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High Energy Physics - Phenomenology · arXiv:hep-ph/0312002 v2 · submitted 29 Nov 2003 · 40 references

Disformal Inflation

Nemanja Kaloper (University of California, Davis)

PDF · arXiv · The abstract, sentence by sentence · Cite

The paper says

“We show how short inflation naturally arises in a non-minimal gravity theory with a scalar field without any potential terms.”

more of the abstract

This field drives inflation solely by its derivatives, which couple to the matter only through the combination ḡμν = gμν−1/(m4)∂μφ∂νφ. The theory is free of instabilities around the usual Minkowski vacuum. Inflation lasts as long as φ̇2 > m4, and terminates gracefully once the scalar field kinetic energy drops below m4. The total number of e-folds is given by the initial inflaton energy φ̇02 as 𝒩 ≃ 1/3ln((φ̇0)/(m2)). The field φ can neither efficiently reheat the universe nor produce the primordial density fluctuations. However this could be remedied by invoking the curvaton mechanism. If inflation starts when φ̇20 ∼ M4P, and m ∼ mEW ∼ TeV, the number of e-folds is 𝒩 ∼ 25. Because the scale of inflation is low, this is sufficient to solve the horizon problem if the reheating temperature is $T_{RH} \ga MeV$. In this instance, the leading order coupling of φ to matter via a dimension-8 operator 1/(m4)∂μφ∂νφ Tμν would lead to fermion-antifermion annihilation channels ff̄ → φφ accessible to the LHC, while yielding very weak corrections to the Newtonian potential and to supernova cooling rates, that are completely within experimental limits.

from the abstract

Pith says

Machine review · deepseek-v4.1-flash · 13 Nov 2026 · what was read was not recorded · not checked by a person

Reviewed in 2026 with later literature in view.

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Holds up, with conditions. A clean, checkable derivative-driven inflation mechanism with a collider handle, but the e-fold count falls one to two short of what the paper's own reheating sector demands. This line is wrong

2 major objections · 10 minor

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The paper says, at Cosmology, Eqs. (31)-(32) and p. 11

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Pith says: Objection 1 of 2 · major

The claim that N ≃ 25 'exactly' agrees with the required e-folds is overstated. Using the paper's own formula N ≃ 67 − ln(M_P/m) − (1/3)ln(m/T_RH), at m = TeV and T_RH = MeV one gets N ≈ 25.4, while the model gives N ≈ 24.5 (Eq. 32).

more of objection 1

The agreement is at the level of the O(1) uncertainty in the constant 67, not exact. At the curvaton's natural reheat temperature T_RH ≈ (m/M_P)^{1/4}m ≈ 100 MeV (Eq. 48), the required N rises to ≈ 26.9, a deficit of ≈ 2.4 e-folds. Since the model's N is capped at ≈ 24.5 by φ̇₀ ≲ M_P², the horizon-problem claim is marginal and depends on the choice of the constant in the required-N formula. The authors should state the marginality explicitly and discuss whether the curvaton sector can be adjusted to lower T_RH toward MeV without spoiling BBN.

The paper says, at Curvature perturbations, Eqs. (34)-(45)

The review did not quote this passage.

Pith says: Objection 2 of 2 · major

The negative result that φ fluctuations do not produce a scale-invariant spectrum is a substantive claim that motivates the curvaton, but the derivation is sketchy. In particular, the statement that 'the long wavelength limit behavior of the modes is encoded in the limit kη ≫ 1' (p. 13) is confusing, since kη ≫ 1 is the late-time/subhorizon limit in the g-frame; the physical argument (modes never freeze out because the g-frame decelerates) should be stated more carefully.

more of objection 2

The frame relation Eq. (38) and the scaling Eq. (39) are asserted without derivation; the authors should show the leading-order calculation or cite where it is done. This matters because the curvaton sector is the paper's answer to both reheating and perturbations.

10 minor objections

The paper says, at Abstract vs. Eq. (31)

Pith says: minor objection 1 of 10

The abstract says N ≃ (1/3)ln(φ̇₀/m²) 'given by the initial inflaton energy φ̇₀²'; since the formula uses φ̇₀, not φ̇₀², the phrase 'energy φ̇₀²' is slightly misleading. Clarify that N = (1/6)ln(φ̇₀²/m⁴).

The paper says, at Eq. (13)

Pith says: minor objection 2 of 10

The cross-section σ ~ s³/m⁸ is given without the numerical coefficient or the full matrix element; for a paper that quotes a collider bound, the reader would benefit from the explicit expression.

show 8 more

The paper says, at Eq. (17)

Pith says: minor objection 3 of 10

The 'latter parameterization' is just algebraic rewriting; the sentence 'makes the comparison with the experimental data more transparent' could be clarified by stating the numerical bound directly.

The paper says, at Eq. (24)

Pith says: minor objection 4 of 10

The derivation of the φ equation from Eq. (6) is not shown; a brief intermediate step would help.

The paper says, at p. 13, Eqs. (40)-(43)

Pith says: minor objection 5 of 10

The phrase 'long wavelength limit ... kη ≫ 1' should be rephrased (see major comment).

The paper says, at Figs. 1 and 2

Pith says: minor objection 6 of 10

The captions are minimal; the diagrams would benefit from labeling the external legs and the background insertions.

The paper says, at Eq. (33)

Pith says: minor objection 7 of 10

The statement T_RH ~ H̄ ~ m²/M_P should be qualified: this is the gravitational reheating estimate, and the paper later notes it is insufficient for BBN at m ~ TeV. The text does say this, but the juxtaposition with the 'suffices to solve the horizon problem' claim could be clearer.

The paper says, at Ref. [25]

Pith says: minor objection 8 of 10

The paper disputes claims of [25] but does not state explicitly which claim is being corrected; a sentence identifying the specific claim would help.

The paper says, at Eqs. (46)-(50)

Pith says: minor objection 9 of 10

The curvaton sector is a sketch; the paper should state clearly that a full treatment is beyond the scope and identify which aspects (e.g., the rapid change of the curvaton mass after inflation, ref. [39]) need separate work.

The paper says, at Abstract, stability claim

Pith says: minor objection 10 of 10

The claim 'the theory is free of instabilities around the usual Minkowski vacuum' (abstract:s2) rests on a perturbative lattice calculation (Eqs. 7-9) valid for ξ ≪ 1; the paper concedes this breaks down as ρ → m⁴. A clearer statement of the regime of validity in the abstract would be appropriate.

What would settle it

Recompute the required number of e-folds using the paper's own formula N ≃ 67 − ln(M_P/m) − (1/3) ln(m/T_RH) with m = 1 TeV and T_RH = 100 MeV from Eq. 48, and compare to the model's N = (2/3) ln(M_P/m) from Eq. 32. If the deficit exceeds ~1 e-fold (it is ~2.2), the claim that N ~ 25 solves the horizon problem is not satisfied by the model's own reheating, and the horizon-problem application must be stated as requiring an additional, unspecified reheating mechanism that lands at T_RH ≲ MeV.

from the skeptic's reading

How the review went

4 readings by deepseek-v4.1-flash · 13 Nov 2026

  1. Reader holds up, with conditions confidence high
  2. Skeptic partly agrees 3 min 41 s · 19,719 tokens read, 11,978 written
  3. Editor wrote the verdict above 51 s · 20,843 tokens read, 2,713 written
  4. Referee major revision: 2 major objections, 10 minor 15 min 28 s · 40,282 tokens read, 50,695 written

Not run on this paper: the simulated authors' defence.

Pith did not check this review's objections against the paper.

The review in full

The review in brief, machine-written

Kaloper's paper is worth your time if you work on low-scale inflation, but read it for the mechanism, not the cosmology: the e-fold budget doesn't quite close against the paper's own reheating sector, and the paper rounds over that gap rather than confronting it. What's new is narrow but real. Bekenstein's disformal coupling is old, and Kaloper says so up front. The claim is that with no potential at all, the derivative coupling alone produces accelerated expansion in the matter frame, with a graceful exit when φ̇² drops below m⁴. The background solution (Eq. 27) is exact and I checked it; the e-fold formula N = (2/3) ln(MP/m) follows cleanly and gives 24.5 at m = TeV. The stability check around Minkowski (Eqs. 8–9) is a perturbative lattice argument valid for ξ ≪ 1, and the paper concedes where it breaks. The experimental section is the strongest part: collider bound m ≳ TeV, table-top and supernova bounds both weaker, and a dimension-8 operator that puts f f̄ → φφ within LHC reach. That is a coherent package — a low-scale inflation model with a collider handle. Where it's soft. The stress-test arithmetic holds up: the paper's own required-N formula gives about 25.6 at T_RH = MeV and about 27 at the curvaton's natural T_RH ≈ 100 MeV (Eq. 48), against 24.5 supplied. So 'exactly N ≃ 25' is rounding over a deficit of one to two e-folds. In fairness, the 67 in that formula is itself uncertain at order unity, so this is a marginal-point criticism, not a demolition — but the direction is right, and the paper's own gravitational reheating (Eq. 33, T_RH ~ 10⁻¹⁰ GeV) means the whole burden falls on a curvaton whose reheat temperature makes the deficit worse. The frame question the reader raises is real but I think less sharp: matter couples to ḡ, so the matter-frame expansion history is the right one for horizon physics, and the environmental argument on pp. 3–4 is defensible. The perturbation and reheating failures are stated plainly by the author, so they are not hidden. Who it's for: anyone building low-scale or derivative-driven inflation, or working on disformal couplings and their phenomenology. The curvaton sector is sketched, not built. Recommendation: send it out. The algebra is checkable, the bounds are worked, and the paper is honest about what it cannot do. A referee should press on the e-fold budget and on whether the curvaton can be made to work at the required T_RH.

The strongest objection

The central physical claim is that N ≈ 25 e-folds 'is sufficient to solve the horizon problem if T_RH ≳ MeV' (abstract:s7, §'cosmology', Eqs. 31-32). The algebra of the mechanism is correct: N = (2/3) ln(M_P/m) = 24.5 at m = TeV, matching Eq. 32. The soft spot is the e-fold budget against the model's own reheating. The paper's required-N formula, N ≃ 67 − ln(M_P/m) − (1/3) ln(m/T_RH), gives N ≈ 25.4 at T_RH = MeV and N ≈ 26.9 at T_RH = 100 MeV. The model supplies N ≈ 24.5. So even at the optimal m = TeV (forced by the collider bound m ≳ m_EW, Eq. 14) and the lowest allowed T_RH, the model is ~0.7 e-folds short; at the curvaton's natural reheat temperature T_RH ~ (m/M_P)^{1/4} m ≈ 100 MeV (Eq. 48), it is ~2.2 e-folds short. The paper's 'exactly N ≃ 25' (p. 11) rounds over this deficit. The gravitational reheating channel (Eq. 33) gives T_RH ~ m²/M_P ~ 10⁻¹⁰ GeV, far below MeV, so the entire burden falls on the curvaton — and the curvaton's own T_RH is too high for the e-fold count to close. This is not the interpretive frame question; it is arithmetic internal to the paper's own reheating sector.

The reader's algebra check is right: Eqs. 27-32 are internally consistent, the disformal transformation is Bekenstein's, and the e-fold count (2/3) ln(M_P/m) ≈ 24.5 is correct. I part company on which concern is load-bearing. The reader's primary worry — that the g-frame decelerates as a ~ t^{1/3} and is singular at t = 0, so the 25 e-folds may not solve the horizon problem — is interpretive, and the paper's position is defensible: the horizon problem concerns the uniformity of the matter/radiation sector, which couples to ḡ_μν, and in ḡ_μν the background is de Sitter with H̄ = m²/(√6 M_P) (Eq. 30). The paper argues this at length (pp. 3-4) and the standard scalar-tensor consensus (matter follows ḡ geodesics) supports it. I would not rest the critique there. The sharper concern is the one the reader lists only as a 'separately': the reheating/e-fold budget. The reader notes gravitational reheating gives T_RH ~ 10⁻¹⁰ GeV and delegates the fix to the curvaton, but does not check whether the curvaton's T_RH is compatible with the e-fold count. It is not: Eq. 48 gives T_RH ≈ 100 MeV, at which the paper's own required-N formula demands N ≈ 27 while the model supplies 24.5. That is a ~2 e-fold deficit, larger than the rounding in the '67' constant, and it directly undercuts the abstract's conditional claim (abstract:s7). This does not overturn the mechanism — the derivation of derivative-driven de Sitter expansion and graceful exit stands — but it means the horizon-problem application is not established by the paper's own dynamics. That supports CONDITIONAL, not a change of verdict. The paper is honest about the perturbation deficit (δ̄ρ/ρ̄ ~ 10⁻³², p. 14) and the curvature problem (pp. 15-16); the e-fold/reheating tension is the one place where the paper's own numbers are in tension without being flagged. Credit where due: the stability analysis (Eqs. 8-9) is a legitimate perturbative check, the collider/Newtonian/supernova bounds (Eqs. 14, 18, 21) are parameter-free and falsifiable, and the mechanism is a genuine, checkable construction. The concrete test above is the single arithmetic step that would settle whether the horizon claim closes with the model's own reheating.

The referee's report

If correct, this is an interesting model-building result: a massless scalar with only derivative couplings can drive inflation, with the inflationary scale set by the disformal coupling m, potentially as low as TeV. The paper is notable for its closed-form e-fold formula, its explicit experimental bounds, and its falsifiable LHC prediction ff̄ → φφ. The negative results (no efficient reheating, no density perturbations) are honestly stated and motivate the curvaton. The paper does not claim to solve the curvature problem. The main caveats are the marginal e-fold budget and the sketchiness of the curvaton sector.

Pith's reading of the paper (a machine's summary, not the authors')

The paper asks whether a scalar field with no potential — no mass term, no self-interaction, protected only by the shift symmetry $varphi to varphi + C$ and the reflection $varphi leftrightarrow -varphi$ — can drive cosmic acceleration. The answer offered is yes, provided the field couples to ordinary matter not through $g_{munu}$ but through the disformal combination $gbar_{munu} = g_{munu} - m^{-4}partial_muvarphipartial_nuvarphi$. In the frame where matter lives, the same cosmological solution that looks like a decelerating stiff fluid in $g_{munu}$ looks like slowly rolling de Sitter expansion with $bar H simeq m^2/(sqrt{6}M_P)$, and it persists as long as $dotvarphi^2 > m^4$. The payoff is that the inflationary energy scale is set by the coupling $m$ rather than by a finely tuned potential, so with $m sim$ TeV and a Planckian initial gradient the universe inflates for about 25 e-folds — short, but the author argues it suffices to solve the horizon problem if reheating reaches an MeV. The paper is explicit that $varphi$ itself can neither reheat the universe nor seed density perturbations, and that both jobs must be delegated to a curvaton; it is equally explicit that the model does not solve the curvature problem and needs an earlier inflationary stage or some other mechanism to start from small spatial curvature.

What carries the argument. The load-bearing object is the disformal metric $gbar_{munu} = g_{munu} - m^{-4}partial_muvarphipartial_nuvarphi$, a special case of the transformation Bekenstein classified as the class that preserves causality and the weak equivalence principle while, unlike a conformal rescaling, bending the angles between geodesics of the two metrics. It does two jobs at once. First, it makes the coupling purely derivative, so the shift symmetry and reflection survive and protect the inflationary regime from Standard Model loop corrections. Second, it makes the frame transformation time-dependent in a way that converts a decelerating stiff-fluid geometry into accelerated expansion: the relation $dbar t = dt sqrt{1 + dotvarphi^2/m^4}$ means that a shrinking $dotvarphi$ stretches conformal time in the matter frame, and the resulting Hubble rate $bar H simeq m^2/(sqrt{6}M_P)$ is nearly constant. The same structure makes the exit automatic rather than tuned: the condition $dotvarphi^2 = m^4$ is the only threshold in the problem, and it fixes both the duration and the end of inflation.

Core claim. The central claim is that derivative self-coupling to matter, with no potential whatsoever, is enough to produce an inflationary epoch. Starting from the action $S = int d^4x {sqrt{g}[M_P^2 R/2 - (partialvarphi)^2/2] - sqrt{gbar}L_M}$, the author shows that in the regime $m^4 lesssim dotvarphi^2 lesssim M_P^4$ every Standard Model contribution to the field equations is subleading to the $dotvarphi$ stress energy, so the background is exactly that of a stiff fluid, $a propto t^{1/3}$, $dotvarphi = sqrt{2/3},M_P/t$. Transforming to the metric $gbar_{munu}$ that matter actually feels, $dbar t = dt sqrt{1 + dotvarphi^2/m^4}$, turns this into $dbar s^2 = -dbar t^2 + a_0^2 e^{(2/3)(m^2/M_P)bar t}dvec x^2$: slow-roll inflation with $bar H simeq m^2/(sqrt{6}M_P)$. Because $dotvarphi$ redshifts, inflation ends by itself when $dotvarphi^2$ drops below $m^4$, and the total number of e-folds is $mathcal{N} simeq (1/3)ln(dotvarphi_0/m^2) simeq (2/3)ln(M_P/m)$, which is about 25 for $m sim$ TeV. The paper also argues that the Minkowski vacuum is perturbatively stable — expanding $varphi$ around a point mass gives a propagator with $xi = M H_0^3/m^4 ll 1$ and all poles at positive $omega^2$ — and that the leading coupling to matter, the dimension-8 operator $m^{-4}partial_muvarphipartial_nuvarphi,T^{munu}$, survives collider, table-top gravity, and supernova-cooling bounds provided $m gtrsim m_{EW}$.

The premise it rests on. The claim that 25 e-folds solve the horizon problem rests on treating the matter-frame metric as the physically relevant one, even though the gravitational-frame geometry decelerates and is singular at $t = 0$.

If the paper is right (Pith's inferences, not the authors')

Inflationary energy scale is set by the disformal coupling: with $m sim$ TeV the effective potential height is $V_{eff} sim$ TeV$^4$, so tensor modes and any direct gravitational-wave signature of inflation are negligible.

The number of e-folds is a fixed function of the coupling, $mathcal{N} simeq (2/3)ln(M_P/m)$, so any independent handle on the duration of inflation translates directly into a constraint on $m$.

The dimension-8 operator $m^{-4}partial_muvarphipartial_nuvarphi,T^{munu}$ opens $fbar f to varphivarphi$ at the LHC for $m sim$ TeV, while contributing to the Newtonian potential only at order $M_P^2 m_1 m_2 r^6/m^8$ and to stellar cooling only at $Gamma sim T^9/m^8$.

Because $varphi$ fluctuations never freeze out — the $g$-frame horizon grows faster than the wavelength — the model predicts no primordial curvature perturbation from the inflaton itself, so the observed spectrum must come entirely from a spectator curvaton.

Reheating must come from the curvaton sector; the model's own gravitational particle production gives $T_{RH} sim bar H sim m^2/M_P$, far below an MeV for $m sim$ TeV.

The horizon argument depends entirely on which metric defines the horizon. In the $g$-frame the same solution is a decelerating $a propto t^{1/3}$ cosmology with a spacelike apparent horizon, and the paper's defence is interpretive: Poincaré breaking by $partialvarphi neq 0$ makes the matter frame the physical one, much as a dielectric slows light without changing electrodynamics. A cleaner discri

If the disformal coupling is real at the TeV scale, $varphi$ is a generic light mediator with purely derivative couplings, and the same operator would contribute to energy loss in neutron-star mergers and to thermal production in the early plasma — channels the paper does not estimate but which are numerically comparable to the supernova bound it does compute.

The curvaton reheating estimate $T_{RH} sim (mu m_psi^3)^{1/4} lesssim 100$ MeV sits uncomfortably close to the nucleosynthesis floor, so the viability of the whole picture turns on a nonlinear treatment of the parametric resonance that the paper only sketches.

Because exit is triggered by $dotvarphi^2 = m^4$ rather than by a potential slope, the model has no graceful-exit fine-tuning problem at all — a structural feature worth contrasting with potential-driven models, where the slow-roll parameters must be small in a way that is radiatively unstable.

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The paper

Abstract

We show how short inflation naturally arises in a non-minimal gravity theory with a scalar field without any potential terms. This field drives inflation solely by its derivatives, which couple to the matter only through the combination ḡμν = gμν−1/(m4)∂μφ∂νφ. The theory is free of instabilities around the usual Minkowski vacuum. Inflation lasts as long as φ̇2 > m4, and terminates gracefully once the scalar field kinetic energy drops below m4. The total number of e-folds is given by the initial inflaton energy φ̇02 as 𝒩 ≃ 1/3ln((φ̇0)/(m2)). The field φ can neither efficiently reheat the universe nor produce the primordial density fluctuations. However this could be remedied by invoking the curvaton mechanism. If inflation starts when φ̇20 ∼ M4P, and m ∼ mEW ∼ TeV, the number of e-folds is 𝒩 ∼ 25. Because the scale of inflation is low, this is sufficient to solve the horizon problem if the reheating temperature is $T_{RH} \ga MeV$. In this instance, the leading order coupling of φ to matter via a dimension-8 operator 1/(m4)∂μφ∂νφ Tμν would lead to fermion-antifermion annihilation channels ff̄ → φφ accessible to the LHC, while yielding very weak corrections to the Newtonian potential and to supernova cooling rates, that are completely within experimental limits.

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. No sentence in this record was written by a model.

abstract compiled · 2026-09-23

The authors' main claim, as the classifier picked it out 0.99

“We show how short inflation naturally arises in a non-minimal gravity theory with a scalar field without any potential terms.”

How the main claim is stated: asserted 1.00

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.95 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.11 · mentions code or data availability 0.01

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We show how short inflation naturally arises in a non-minimal gravity theory with a scalar field without any potential terms. contribution 0.91 0.93 0.78 asserted 1.00
This field drives inflation solely by its derivatives, which couple to the matter only through the combination $\bar g_{\mu\nu} = g_{\mu\nu} - \frac{1}{m^4} \partial_\mu \phi \partial_\nu \phi$. method 0.54 0.67 0.14 asserted 1.00
The theory is free of instabilities around the usual Minkowski vacuum. result 1.00 0.77 0.06 asserted 1.00
Inflation lasts as long as $\dot \phi^2 > m^4$, and terminates gracefully once the scalar field kinetic energy drops below $m^4$. result 0.91 0.81 0.13 asserted 1.00
The total number of e-folds is given by the initial inflaton energy $\dot \phi_0^2$ as ${\cal N} \simeq \frac13 \ln(\frac{\dot \phi_0}{m^2})$. result 1.00 0.88 0.11 asserted 1.00
The field $\phi$ can neither efficiently reheat the universe nor produce the primordial density fluctuations. limitation 0.94 0.77 0.14 asserted 0.96
However this could be remedied by invoking the curvaton mechanism. future work 0.65 0.18 0.05 hedged possibility 1.00
If inflation starts when $\dot \phi^2_0 \sim M^4_P$, and $m \sim m_{EW} \sim TeV$, the number of e-folds is ${\cal N} \sim 25$. result 0.93 0.78 0.08 asserted 0.85
Because the scale of inflation is low, this is sufficient to solve the horizon problem if the reheating temperature is $T_{RH} \ga MeV$. interpretation 0.93 0.61 0.08 asserted 0.81
In this instance, the leading order coupling of $\phi$ to matter via a dimension-8 operator $\frac{1}{m^4}\partial_\mu \phi \partial_\nu \phi ~ T^{\mu\nu}$ would lead to fermion-antifermion annihilation channels $f\bar f \to \phi \phi$ accessible to the LHC, while yielding very weak corrections to the Newtonian potential and to supernova cooling rates, that are completely within experimental limits. interpretation 0.54 0.69 0.09 asserted 0.77

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97

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Figures (3)
Figure 1 of the paper
Figure 1. Feynman diagrams for the force mediated by φ. Both of the cutoff-dependent terms are contact interactions, corresponding to shrinking both, or one of the propagators in the loop to a point, and they should be subtracted away, leaving the ∝ ~k 4 log ~k 2 term as the physical loop contribution. This yields V1 ∼ 1 m8 m1m2 r 7 = 1 M2 P m1m2 r M2 P m8r 6 , (17) where the latter parameterization makes the comparison with the experimental data more transparent. Because of the rapid drop of this potential with distance, the strongest bounds will come from the shortest scales that have been…
Figure 2 of the paper
Figure 2. The process for the p → p + φ + φ “decay”. by thermal effects, as denoted by the double-line in the
Figure 3 of the paper
Figure 3. Apparent horizons lH = H−1 , lH¯ = H¯ −1 and the wavelength λ of a typical fluctuation of φ as functions of time t. the horizon lH remains inside of it forever. The fact that its wavelength will become greater than the apparent horizon in the matter frame, lH¯ = H¯ −1 , is of little dynamical consequence since in this frame the fluctuations do not have canonical kinetic terms. This only serves to set the proper normalization for the momenta, and wavelengths, of the fluctuations after inflation. The perturbations which are generated from the quantum fluctuations of φ will therefore co

Figures are the authors', reproduced from the paper.

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How the literature uses it

38 arXiv papers cite this in 54 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 · 26 sentences without a confident label

Compares with it 1 paper
  • Comparing our results with those of [ref] , who study the quantum loop corrections arising from the disformal coupling $T^∂_μϕ∂_νϕ/ℳ^4$, we find that $ℳ𝒪(eV)$ whereas they find $ℳ𝒪(10^2GeV)$ using mono-photon searches at the LHC.

    Disformal Theories of Gravity: From the Solar System to Cosmology · Introduction · 0.99

Cites it as background 24 papers
  • They have been studied mainly in cosmology [ref] and have also been shown to allow for spontaneous scalarization of NSs [ref] .

    Cosmological attractors to general relativity and spontaneous scalarization with disformal coupling · Introduction · 0.93

  • The term proportional to $D$ is known as the disformal coupling and, in contrast to the first term—the conformal coupling—it has only recently begun to be studied in detail [ref] .

    Solar System Constraints on Disformal Gravity Theories · Introduction · 0.96

  • Kaloper [ref] proposed a model with a disformal coupling of a massless inflaton to the Standard model, and found that such coupling could be well constrained by collider experiments such as the LHC, as confirmed by more recent studies [ref] , though these constraints can be avoided if the disformal coupling is suppressed in the Standard model sector after reheating.

    Disformally coupled inflation · Introduction · 0.91

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