What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?

David H. Lyth (Lancaster)

REVIEW

What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?

David H. Lyth (Lancaster)

High Energy Physics - Phenomenology · Submitted 20 Jun 1996 · 36 references

Pith's verdict: The paper that turned r into a statement about inflaton field range; the algebra is two lines and it holds up, with a scope caveat we would now state more loudly.

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arXiv IDhep-ph/9606387 (version 1)

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CitationDavid H. Lyth (Lancaster). "What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?." arXiv:hep-ph/9606387 (1996). https://pith.science/paper/NCBS5OKY

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Editor's note

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Short version: this is the paper that turned a tensor-to-scalar measurement into a statement about field range, and the algebra checks out. It is three pages and it earned its citations the hard way — by being right and being useful at the same time. What is new is not the slow-roll machinery. Eqs. (1) and (2) are Starobinsky and Liddle-Lyth, and the COBE normalization is Bunn-Scott-White. The new thing is the chain: combine (2) with dφ/dN = m_Pl V'/V, integrate over the ΔN ≈ 4.6 that maps onto l ≲ 100, and you get Δφ/m_Pl ≈ 0.46 (r/.07)^{1/2}. I checked it — 1.75√r at r = 0.07 gives 0.46. Eq. (3), V^{1/4} ≈ (r/.07)^{1/4} × 1.8×10^16 GeV, follows the same way. Two lines of algebra, and they have been quoted ever since. Credit where it is due: footnote * is the honest part. He works through the near-maximum potentials, V ≃ V0 − ½m²φ² and V0[1 − (φ/M)^p], and shows that even where Δφ is large, r lands below detectability. That is the author arguing against his own headline case, which is more than most short papers bother to do. He also says plainly that Eq. (5) is a floor rather than an estimate, since inflation keeps going past the observable window. Soft spots, in order of size. The one the stress-test flags is real but small: Eq. (4) assumes a single inflaton, a canonical kinetic term, and Einstein gravity, while the abstract states the conclusion without that qualifier. Non-canonical kinetic terms can buy the same r with a smaller excursion. Worth remembering that in 1996 there was no DBI inflation to worry about, so this is a scope caveat we would add now, not a mistake he made. Second, the r ≲ 1 bound in [12] is a personal communication he himself calls unquantified; it carries no weight in the argument, but it is the softest number in the paper. Third, the particle-physics claims in the abstract — no ordinary Standard Model extension, no string moduli — are argued rather than derived. He hedges them with 'probably' and the body concedes 'for a generic field one has no idea what to expect.' That is the right register for what the evidence supports. Who should read it: anyone connecting tensor modes to field range, and anyone teaching inflation who wants the three-page version of the argument. Send it to referees.

Referee report

Significance

The paper isolates a clean, parameter-free relation between an observable (r) and a model-building quantity (the inflaton excursion), and it does so with algebra that is easy to check: combining Eq. (2) with Eq. (4) and ΔN ≃ 4.6 reproduces Eq. (5) exactly, and Eq. (3) follows from Eq. (1) plus the cited COBE amplitude. The result is falsifiable in the operative sense: it tells observers what value of r would force a qualitative revision of inflationary model building, and it tells model builders what potential height and field range to target. The paper is also candid about its own assumptions (footnote 5 spells out the slow-roll paradigm, and the text flags the Einstein-gravity restriction) and about the strength of the inference, conceding that for a generic field 'one has no idea what to expect in this regime.' These are the qualities one wants in a short note of this kind, and they are why the Δφ–r relation has had staying power.

Major objections (2)

[Abstract, sentence 1; Eq. (5)] The abstract states unconditionally that gravitational waves are observable 'only if the inflaton field variation is at least of order the Planck scale,' but Eq. (5) is derived from Eq. (4), which assumes a single inflaton with a canonical kinetic term in Einstein gravity. The body acknowledges this only in passing ('confining ourselves to the case of Einstein gravity'), and footnote 5 defines the paradigm but does not carry the qualifier into the headline statement. Within the stated paradigm the algebra is correct, so this is a scope issue rather than an error; the fix is a short qualifier in the abstract or immediately after Eq. (5) making clear that the bound is a canonical-single-field statement and that a non-canonical kinetic term or modified gravity would weaken it. As written, a reader could take Eq. (5) as a theorem about inflation in general rather than about the standard slow-roll paradigm.
[Abstract, sentence 1; §I, Eq. (6) and following paragraph] The inference that a large field variation 'would imply that the model of inflation cannot be part of an ordinary extension of the standard model' is stronger than the argument given supports. The support is the supergravity expansion of Eq. (6) together with the expectation that the higher-dimension operators are present with coefficients of order one, which is a naturalness expectation rather than a derived result; the body itself concedes that for a generic field 'one has no idea what to expect in this regime.' I would ask that 'cannot' be softened to something like 'would be difficult to accommodate,' or that the order-one-coefficient assumption behind Eq. (6) be stated explicitly at the point where the inference is drawn. The same applies, with the paper's own 'probably' hedge already in place, to the superstring-moduli conclusion.

Minor objections (5)

[References [24], [25]] Reference [24] is truncated ('Phys. Lett. B345,') with no page number, and reference [25] is a placeholder ('hep-ph/9606nnn'). Both need to be completed before publication; the placeholder in particular cannot stand in a published reference list.
[Eq. (5) and the sentence preceding it] The text says a detectable r requires Δφ >~ 0.5 m_Pl, while the abstract says 'at least of order the Planck scale.' It would help to state explicitly that Eq. (5) is a lower bound on the variation over the 4.6 e-folds probed by the CMB only, and that the total excursion is larger by an amount depending on the subsequent e-folds, as the following paragraph indeed explains.
[Eq. (3) and footnote 11] The quoted range V^{1/4} = 2–4 × 10^16 GeV should be tied explicitly to the corresponding range of r (roughly 0.07 to 1) so the reader can see where the endpoints come from, and the dropping of the (1+r) factor noted in footnote 11 should be mentioned at Eq. (3) rather than only in the footnote.
[§I, notation around Eq. (1) and the COBE normalization] The paper defines δ²_H as the spectrum in Eq. (1) and then quotes the COBE normalization as δ_H ≃ 1.9(1+r)^{1/2} × 10^-5. The switch between the squared and unsquared quantity is easy to miss; a one-word clarification at the normalization would remove the ambiguity.
[§I, the bound r <~ 1] The current upper bound is described as 'not been quantified properly but is something like r <~ 1,' supported by a personal communication (ref. [12]). Since this bound sets the upper end of the V^{1/4} range, it would be preferable to cite a published analysis or to state plainly that the number is provisional.

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The paper

The paper claims

A detectable gravitational-wave imprint in the microwave background would force the inflaton to move at least half a Planck mass and fix the inflationary energy scale near $10^{16}$ GeV, pushing inflation beyond ordinary particle physics.

The reading

Lyth asks a conditional question: if a gravitational-wave contribution is ever seen in the low multipoles of the cosmic microwave background, what would that tell us about the physics that produced it? Working inside the standard slow-roll picture of inflation, he shows that a tensor contribution large enough to be detected, roughly $r > 0.07$, requires the inflaton field to move by at least about half a Planck mass while observable scales leave the horizon, and the total excursion over the whole of inflation is larger still. The same detection would fix the height of the inflationary potential at $V^{1/4} = 2$ to $4 times 10^{16}$ GeV. The force of the argument is the squeeze this puts on model building: small-field models such as hybrid inflation stay under theoretical control, whereas any model able to produce a visible signal sits where known particle physics offers no guidance. Lyth's conclusion is that such a detection would be a statement about quantum gravity and string theory as much as about cosmology.

What carries the argument

The load-bearing device is the slow-roll dictionary between observables and the potential: the curvature spectrum fixes $V^3/V'^2$, the tensor fraction fixes $(V'/V)^2$, and the field excursion follows from integrating $dvarphi/dN = -V'/3H^2$ over the range of scales probed. Two auxiliary inputs complete the chain: the cosmic-variance argument that $r > 0.07$ is needed for a better-than-even chance of eventual detection, and the COBE amplitude normalization that anchors the overall scale of $V$.

Extended reading notes

Core claim

The paper establishes a two-way link between an observable tensor signal and the size of the inflationary energy budget. Using the slow-roll expressions $delta_H^2 = V^3/(75 pi^2 m_{Pl}^6 V'^2)$ and $r = 6.9, m_{Pl}^2 (V'/V)^2$, together with the COBE normalization $delta_H simeq 1.9(1+r)^{1/2} times 10^{-5}$, Lyth converts a detectable $r$ into a statement about the potential: $V^{1/4} simeq (r/0.07)^{1/4} times 1.8 times 10^{16}$ GeV, so a detection means $V^{1/4} = 2$ to $4 times 10^{16}$ GeV. The same relations give the field motion per Hubble time, $m_{Pl}^{-1}|dvarphi/dN| = m_{Pl}|V'/V| = (r/6.9)^{1/2}$, and integrating over the $Delta N simeq 4.6$ e-folds spanned by multipoles $1 < ell lesssim 100$ yields $Delta varphi/m_{Pl} simeq 0.46,(r/0.07)^{1/2}$, a minimum total excursion since inflation continues afterwards. From this Lyth draws the consequences he wants on record: the inflaton cannot be a field of an ordinary extension of the standard model, cannot plausibly be a superstring modulus, and cannot sit in a hybrid model unless the vacuum expectation values and the masses of the GUT Higgs fields are both of order $10^{16}$ GeV.

Load-bearing premise

The whole chain rests on the standard slow-roll relations for a single inflaton field with a canonical kinetic term in Einstein gravity, $m_{Pl}|V'/V| = (r/6.9)^{1/2}$; the paper notes the Einstein-gravity restriction only in passing, and a non-canonical kinetic term or modified gravity would let the same $r$ arise from a much smaller field excursion.

Editorial extensions

If this is right

If $r$ is detected, the inflaton excursion over observable scales is at least $sim 0.5,m_{Pl}$, and the total excursion across all of inflation is larger, so the model cannot be an ordinary extension of the standard model.
A detection fixes the inflationary potential height at $V^{1/4} = 2$ to $4 times 10^{16}$ GeV, orders of magnitude above what particle physics would naturally suggest.
Superstring moduli are disfavoured as the inflaton, because the region of moduli space where inflation can occur is expected to be only of order $m_{Pl}$ and inflation would likely start near a maximum of the potential, which suppresses $r$.
A GUT-Higgs hybrid model could reach the required scale only if both the Higgs vacuum expectation values and the Higgs masses are of order $10^{16}$ GeV, which coupling unification does not by itself require.
A firm upper bound $r lesssim 0.07$ would leave small-field hybrid models as the natural home for inflation, and would keep the potential under theoretical control.

Reading between the lines

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

The argument is a conditional forecast rather than a prediction, so its value grows with every improvement in the upper bound on $r$: a bound well below $0.07$ would convert Lyth's warning into a positive statement that inflation is a small-field, low-scale affair.
The chain would weaken for non-canonical kinetic terms or modified gravity, where the same $r$ can arise from a much smaller field excursion; the paper restricts itself to Einstein gravity only in passing, so the Planck-scale conclusion is tied to that choice.
The reasoning is symmetric in time: the same relations that let a future tensor measurement reconstruct $V$ and $Delta varphi$ already let present bounds constrain how far any viable model may stray into large-field territory.
If a large tensor fraction is ever measured, the natural next question is whether the spectral index and its running match the same slow-roll trajectory, which would turn a single number into an over-determined test of the potential's shape.

Original abstract

Inflation generates gravitational waves, which may be observable in the low multipoles of the cosmic microwave background (cmb) anisotropy but only if the inflaton field variation is at least of order the Planck scale. Such a large variation would imply that the model of inflation cannot be part of an ordinary extension of the standard model, and combined with the detection of the waves it would also suggest that the inflaton field cannot be one of the superstring moduli. Another implication of observable gravitational waves would be a potential $V^{1/4}=2$ to $4\times 10^{16}\GeV$, which is orders of magnitude bigger than is expected on the basis of particle theory. It might emerge in a hybrid inflation model where most of the energy density comes from the Higgs sector of a GUT, but only if both the vacuum expectation values {\em and the masses } of the Higgs fields are of this order.

The compiled record

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

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,823 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.09 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Inflation generates gravitational waves, which may be observable in the low multipoles of the cosmic microwave background (cmb) anisotropy but only if the inflaton field variation is at least of order the Planck scale. Such a large variation would imply that the model of inflation cannot be part of an ordinary extension of the standard model, and combined with the detection of the waves it would also suggest that the inflaton field cannot be one of the superstring moduli. Another implication of observable gravitational waves would be a potential $V^{1/4}=2$ to $4\times 10^{16}\GeV$, which is orders of magnitude bigger than is expected on the basis of particle theory. It might emerge in a hybrid inflation model where most of the energy density comes from the Higgs sector of a GUT, but only if both the vacuum expectation values {\em and the masses } of the Higgs fields are of this order.

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	Inflation generates gravitational waves, which may be observable in the low multipoles of the cosmic microwave background (cmb) anisotropy but only if the inflaton field variation is at least of order the Planck scale.	background 0.94	0.08	0.25	hedged possibility 0.97
s1	Such a large variation would imply that the model of inflation cannot be part of an ordinary extension of the standard model, and combined with the detection of the waves it would also suggest that the inflaton field cannot be one of the superstring moduli.	interpretation 1.00	0.17	0.24	hedged possibility 0.60
s2	Another implication of observable gravitational waves would be a potential $V^{1/4}=2$ to $4\times 10^{16}\GeV$, which is orders of magnitude bigger than is expected on the basis of particle theory.	interpretation 0.89	0.19	0.23	hedged possibility 0.70
s3	It might emerge in a hybrid inflation model where most of the energy density comes from the Higgs sector of a GUT, but only if both the vacuum expectation values {\em and the masses } of the Higgs fields are of this order.	interpretation 0.93	0.13	0.12	speculative 0.94

What kind of paper the classifier reports this is: theoretical result 0.69 · evidence from argument 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 (36)

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An explicit toric Calabi-Yau orientifold with h^{1,1}=3, a K3 fibration and a shrinkable del Pezzo divisor is shown to reproduce the fibre inflation potential from string loop corrections.
Scale-dependent gravitational waves from a rolling axion
astro-ph.CO 2015-09 conditional novelty 6.0 of 10

A transiently rolling axion sources a localized bump of chiral gravitational waves that can be observable in CMB B-modes even for low-scale inflation, with scalar perturbations staying under WMAP temperature limits.
Pole Inflation - Shift Symmetry and Universal Corrections
hep-th 2015-07 conditional novelty 6.0 of 10

Higher-order poles in the inflaton kinetic function produce universal, calculable corrections to the spectral index and tensor-to-scalar ratio, and a pole exactly one order above the leading one cancels at leading order.
Weak Gravity Strongly Constrains Large-Field Axion Inflation
hep-th 2015-06 conditional novelty 6.0 of 10

Extending the magnetic Weak Gravity Conjecture to multiple axions, plus two new conjectures about how particle masses shift across moduli space, bounds axion inflation field ranges at the Planck scale.
Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture
hep-th 2015-04 conditional novelty 6.0 of 10

A general recurrence relation for the effective axion decay constant in N-axion models shows power-law and exponential enhancement regimes, and implies that stopping this enhancement at large N requires an enormous, p...
Cosmological Attractors from $\alpha$-Scale Supergravity
hep-th 2015-03 accept novelty 6.0 of 10

A single chiral superfield with a logarithmic Kaehler potential of curvature set by alpha reproduces alpha-attractor inflation, with the Kaehler curvature controlling both the stability of the de Sitter plateau and th...
Gauge-preheating and the end of axion inflation
astro-ph.CO 2015-02 accept novelty 6.0 of 10

Lattice simulations show that axion-gauge Chern-Simons couplings allowed by CMB and primordial-black-hole bounds can preheat the universe within a few axion oscillations, with rescattering unpolarizing the sub-horizon...
Planck 2015 results. XIII. Cosmological parameters
astro-ph.CO 2015-02 accept novelty 6.0 of 10

Full-mission Planck temperature and polarization data are consistent with six-parameter flat Lambda-CDM, yielding H0 = 67.8 +/- 0.9, Omega_m = 0.308 +/- 0.012, ns = 0.968 +/- 0.006, and tau = 0.066 +/- 0.016.
Dynamically Induced Planck Scale and Inflation
astro-ph.CO 2015-02 conditional novelty 6.0 of 10

Dimensionless, scale-invariant models that generate the Planck scale dynamically predict n_s around 0.96 and r between 0.003 and 0.13, interpolating between quadratic and Starobinsky inflation.
The Challenge of Realizing F-term Axion Monodromy Inflation in String Theory
hep-th 2014-09 conditional novelty 6.0 of 10

A no-go theorem rules out the universal axion C0 as a single-field F-term axion monodromy inflaton in type IIB flux compactifications, and an explicit working example is constructed from a complex-structure axion instead.
B-modes and the Nature of Inflation
hep-th 2014-07 conditional novelty 6.0 of 10

A detection of primordial B-modes with r > 0.01 would imply a lower bound on the inflationary sound speed stronger than the current Planck non-Gaussianity limit, with r > 0.1 approaching a critical threshold c_s = 0.47.
Inflation in Supergravity with a Single Chiral Superfield
hep-th 2014-06 conditional novelty 6.0 of 10

Single-chiral-superfield supergravity can produce both quadratic and Starobinsky-like inflationary potentials, contrary to earlier no-go claims, by adding a stabilizing quartic term to the Kähler potential and using c...
On Inflation and de Sitter in Non-Geometric String Backgrounds
hep-th 2014-05 conditional novelty 6.0 of 10

Elliptic nongeometric fluxes in double field theory give potentials with Minkowski and de Sitter minima, and a toy quadratic inflation model whose slow roll requires fluxes tuned to about 10^-5.
D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation
hep-th 2014-05 conditional novelty 6.0 of 10

The paper derives a corrected Type IIB D7-brane superpotential, shows the extended no-scale cancellation survives a light brane modulus, and argues fluxbrane inflation can be made parametrically consistent, though onl...
Inflation with moderately sharp features in the speed of sound: GSR and in-in formalism for power spectrum and bispectrum
astro-ph.CO 2014-04 conditional novelty 6.0 of 10

For moderately sharp, brief dips in the inflaton speed of sound, three analytic methods agree with each other and with a numerical solution, validating the predicted correlation between features in the primordial powe...
Natural inflation with multiple sub-Planckian axions
hep-th 2014-04 accept novelty 6.0 of 10

Extending the Kim-Nilles-Peloso alignment mechanism to N axions shows that super-Planckian effective decay constants can be obtained with order-one anomaly coefficients if N ln N exceeds twice the log of the required ...
Agravity
hep-ph 2014-03 conditional novelty 6.0 of 10

A scale-free gravity theory with a four-derivative graviton can generate the Planck scale, drive inflation with r around 0.13, and keep the Higgs mass naturally small, at the cost of a ghost state.
Gauge-flation confronted with Planck
astro-ph.CO 2013-08 conditional novelty 6.0 of 10

A corrected calculation of the scalar and tensor perturbations of Gauge-flation shows that no value of its single parameter reproduces both the Planck spectral index and the Planck tensor-to-scalar ratio, ruling the m...
The importance of being warm (during inflation)
hep-ph 2013-07 conditional novelty 6.0 of 10

Warm inflation with a thermalized inflaton bath at T > H brings the quartic chaotic potential into agreement with Planck and predicts a suppressed tensor-to-scalar ratio, r approximately 8(1 - ns)(H/T).
Planck 2013 results. XXII. Constraints on inflation
astro-ph.CO 2013-03 conditional novelty 6.0 of 10

Planck 2013 measures the scalar spectral index at 0.9603 plus or minus 0.0073 and bounds the tensor-to-scalar ratio below 0.11, ruling out exact scale invariance and disfavouring steep, exponential, and simple hybrid ...
Stability analysis of chromo-natural inflation and possible evasion of Lyth's bound
astro-ph.CO 2012-12 conditional novelty 6.0 of 10

Chromo-natural inflation is stable only for m_g > 2H; below that, scalar perturbations grow rapidly inside the horizon, but the model can still evade Lyth's bound by producing chiral gravitational waves.
New Sources of Gravitational Waves during Inflation
hep-th 2011-09 conditional novelty 6.0 of 10

Particle and string sources produced during inflation can generate detectable gravitational waves that dominate over vacuum fluctuations, so a tensor-mode detection does not uniquely measure the inflationary Hubble scale.
Large slow-roll corrections to the bispectrum of noncanonical inflation
astro-ph.CO 2011-03 accept novelty 6.0 of 10

The next-order slow-roll corrections to the inflationary bispectrum for general P(X,phi) Lagrangians are derived in closed form, yielding tens-of-percent corrections in DBI inflation and a new bispectrum shape orthogo...
Non-Abelian Gauge Field Inflation
hep-ph 2011-02 conditional novelty 6.0 of 10

A non-Abelian gauge field with a specific higher-derivative term can drive slow-roll inflation and match WMAP data, predicting a tensor-to-scalar ratio above 0.02.
Dante's Inferno
hep-th 2009-12 conditional novelty 6.0 of 10

Two axions with a small mixing angle produce an effective inflaton whose field excursion is superplanckian even though each fundamental field stays subplanckian, evading the usual UV-sensitivity of large-field inflation.
Gravity Waves and Linear Inflation from Axion Monodromy
hep-th 2008-08 conditional novelty 6.0 of 10

Wrapped branes give closed-string axions a monodromy-extended, super-Planckian field range with a linear potential, predicting a tensor-to-scalar ratio of about 0.07.
Effects of Scale-Dependent Non-Gaussianity on Cosmological Structures
astro-ph 2007-11 conditional novelty 6.0 of 10

Scale-dependent primordial non-Gaussianity can evade CMB bounds while changing cluster counts by 10 to 40 percent, and forthcoming cluster surveys can constrain its running parameter kappa.
A Microscopic Limit on Gravitational Waves from D-brane Inflation
hep-th 2006-10 accept novelty 6.0 of 10

Warped D-brane inflation caps the inflaton field range at (delta phi / M_P)^2 < 4/N, so a tensor-to-scalar ratio above 0.01 would falsify slow-roll versions of the model.
Observational Signatures and Non-Gaussianities of General Single Field Inflation
hep-th 2006-05 accept novelty 6.0 of 10

For any single-field inflation model whose Lagrangian depends only on the inflaton and its first derivative, the full primordial three-point function at first order in slow variation is fixed by five parameters and de...
Hilltop Inflation
hep-ph 2005-02 conditional novelty 6.0 of 10

Hilltop inflation, starting near a potential maximum, is shown to be generic, to predict r < 0.002, and to arise naturally from F- and D-term models once Planck-suppressed terms are included.
Very-High-Frequency Gravitational Waves from Multi-Monodromy Inflation
hep-ph 2026-01 conditional novelty 5.0 of 10

In multi-stage axion monodromy inflation, an interruption 50–52 efolds before the end of inflation produces a narrow gravitational-wave background peaked at ~10–300 kHz, at strains near proposed detector sensitivities.
A Match Made in Heaven: Linking Observables in Inflationary Cosmology
hep-th 2025-05 unverdicted novelty 5.0 of 10

In dynamical Chern-Simons inflation the parity-odd trispectrum is a double copy of the mixed bispectrum and parity-odd power spectrum via a prior factorization formula.
Bounds on Field Range for Slowly Varying Positive Potentials
hep-th 2023-05 conditional novelty 5.0 of 10

A slowly varying positive scalar potential can only extend over a field range bounded by sqrt((d-1)(d-2)) log(1/V) plus a negative order-one constant, derived from the species scale and checked in three string compact...
No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation
astro-ph.CO 2023-01 conditional novelty 5.0 of 10

After renormalizing one-loop corrections, the authors claim single-field slow-roll-to-ultra-slow-roll inflation can produce only very light primordial black holes, around 100 grams, with the ultra slow roll phase last...
Towards hybrid inflation with $n_s=1$ in light of Hubble tension and primordial gravitational waves
astro-ph.CO 2022-05 conditional novelty 5.0 of 10

Hybrid inflation ending in a waterfall instability can lift the scalar spectral index to ns = 1, reviving chaotic φ² inflation when combined with early dark energy.
The Swampland Conjecture and F-term Axion Monodromy Inflation
hep-th 2017-03 conditional novelty 5.0 of 10

In every string model examined, delaying backreaction of the axion inflaton to trans-Planckian field ranges requires flux choices that push moduli masses above the Kaluza-Klein scale, so the effective theory breaks do...
The Conformal Limit of Inflation in the Era of CMB Polarimetry
hep-th 2016-09 accept novelty 5.0 of 10

In single-field slow-roll inflation with epsilon much less than eta, conformal symmetry fixes the bispectrum and gives f_NL^conf = -25/36 alpha_s.
Higgsed Chromo-Natural Inflation
hep-th 2016-09 conditional novelty 5.0 of 10

Spontaneously breaking the SU(2) gauge symmetry in Chromo-Natural Inflation boosts scalar fluctuations relative to tensor ones, bringing the model within observational bounds while predicting observable chiral gravita...
Primordial Gravitational Waves from Axion-Gauge Fields Dynamics
astro-ph.CO 2016-08 conditional novelty 5.0 of 10

Coupling a spectator axion to SU(2) gauge fields during inflation produces chiral gravitational waves large enough to be detectable even when the inflationary energy scale is too low for standard vacuum tensor modes.

See all 115 Pith citations

How later papers used it

288 later papers cite it

Evidence: substantial. 288 of the citing papers share no author with it, and 13 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 364 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 1 built on it, 1 used its method or tool and 1 cited it as support.

Builds on it 1 of 3 papers with this label

Generalized the Lyth bound of this paper.

Observational Signatures of Gravitational Couplings in DBI Inflation (2009) · 0.99 · paraphrased: the licence does not allow quoting

Uses its method or tool 1 of 4 papers with this label

Used the well known Lyth bound of this paper to estimate the field excursion during PBH formation in the USR period.

No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation (2023) · 0.98 · paraphrased: the licence does not allow quoting

Cites it as support 1 paper

Said that the smallness of epsilon implies the absence of observable primordial tensor modes, in agreement with this paper's sub-Planckian inflaton range during inflation.

Poly-instanton Inflation (2011) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

264 arXiv papers cite this in 334 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 · 261 sentences without a confident label

Builds on it 3 papers

The modified canonical transformations become [equation] The Lyth bound [ref] in such a model takes the form [equation] where $ΔN_*$ corresponds to the amount of visible inflation.

Bounds on Tensor wave and Twisted Inflation · Tensor constraints · 0.82
We now discuss the origin of the upper bound, originally due to Lyth [ref] , in the context of multi-field DBI inflation.

Multi-field DBI inflation: introducing bulk forms and revisiting the gravitational wave constraints · Gravitational wave constraints on DBI inflation · 0.81
It is now a simple matter to generalize the Lyth bound of [ref] (see Appendix [ref]).

Observational Signatures of Gravitational Couplings in DBI Inflation · Results · 0.99

Uses its method or tool 3 papers

Using the slow-roll conditions, $δϕ$ is related to the variation in the number of $e$-folds $δN$ by [ref] δϕ= M_p ( r/6.9)^1/2 δN .

Constraining inflation with future galaxy redshift surveys · Potential reconstruction · 0.85
For each value of $ξ$, we compute the scalar spectral index $n_s$, tensor-to-scalar ratio $r$, running $α_s ≡dn_s/dlnk$, running of the running $β_s ≡dα_s/dlnk$, inflaton excursion $Δϕ$ (via the modified Lyth bound [ref] ), energy scale $V_inf$, Hubble scale $H_inf$, and reheating temperature $T_reh$.

What new physics can we extract from inflation using the ACT DR6 and DESI DR2 Observations? · Hilltop Quartic Model · 0.98
Further, using the above estimates one can give the following estimation of the field excursion during PBH formation in the USR period using the well known Lyth bound [ref] : |Δϕ|_USR/M_pl=√(r_*/8)ΔN_USR≈O(0.16)<1 where |Δϕ|_USR:=|ϕ_e-ϕ_s|.

No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation · Numerical results and further estimations: A no-go theorem for PBH formation · 0.98

Uses its data or values 3 papers

Therefore, similar to the Lyth bound [ref] , there is a lower bound on the field excursion for the tachyon, [equation] where we use the observational value $ln(10^10 A_s)=3.094$ [ref] .

The reconstruction of tachyon inflationary potentials · Field excursion · 0.84
By using the observational data of WMAP satellite [ref] and the COBE normalization [ref] we found two conditions, Eqs.[ref] and [ref], that should be satisfied by the coefficients in the action.

Mutated hybrid inflation in $f(R,{\Box}R)$-gravity · Conclusions and discussions · 0.99
Even after the recent release of the combined Planck/BICEP2 results [ref] , the updated bound $r < 0.12$ on the tensor-to-scalar ratio of primordial fluctuations is still well above the Lyth bound $r < 0.01$ [ref] such that models of large-field inflation remain viable scenarios compatible with observations.

Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture · Introduction · 0.80

Compares with it 2 papers

[ref] with the famous Lyth bound [ref] , which provides a minimum for the field excursion of slow-roll inflationary models[The original bound derived by Lyth [ref] was taking into account just the small observable window which CMB experiments have access to.

Swampland Distance Conjecture, Inflation and $\alpha$-attractors · SDC and inflation · 1.00
While the Lyth estimate [ref] gives [equation] we find that this bound is very conservative, and indeed our hilltop trajectories are better approximated by [equation] as shown in figure [ref].

Learning to Inflate · Large-Field Inflation at Fixed $N_e$, Variable $Λ_h$ · 0.91

Cites it as support 1 paper

The smallness of $ϵ$ implies the absence of observable primordial tensor modes in agreement with the fact that the inflaton range during inflation is sub-Planckian [ref] .

Poly-instanton Inflation · Inflationary observables · 0.98

Cites it as background 55 papers

An interesting perspective on high-scale inflation is given by the Lyth bound [ref] .

Dante's Inferno · Introduction · 0.95
The first is the implied large value of $V$ around the GUT scale, the second is the Lyth bound [ref] .

Large Gravitational Waves and Lyth Bound in Multi Brane Inflation · Introduction · 0.89
Lyth [ref] found a long time ago that canonical single-field slow-roll inflation generically predicts that the overall field displacement $Δϕ$ experienced by the inflaton during the quasi-de Sitter phase must satisfy a lower bound.

A Tip for Landscape Riders: Multi-Field Inflation Can Fulfill the Swampland Distance Conjecture · The Lyth Bound · 0.98

Discussion

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

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