $ _i(M^{ij}_j)=0 $, whose solutions are fixed by boundary data at spatial infinity rather than by initial data. That is what turns the scalar into a constrained field: fixing the field at the edges of a constant-field surface fixes the whole surface, and different surfaces decouple from one another in the action, which is written as a sum over surfaces of an area term plus a volume term, in direct analogy with the energy of a soap film under a pressure difference.

Extended reading notes

Core claim

The paper shows that the low-energy action of non-projectible Horava-Lifshitz gravity, $S_{HL}=S_{EH}+(1-2)/(16G_N)$... more precisely $S_{HL}=S_{EH}+(1-2)/(16G_N)$ with the correction written as $(1-2)/(16G_N)$ times $K^2$, is the same action as the quadratic cuscuton, $S_{qc}= (2-2)/(8G_N)$ with the identification $^2=-m^2=-(1-2)/(8G_N)$ and the unit vector $u_$ equal to the normalized gradient of the cuscuton field. The correction term in Horava-Lifshitz gravity is the square of the mean extrinsic curvature of constant-time surfaces; the cuscuton is a scalar whose equation of motion forces its own constant-field surfaces to have uniform mean curvature. Matching the two makes the apparent extra scalar non-dynamical to all orders in perturbation theory. Because the cuscuton's effect is a mismatch between the sub-horizon and super-horizon Planck masses, $M_{p,IR}^2=[1+3(1-2)]M_{p,UV}^2$ with the coefficient fixed by the same parameters, existing cosmological constraints on that mismatch give $|-1|<0.014$ at 95% confidence. The paper also identifies the preferred foliation of the low-energy theory as constant mean curvature (uniform expansion) surfaces, and exhibits a family of field-dependent coordinate transformations under which the cuscuton action is invariant, which it offers as a symmetry that could keep the scalar non-dynamical against higher-derivative corrections.

Load-bearing premise

The equivalence holds only if the cuscuton's gradient condition is enforced by boundary conditions at spatial infinity, since Horava-Lifshitz gravity imposes that condition in the action while the cuscuton imposes it only through its equations of motion; the paper argues this is automatic for asymptotically FRW geometries but does not prove it in general.

Editorial extensions

If this is right

The scalar mode that dominated early worries about Horava-Lifshitz gravity is not a propagating degree of freedom at low energies, so ghost and tachyon instabilities attributed to it are absent at the perturbative level.
The one low-energy Lorentz-breaking parameter is bounded by cosmology: $|-1|<0.014$ at 95% confidence, since it controls the running of the Planck mass between sub-horizon and super-horizon scales.
The preferred time foliation of the low-energy theory is the constant mean curvature (uniform expansion) foliation, which is a geometrically natural choice rather than an arbitrary gauge fixing.
A family of field-dependent coordinate transformations leaves the cuscuton action invariant, which the paper proposes as a symmetry that could protect the non-dynamical character of the scalar from higher-derivative quantum corrections.
For $<1$ the low-energy Hamiltonian of the scalar sector is unbounded below at short wavelengths, which the paper flags as a possible non-perturbative instability even though no ghost degree of freedom exists.

Reading between the lines

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

If the identification is exact, the long-running dispute over the scalar mode in Horava-Lifshitz gravity is largely a dispute about gauge choice and boundary conditions rather than about physics, which would explain why different groups reached opposite conclusions from the same action.
The equivalence suggests a practical route: any cosmological observable that probes the cuscuton's Planck-mass running becomes a measurement of the Lorentz-breaking parameter, so future large-scale structure or CMB data could tighten the bound well past the current 1.4 percent.
The soap-film analogy hints at a geometric reformulation in which the scalar is eliminated entirely and the theory is written as a functional of foliation surfaces, which would make the non-dynamical character manifest and might suggest which higher-derivative terms are allowed.
The claim that the flat foliation of Minkowski space is not a solution when $ $ is not 1 implies that perturbation theory expanded around that background is studying the wrong point, so instability results obtained that way should be re-examined around a constant-mean-curvature background.

Original abstract

A proposal for a power-counting renormalizable theory of quantum gravity at a Lifshitz point was recently put forth by Horava (arXiv:0901.3775), and has been since dubbed as Horava-Lifshitz gravity. The theory explicitly breaks Lorentz invariance, which introduces an apparent extra scalar degree of freedom. In this note, we show that the low energy limit of (non-projectible) Horava-Lifshitz gravity is uniquely given by the quadratic cuscuton model: a covariant scalar field theory with an infinite speed of sound and a quadratic potential, which is minimally coupled to Einstein gravity. This implies that the extra scalar is non-dynamical to all orders in perturbation theory. Using current cosmological constraints on the quadratic cuscuton model, we can constrain the low energy Lorentz breaking parameter of Horava-Lifshitz theory (which leads to a running of Planck mass on the Hubble scale) to |lambda-1| < 0.014 (at 95% confidence level). We also point out that, with reasonable boundary conditions, the spatial hypersurfaces in this theory are constant mean curvature (CMC) or uniform expansion surfaces at low energies, and introduce geometrical symmetries that can protect the non-dynamical nature of these theories from quantum corrections. We also notice that the theory with lambda < 1 might suffer from a non-perturbative UV instability.

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, 5,887 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.82 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.24 · 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.

A proposal for a power-counting renormalizable theory of quantum gravity at a Lifshitz point was recently put forth by Horava (arXiv:0901.3775), and has been since dubbed as Horava-Lifshitz gravity. The theory explicitly breaks Lorentz invariance, which introduces an apparent extra scalar degree of freedom. In this note, we show that the low energy limit of (non-projectible) Horava-Lifshitz gravity is uniquely given by the quadratic cuscuton model: a covariant scalar field theory with an infinite speed of sound and a quadratic potential, which is minimally coupled to Einstein gravity. This implies that the extra scalar is non-dynamical to all orders in perturbation theory. Using current cosmological constraints on the quadratic cuscuton model, we can constrain the low energy Lorentz breaking parameter of Horava-Lifshitz theory (which leads to a running of Planck mass on the Hubble scale) to |lambda-1| < 0.014 (at 95% confidence level). We also point out that, with reasonable boundary conditions, the spatial hypersurfaces in this theory are constant mean curvature (CMC) or uniform expansion surfaces at low energies, and introduce geometrical symmetries that can protect the non-dynamical nature of these theories from quantum corrections. We also notice that the theory with lambda < 1 might suffer from a non-perturbative UV instability.

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	A proposal for a power-counting renormalizable theory of quantum gravity at a Lifshitz point was recently put forth by Horava (arXiv:0901.3775), and has been since dubbed as Horava-Lifshitz gravity.	background 1.00	0.03	0.02	asserted 0.99
s1	The theory explicitly breaks Lorentz invariance, which introduces an apparent extra scalar degree of freedom.	background 0.99	0.05	0.02	asserted 0.97
s2	In this note, we show that the low energy limit of (non-projectible) Horava-Lifshitz gravity is uniquely given by the quadratic cuscuton model: a covariant scalar field theory with an infinite speed of sound and a quadratic potential, which is minimally coupled to Einstein gravity.	result 0.83	0.95	0.94	asserted 1.00
s3	This implies that the extra scalar is non-dynamical to all orders in perturbation theory.	interpretation 0.92	0.86	0.16	asserted 1.00
s4	Using current cosmological constraints on the quadratic cuscuton model, we can constrain the low energy Lorentz breaking parameter of Horava-Lifshitz theory (which leads to a running of Planck mass on the Hubble scale) to \|lambda-1\| < 0.014 (at 95% confidence level).	result 0.98	0.85	0.16	asserted 0.85
s5	We also point out that, with reasonable boundary conditions, the spatial hypersurfaces in this theory are constant mean curvature (CMC) or uniform expansion surfaces at low energies, and introduce geometrical symmetries that can protect the non-dynamical nature of these theories from quantum corrections.	result 0.69	0.89	0.04	asserted 0.84
s6	We also notice that the theory with lambda < 1 might suffer from a non-perturbative UV instability.	limitation 0.75	0.68	0.03	hedged possibility 0.63

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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
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: A cartoon of constant field hypersurfaces of cuscu

Figures reproduced from arXiv:0907.5201 by the authors.

References

Works cited (21)

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[21]

Note that ϕ = ∇νuν follows from varying Sλ with respect to ϕ

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Forward citations

Cited by 17 Pith papers

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

A Cuscuton Representation of the Loop Quantum Cosmology Bounce
gr-qc 2026-09 accept novelty 7.0 of 10

An angular cuscuton action with field theta = 2 lambda b reproduces the exact flat-FLRW LQC bounce with no additional propagating degrees of freedom.
General Covariance in Quantum Gravity at a Lifshitz Point
hep-th 2010-07 accept novelty 7.0 of 10

Gauging a local U(1) symmetry in Hořava gravity eliminates the scalar graviton, forces the kinetic coupling to λ=1, and leaves only general relativity's two tensor polarizations.
Fast Scrambling Cosmology
astro-ph.CO 2026-11 conditional novelty 6.0 of 10

The proposed fast-scrambling correction yields slowly evolving dark energy, a neutrino-mass-dependent residual, and a proxy estimate Gamma about -2.8.
Is DESI Seeing Dynamical Dark Energy, or a Cosmic Glitch in Gravity?
astro-ph.CO 2026-09 conditional novelty 6.0 of 10

A one-parameter model with cosmological gravity about 0.8 percent weaker than Newton's constant fits the CMB and DESI BAO data at 3.3 sigma and forecasts DESI distances that w0waCDM cannot predict.
Spatially covariant gravity theories with two tensorial degrees of freedom: the formalism
gr-qc 2019-10 conditional novelty 6.0 of 10

Two necessary and sufficient conditions on the Lagrangian of a spatially covariant gravity theory eliminate the scalar degree of freedom, leaving only the two tensorial modes.

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Extended Cuscuton: Formulation
gr-qc 2018-09 conditional novelty 6.0 of 10

A new class of scalar-tensor theories, the extended cuscuton, is derived in which only two gravitational degrees of freedom propagate in the unitary gauge, generalizing the original cuscuton.
On Lorentz violation in Horava-Lifshitz type theories
hep-th 2010-10 conditional novelty 6.0 of 10

One-loop graviton corrections in Horava-Lifshitz gravity induce species-dependent speed-of-light differences; spin-2 and spin-0 modes are protected by the Lifshitz scale, but the spin-1 mode stays quadratically diverg...
Strong coupling in extended Horava-Lifshitz gravity
hep-th 2009-11 accept novelty 6.0 of 10

The extended Horava-Lifshitz gravity proposed by Blas, Pujolas and Sibiryakov still exhibits strong coupling at cubic order as the Lorentz-preserving limit is approached, so it cannot serve as a UV completion of gener...
Scalar field perturbations in Horava-Lifshitz cosmology
hep-th 2009-09 accept novelty 6.0 of 10

In Horava-Lifshitz gravity with projectability, single-field slow-roll inflation conserves the super-horizon curvature perturbation, but through slow-roll attractor dynamics rather than the local Hamiltonian constrain...
On the consistency of the Horava Theory
hep-th 2010-04 accept novelty 5.0 of 10

The lowest-order truncation of nonprojectable Horava gravity with detailed balance is exactly equivalent to general relativity in the partial gauge where the trace of the canonical momentum vanishes, not a physically ...
Observational constraints on Horava-Lifshitz cosmology
hep-th 2009-11 conditional novelty 5.0 of 10

Horava-Lifshitz cosmology survives current cosmological data only with its curvature and dark-radiation terms constrained to be very small, and the detailed-balance version requires an ad hoc analytic continuation.
Phase-space analysis of Horava-Lifshitz cosmology
hep-th 2009-09 conditional novelty 5.0 of 10

Phase-space analysis shows Horava-Lifshitz cosmology admits late-time dark-energy-dominated attractors, oscillatory under detailed balance and eternally expanding without it.
An analysis of the phase space of Horava-Lifshitz cosmologies
hep-th 2009-09 conditional novelty 5.0 of 10

A dynamical systems analysis of Horava-Lifshitz cosmology finds that a viable Friedmann-to-dark-energy history requires breaking the detailed balance condition.
Problem of Time in Quantum Gravity
gr-qc 2012-06 conditional novelty 4.0 of 10

The Problem of Time is a package of eight interacting facets, and quantum-gravity approaches should be classified by their full ordering of constraint, quantization, time or history, and observables.
Horava-Lifshitz Dark Energy
hep-th 2009-05 conditional novelty 4.0 of 10

Grouping a second scalar field with the Horava-Lifshitz dark radiation and cosmological constant terms yields an effective dark energy that is phantom in a non-flat universe and can cross minus one.
Tests of Lorentz invariance: a 2013 update
gr-qc 2013-04 accept novelty 3.0 of 10

Lorentz-violation constraints from particle physics and astrophysics are collected and tabulated, and applying them to Horava-Lifshitz gravity is argued to force that theory's Lorentz-breaking scale well below the Pla...
Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
gr-qc 2016-12 accept novelty 2.0 of 10

Mimetic gravity can geometrically mimic dark matter and, with a chosen potential, reproduce arbitrary cosmic expansion histories, but the minimal model has a vanishing sound speed and a known ghost instability.

How later papers used it

67 later papers cite it

Evidence: substantial. 61 of the citing papers share no author with it, and 5 of those carry a confident label from Pith's citation classifier.

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1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 paper

Reviewed a reformulation of the cuscuton as a scalar-vector-tensor theory following this paper.

Revisiting the cuscuton as a Lorentz-violating gravity theory (2016) · 0.81 · paraphrased: the licence does not allow quoting

How the literature uses it

66 arXiv papers cite this in 94 sentences

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Papers citing it · 60 sentences without a confident label

Builds on it 2 papers

In this section we discuss the renormalization of an adapted version of the cuscuton model [ref] coupled to the Einstein-Hilbert truncation of general relativity in order to investigate the quantum behavior of the $K^2$ term in the Lorentz violating action ([ref]).

Preferred foliation effects in Quantum General Relativity · Explicit renormalization of the cuscuton model · 0.91
For nonzero $ε$ the stability analysis can be done by explicitly integrating out all constraints, leading to a classically equivalent theory involving a multiple-field but single-clock (and finite speed of sound) generalization of the Cuscuton models considered in [ref] .

Magnon Inflation: Slow Roll with Steep Potentials · Introduction · 0.90

Uses its method or tool 1 paper

We start by reviewing a reformulation of the cuscuton as a scalar-vector-tensor theory following [ref] .

Revisiting the cuscuton as a Lorentz-violating gravity theory · Reformulation of the cuscuton · 0.81

Compares with it 2 papers

Thus magnon inflation is classically equivalent to cusc, which bears a superficial resemblance to the Cuscuton model [ref] (see also [ref] ), though with multiple fields and with a dyadic (and so degenerate — more about which below) target space metric: $_a b(ϕ) = _a_b$.

Magnon Inflation: Slow Roll with Steep Potentials · An equivalent effective description · 0.81
The authors of Ref. [ref] extended the cuscuton theory to include $G_3(ϕ,X)ϕ$ to obtain consistently a generalization of the McVittie solution.

Extended Cuscuton: Formulation · Comparison with other related theories · 0.84

Cites it as support 1 paper

The conformal symmetry of the theory in the UV [ref] not only fixes the potential but requires exact flatness (Eqs.([ref]) lead to a contradiction in the presence of spatial curvature).

The critical geometry of a thermal big bang · Introduction · 0.97

Cites it as background 24 papers

The concept of cuscuton gravity [ref] arises when trying to minimally modify GR by introducing a scalar field that does not propagate any new degrees of freedom.

Cuscuton gravity as a classically stable limiting curvature theory · Introduction · 0.84
This is the action of the Cuscuton field [ref] , which has been studied in the context of Dark Energy in [ref] and of inflation in [ref] .

Symmetric Scalars · Degree zero · 0.83
The status of Hořava's original proposal [ref] as well as its various extensions [ref] , both on theoretical and phenomenological ground, is still being actively discussed and debated in the literature [ref] .

On Lorentz violation in Horava-Lifshitz type theories · Introduction · 1.00

What it cites · 18 sentences without a confident label

Contests 3 papers

We should point out that neglecting this non-local constraint has led others to infer instabilities/ghosts, or inconsistencies in the Ho$ř$ava-Lifshitz theory (e.g. [ref] ).

A Trouble with Ho\v{r}ava-Lifshitz Gravity · Geometric symmetries and lack of dynamics · contest 0.77
We should point out that neglecting this non-local constraint has led others to infer instabilities/ghosts, or inconsistencies in the Ho$ř$ava-Lifshitz theory (e.g. [ref] ).

Is nonrelativistic gravity possible? · Geometric symmetries and lack of dynamics · contest 0.77
We should point out that neglecting this non-local constraint has led others to infer instabilities/ghosts, or inconsistencies in the Ho$ř$ava-Lifshitz theory (e.g. [ref] ).

On the Extra Mode and Inconsistency of Horava Gravity · Geometric symmetries and lack of dynamics · contest 0.77

Uses data or values from 1 paper

[ref] finds the cosmological constraints on this phenomenon for the quadratic cuscuton model, which yields: λ-1 = 0.003 ±0.014 (95% CL).

Does Planck mass run on the cosmological horizon scale? · CMC gauge and Cosmology · 0.92

Compares with 1 paper

It is interesting to notice a possible connection with the emergence of the CMC gauge in the timeless formulation of spatially conformal gravity in [ref] .

The physical gravitational degrees of freedom · Conclusions · 0.81

Cites as background 4 papers

Now, let us turn to the quadratic cuscuton action [ref] : S_qc = ∫d^4x √(-g) (μ^2√(∂^νφ∂_νφ)-1/2m^2φ^2), where $μ$ and $m$ are constants of the theory.

Cuscuton: A Causal Field Theory with an Infinite Speed of Sound · Equivalence of cuscuton and Ho$Ř$ava-Lifshitz gravities · 0.86
An explicit example of this possibility is a power-counting renormalizable theory of gravity which includes higher spatial (but not time) derivatives of the 3-curvature tensor [ref] (also see [ref] ).

Quantum Gravity at a Lifshitz Point · Introduction · 0.84
An explicit example of this possibility is a power-counting renormalizable theory of gravity which includes higher spatial (but not time) derivatives of the 3-curvature tensor [ref] (also see [ref] ).

Quantum Gravity, the Origin of Time and Time's Arrow · Introduction · 0.84

Discussion

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