Evading the Lyth Bound in Hybrid Natural Inflation

Alexander Westphal; Arthur Hebecker; Sebastian C. Kraus

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Evading the Lyth Bound in Hybrid Natural Inflation

Arthur Hebecker, Sebastian C. Kraus, Alexander Westphal

High Energy Physics - Theory · Submitted 8 May 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.43 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.81 · mentions code or data availability 0.02.

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

Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field-range of the inflaton is much smaller than the Planck scale. We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models. More specifically, we consider models where an axion-like shift symmetry keeps the inflaton potential flat (up to non-perturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall-regime, as is typical for hybrid inflation. In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter $\epsilon$ can be sizable during an early period (relevant for the CMB spectrum). Subsequently, $\epsilon$ quickly becomes very small before the tachyonic instability eventually terminates the slow roll regime. In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation. While non-observation of tensors by Planck is certainly not a problem, a discovery in the medium to long term future is realistic.

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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	Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field-range of the inflaton is much smaller than the Planck scale.	background 1.00	0.05	0.03	asserted 0.90
s1	We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models.	contribution 0.49	0.88	0.69	asserted 1.00
s2	More specifically, we consider models where an axion-like shift symmetry keeps the inflaton potential flat (up to non-perturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall-regime, as is typical for hybrid inflation.	contribution 0.57	0.31	0.08	asserted 0.94
s3	In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter $\epsilon$ can be sizable during an early period (relevant for the CMB spectrum).	result 0.44	0.67	0.13	asserted 0.54
s4	Subsequently, $\epsilon$ quickly becomes very small before the tachyonic instability eventually terminates the slow roll regime.	result 0.73	0.63	0.07	asserted 1.00
s5	In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation.	result 0.99	0.77	0.65	asserted 0.97
s6	While non-observation of tensors by Planck is certainly not a problem, a discovery in the medium to long term future is realistic.	interpretation 0.99	0.11	0.10	hedged possibility 0.92

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.78.

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The paper

Original abstract

Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field-range of the inflaton is much smaller than the Planck scale. We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models. More specifically, we consider models where an axion-like shift symmetry keeps the inflaton potential flat (up to non-perturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall-regime, as is typical for hybrid inflation. In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter $\epsilon$ can be sizable during an early period (relevant for the CMB spectrum). Subsequently, $\epsilon$ quickly becomes very small before the tachyonic instability eventually terminates the slow roll regime. In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation. While non-observation of tensors by Planck is certainly not a problem, a discovery in the medium to long term future is realistic.

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References

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Cited by 4 Pith papers

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

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...
D7-Brane Chaotic Inflation
hep-th 2014-04 conditional novelty 6.0 of 10

D7-brane position moduli in Type IIB orientifolds can serve as large-field inflatons, with a mirror-symmetry shift symmetry and flux-induced monodromy, provided the flux coefficients can be tuned small.
String Inflation After Planck 2013
hep-th 2013-06 conditional novelty 3.0 of 10

A survey of string-inflation models finds that their pre-Planck predictions mostly sit near the observed spectral index with very small tensor-to-scalar ratio, so future tensor detection would rule out most of them.
Inflation and String Theory
hep-th 2014-04 accept novelty 1.0 of 10

A survey arguing that inflation is ultraviolet-sensitive and therefore requires a quantum gravity completion, then cataloguing the string theory constructions that attempt to provide one.

How the literature uses it

12 arXiv papers cite this in 16 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

This shows that non-trivial dynamics can't evade the Lyth bound.

A Field Range Bound for General Single-Field Inflation · 0.81

Papers citing it · 12 sentences without a confident label

Uses its data or values 1 paper

There, a constraint on $f$ coming from an embedding of the effective potential of Eq. [ref] into a string theory guide the authors to choose the fiducial bound $f≲√(3)/4π$ giving an upper bound $r≃7.6 ×10^-4$ [ref] .

General bounds in Hybrid Natural Inflation · Hybrid Natural Inflation, bounds in the restricted case · 0.88

Compares with it 2 papers

The achievable enhancement of $r$ is bounded by the amount of running $α≲0.01$ of the spectral index $n_s$ allowed by data (see e.g. [ref] where similarly the $r$-enhancement is bounded by the allowed running $α$.) * Inflation is driven by a combination of the volume modulus and its $C_4$ RR-form axion partner on one of two local symmetrically arranged saddle/inflection points.

Accidental Inflation from K\"ahler Uplifting · Introduction · 0.90
This corresponds to the situation where $ϵ$ and therefore the tensor to scalar ratio $r = 16ϵ$ is maximal and given by [equation] This is smaller than the value $r ≃7.6·10^-4$ found in the related work [ref] .

D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation · Consequences of Experimental Constraints · 0.99

Cites it as background 1 paper

In Ref. [ref] , HNI was already given a detailed analysis for its feasibility to reach large values of $r$, for sub-Planckian axion decay constant and sub-Planckian field range.

General bounds in Hybrid Natural Inflation · Hybrid Natural Inflation, bounds in the restricted case · 0.80

What it cites · 68 sentences without a confident label

Uses data or values from 1 paper

Now, the most recent value [ref] for the power spectrum is $Δ_R^2≡A_S ≃2.2 ×10^-9$ at the fiducial scale $k = 0.05 Mpc^-1$.

Planck 2013 results. XXII. Constraints on inflation · Production of Primordial Black Holes · 0.99

Compares with 1 paper

By contrast, the authors of [ref] achieve waterfall near the minimum through field theory model building, but they do not consider tensor modes. ] From the fluxbrane perspective, however, things look different: The energy of the two-brane system is minimized in a situation where the branes come very close to each other.

Inflationary models with a flat potential enforced by non-abelian discrete gauge symmetries · Introduction · 0.95

Cites as background 39 papers

This coupling may provide an efficient channel for reheating [ref] .] This discussion can be taken to the more advanced level of supergravity, where it takes the form of arguing about natural sizes of higher-order terms in the Kähler potential [ref] .

Gauge Field Production in Axion Inflation: Consequences for Monodromy, non-Gaussianity in the CMB, and Gravitational Waves at Interferometers · Introduction · 0.81
This coupling may provide an efficient channel for reheating [ref] .] This discussion can be taken to the more advanced level of supergravity, where it takes the form of arguing about natural sizes of higher-order terms in the Kähler potential [ref] .

False Vacuum Inflation with Einstein Gravity · Introduction · 0.81
This coupling may provide an efficient channel for reheating [ref] .] This discussion can be taken to the more advanced level of supergravity, where it takes the form of arguing about natural sizes of higher-order terms in the Kähler potential [ref] .

Hybrid Inflation in Supergravity · Introduction · 0.81

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