Natural Inflation: Particle Physics Models, Power Law Spectra for Large Scale Structure, and Constraints from COBE

Angela Olinto; Fred Adams; Joshua Frieman; J. R. Bond; Katherine Freese

REVIEW

Natural Inflation: Particle Physics Models, Power Law Spectra for Large Scale Structure, and Constraints from COBE

Fred Adams, J. R. Bond, Katherine Freese, Joshua Frieman, Angela Olinto

High Energy Physics - Phenomenology · Submitted 17 Jul 1992 · 73 references

Pith's verdict: A solid, mostly-derivative follow-up to Paper I: the n_s derivation and the LSS/COBE analysis are real work, but the abstract oversells the string example, which fails by the paper's own numbers.

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CitationAngela Olinto, Fred Adams, Joshua Frieman, J. R. Bond, Katherine Freese. "Natural Inflation: Particle Physics Models, Power Law Spectra for Large Scale Structure, and Constraints from COBE." arXiv:hep-ph/9207245 (1992). https://pith.science/paper/AM7ZWLVR

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Editor's note

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Worth your time, but read it as two papers stapled together. The first is a genuine extension of Freese-Frieman-Olinto (their ref. [8]): the technicolor-like condensate construction in Sec. II.A, the multiple-gaugino-condensation exercise in Sec. II.B, the numerical integration of the rolling field cross-checked against a small-angle analytic solution (Eqs. 3.13-3.16), and the whole large-scale-structure analysis in Sec. IV. The second is the original scenario, restated. The n_s = 1 - M_Pl^2/(8 pi f^2) result is a clean slow-roll derivation from the cosine potential and I checked it against Eq. 4.3; it holds. The LSS section is the best part: they quote real error bands on sigma_8(n_s), handle cosmic variance on the quadrupole honestly, and keep separate what APM prefers (n_s below 0.6) from what COBE plus structure formation permits (above 0.6). That distinction is the paper's actual contribution to the debate, and it is made carefully. On the reader's worry about Lambda: it runs backwards. Eq. 3.23 is an upper bound on Lambda, T_RH goes as Lambda^3, so a smaller Lambda gives a lower reheat temperature and a stronger bound on f. The f > 0.3 M_Pl number is the weakest the COBE normalization allows, not an overstatement. Two soft spots do land. First, the abstract claims an explicit string example; Sec. II.B delivers f <= 0.11 M_Pl, which by the paper's own Sec. III and IV gives too little reheating and too much large-scale power. The authors say so in the text and then don't say it in the abstract. Second, the n_s > 0.6 bound is a statement about standard CDM with h = 0.5, Omega_B = 0, BBKS transfer function. The exponent 3.63 in Eq. 4.25 amplifies any shift, and the three supporting legs (galaxy formation redshift, bulk flows, cluster abundance) all ride the same COBE normalization, so they aren't independent confirmations. The margin between 0.6 and the APM-preferred 0.6-0.7 is about the size of these systematics. Minor: the zero initial-velocity assumption rests on ref. [32], unpublished. Who should read it: anyone working on inflationary spectra or on the pre-1992 large-scale-structure tension, and anyone who wants the natural-inflation reference with the cosmology attached. Send it out. The referees will push on the abstract's string claim and on the CDM dependence, and both are fixable.

Referee report

Significance

The paper's central derivation is sound and its predictions are falsifiable. The spectral index n_s = 1 − M_Pl²/(8πf²) follows cleanly from the standard slow-roll expressions for this potential, and I verified Eq. (4.3) reduces to it in the small-angle limit; the two independent analytic approximations (slow roll and small angle) are cross-checked against the numerical integration of Eq. (3.10) in Fig. 2, which is exactly the right way to validate a result that spans the f range of interest. The prediction that natural inflation produces a negligible gravitational-wave contribution (Sec. IV.B.5, Eq. 4.27) is a genuine, testable discriminant against power-law and extended inflation, and the paper states plainly that detecting a tensor component would rule the model out. The string construction in Sec. II.B is worked through in enough detail to be checked (I confirmed Eqs. 2.17–2.20 and the quoted f/M_Pl values for δΔ = 2.8 and δΔ = 1), and the authors are candid that the SU(9)×SU(10) example falls short of their own viability criteria. The reheating bound f ≳ 0.28 M_Pl is derived independently of the large-scale-structure arguments, which gives the central claim a second leg.

Major objections (2)

[Sec. IV.B.6 and abstract sentence s4] The claim that the n_s ≳ 0.6 limit 'comes from a variety of arguments' and is therefore 'quite robust' overstates the independence of the supporting evidence. The epoch-of-galaxy-formation bound (Eq. 4.25), the bulk-flow bound (Eq. 4.23), and the cluster-abundance argument (Fig. 8) all draw on the same σ8(n_s) relation of Eq. (4.16), which is itself a fit within standard CDM with h = 0.5, Ω_B = 0, and the BBKS transfer function. These are three applications of one normalization, not three confirmations. The paper's own numbers show the systematic shifts are comparable to the margin being claimed: Ω_B = 0.06 lowers σ8 by about 15%, and the authors note that h = 0.4 or Ω_B = 0.1 makes n_s ≈ 0.7 feasible (Sec. IV.B.1). Since the exponent 3.63 in Eq. (4.25) amplifies any such shift, the abstract's unqualified 'n_s > 0.6' should be stated as a bound within standard CDM, with the model dependence made explicit. This does not undermine the central result, because the reheating bound of Eq. (3.37) is independent and gives essentially the same f, but the abstract should not present the two as if they were separately established.
[Sec. IV.B.1, Figs. 3–4] The APM comparison that fixes the preferred range 0 ≲ n_s ≲ 0.6 uses a CDM transfer function computed in the Ω_B → 0 limit, while the paper elsewhere adopts Ω_B ≈ 0.06 as the nucleosynthesis-favoured value and states that this lowers σ8 by about 15%. The shape change in T(k) from a nonzero baryon fraction is not computed, yet the conclusion in Sec. IV.B.6 that extended inflation is nearly excluded rests on comparing a lower bound n_s ≳ 0.76 (with tensors) against an upper bound of 0.77–0.84 from large-bubble limits. A 15% amplitude shift moves the APM-preferred index by roughly 0.04, which is a substantial fraction of that gap. The authors should either recompute w_gg(θ) and the transfer function at Ω_B = 0.06 and show the preferred range is stable, or state explicitly that the extended-inflation exclusion is conditional on the Ω_B = 0 transfer function.

Minor objections (7)

[Sec. III.C.1, Eqs. (3.23) and (3.35)] The text notes that Eq. (3.23) is 'strictly only an upper bound on the scale Λ', but does not point out that this makes the reheating bound conservative: since T_RH ∝ Λ³, a smaller Λ gives a smaller T_RH and hence a stronger lower bound on f. Stating this explicitly in Sec. III.C.5 would preempt the natural misreading that the COBE normalization is being used to inflate the bound.
[Sec. II.B, Eq. (2.20) and following] The worked string example yields f ≲ 0.11 M_Pl for SU(9)×SU(10), which by the paper's own Sec. III.C.5 and Sec. IV criteria is excluded, and reaching f/M_Pl ≈ 0.36 requires δΔ ≈ 1 with N₁, N₂ ≈ 16, 17, which violates the central-charge bound. The abstract's phrase 'work out an explicit string example' may read as a success; it would be more accurate to say the example comes close but falls short, and to say so in the abstract.
[Sec. III.C.6] The argument that radial-mode inflation damps angular gradients requires √λ/ξ ≲ 1 to avoid order-unity Hubble-radius fluctuations collapsing into black holes. For λ of order unity and ξ of order unity this is only marginally satisfied, and the consequence of violating it deserves one explicit sentence rather than a parenthetical.
[Eq. (3.17)] The prefactor 3/(2π) in P_ζ^{1/2} = (3/2π)H²/|φ̇| differs from the more common H²/(2π|φ̇|) by a convention-dependent factor. A short note identifying the gauge choice would help readers compare the normalization with other treatments.
[Sec. IV.B.2, Eq. (4.9a)] Only the Sachs-Wolfe term is retained in the multipole expansion. At the ℓ ≈ 20 scales probed by DMR the Doppler and integrated-Sachs-Wolfe contributions are small, but the paper should say so explicitly rather than leaving the omission implicit.
[Fig. 5 and Eq. (4.30)] It should be stated whether the tensor contribution A₂ is added in quadrature to σ_T(10°) after applying the same 10° filter, and whether the quoted σ8 shifts for power-law inflation include the change in the shape of C_ℓ or only the amplitude rescaling.
[Typesetting] Stray numeral '8' characters appear in several places in the supplied text, for example 'appears to have 8too little power' in Sec. IV.B.1, 'it would 8not only allow' in Sec. IV.B.5, and 'the 8familiar N_I(k) ∼ 60' in Sec. IV.A.4. These should be cleaned up before publication.

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The paper

The paper claims

A pseudo-Nambu-Goldstone boson — an axion-like field with a cosine potential — can drive inflation, and it leaves a measurable tilt in the primordial density spectrum that ties the symmetry-breaking scale $f$ to observations of the cosmic微波

The reading

The paper asks whether the inflaton — the field whose potential energy drives the early exponential expansion — can be a pseudo-Nambu-Goldstone boson, the light angular degree of freedom left over when a global symmetry breaks spontaneously. Such a field has a potential $V(φ) = Λ^4[1 + cos(φ/f)]$ set by just two scales, and the authors argue that the values inflation needs, $f$ near the Planck mass and $Λ$ near the grand-unification scale, arise naturally in technicolor-like and string constructions rather than being put in by hand. The payoff is a definite prediction: the density fluctuations produced are a power law with index $n_s = 1 - M_{Pl}^2/(8π f^2)$, so the spectrum has more power on large scales than the standard scale-free case. That tilt is a feature, not a blemish, because the cold dark matter model with $n_s = 1$ has long seemed short of large-scale power. The authors then use the newly reported COBE microwave anisotropy, together with the requirement that galaxies form early enough and that bulk flows reach the observed speeds, to turn the tilt into a bound: $n_s > 0.6$, hence $f > 0.3 M_{Pl}$.

What carries the argument

The load-bearing object is the PNGB potential $V(φ) = Λ^4[1 + cos(φ/f)]$, whose height $Λ^4$ and width $f$ set everything else, with the curvature at the extremum giving $m_φ = Λ^2/f$. Because the field rolls slowly near the top, the slow-roll parameters are computable in closed form, and the scalar spectral index reduces to $n_s = 1 - M_{Pl}^2/(8π f^2)$ over the waveband probed by large-scale structure; the paper checks that the index is nearly constant across three decades in wavelength, so the power-law approximation is not an abuse. The second piece of machinery is the naturalness argument: $Λ$ is generated dynamically by a gauge group that becomes strong near the GUT scale, so the small ratio $Λ/f ∼ 10^{-4}$ is exponential rather than put in by hand. The authors work this out explicitly in a multiple-gaugino-condensation string model, identifying the model-independent axion (the imaginary part of the dilaton) as the inflaton and deriving $f/M_{Pl} = [√{16π}(ln(k_1/k_2) + ln(N_1/N_2) + δΔ/2)]^{-1}$ for a hidden sector $SU(N_1) × SU(N_2)$.

Extended reading notes

Core claim

The central claim is that a cosine-potential pseudo-Nambu-Goldstone boson is a viable inflaton whose parameters are fixed, not tuned, and that its fluctuations are a power law with $n_s ≃ 1 - M_{Pl}^2/(8π f^2)$ rather than the scale-invariant Harrison-Zeldovich form. Two independent arguments converge on the same lower bound on $f$. First, reheating: the amplitude of density perturbations fixes $Λ$ as a function of $f$, and the reheat temperature falls exponentially as $f$ drops below the Planck mass, so getting above the electroweak scale for baryogenesis requires $f > 0.3 M_{Pl}$. Second, large-scale structure: the low-$n_s$ spectra that fit the APM angular correlation function also require, once COBE's $10°$ anisotropy amplitude is imposed, a normalization $σ_8 ≲ 0.5$, which pushes galaxy formation to uncomfortably late times and predicts bulk flows smaller than observed; demanding early galaxy formation or the measured flows gives $n_s > 0.6$, essentially the same bound. The authors also show that for power-law and extended inflation the same reasoning bites harder, $n_s > 0.7$, which combined with the separate upper bound $n_s < 0.77$–$0.84$ from large-bubble limits leaves little room for most extended models, while chaotic inflation with power-law potentials sits at $n_s ≳ 0.95$ and is untouched.

Load-bearing premise

The reheating bound $f > 0.3 M_{Pl}$ is obtained by fixing $Λ$ from the COBE amplitude with bias $b_g = 1$, and the paper itself notes in Section III.C.1 that this $Λ$ is strictly only an upper bound because large-scale structure could in principle be seeded by some non-inflationary mechanism — a caveat that does not propagate into the abstract's headline number.

Editorial extensions

If this is right

The primordial spectral index becomes a direct handle on a particle-physics scale: measuring $n_s$ measures $f$, the symmetry-breaking scale of the axion-like field.
Extended and power-law inflation are squeezed from both sides — $n_s > 0.7$ from structure formation and $n_s < 0.77$–$0.84$ from large-bubble microwave limits — leaving little viable parameter space in most versions.
Natural inflation predicts essentially no gravitational-wave contribution to the microwave anisotropy, with the tensor-to-scalar ratio below about 0.04 for $f ≤ M_{Pl}$, so a detected tensor component would discriminate it sharply from power-law and extended models.
Lowering $n_s$ alone does not rescue the cold dark matter model's large-scale problems; it must be combined with other fixes such as a few-eV neutrino, a cosmological constant, a lower Hubble constant, or a larger baryon density.
The reheating constraint $f > 0.3 M_{Pl}$ implies $n_s ≥ 0.5$ if inflation produces the dominant fluctuations on all scales, tying baryogenesis to the shape of the perturbation spectrum.

Reading between the lines

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

The string realization the authors construct lands on the wrong side of their own bound: for $SU(9) × SU(10)$ with $δΔ = 2.8$ one gets $f ≈ 0.11 M_{Pl}$, which is excluded by both reheating and the spectral tilt, and reaching $f ≈ 0.36 M_{Pl}$ needs $δΔ ≈ 1$, which in turn needs hidden groups around $SU(16)$–$SU(17)$ that exceed the central-charge budget. The paper's framing of string models as 'v
Because the tilt is a one-parameter effect, a future measurement of $n_s$ with error below about 0.05 would either pin $f$ to a few percent or exclude the whole cosine-potential family, independently of how the potential is embedded in particle physics.
The paper's own caveat that the COBE-derived $Λ(f)$ is 'strictly only an upper bound' since large-scale structure could be seeded by something non-inflationary means the reheating bound should be read as conditional: it holds if inflation is the sole source of the observed fluctuations.
The near-coincidence of the reheating bound and the structure-formation bound on $f$ is worth noting as a consistency check rather than a derivation — two very different physical arguments landing on $0.3 M_{Pl}$ suggests the model has little slack, so a modest tightening of either COBE normalization or the galaxy-formation redshift would close the window.

Original abstract

A pseudo-Nambu-Goldstone boson, with a potential of the form $V(\phi) = \Lambda^4[1 \pm \cos(\phi/f)], naturally gives rise to inflation if $f \sim M_{Pl}$ and $\Lambda \sim M_{GUT}$. We show how this can arise in technicolor-like and superstring models, and work out an explicit string example in the context of multiple gaugino condensation models. We study the cosmology of this model in detail, and find that sufficient reheating to ensure that baryogenesis can take place requires $f > 0.3 M_{Pl}$. The primordial density fluctuation spectrum generated is a non-scale-invariant power law, $P(k) \propto k^{n_s}$, with $n_s \simeq 1 - (M^2_{Pl}/8\pi f^2)$, leading to more power on large length scales than the $n_s = 1$ Harrison-Zeldovich spectrum. The standard CDM model with $0 \la n_s \la 0.6-0.7$ could in principle explain the large-scale clustering observed in the APM and IRAS galaxy surveys as well as large-scale flows, but the COBE microwave anisotropy implies such low amplitudes (or high bias factors, $b>2$) for these CDM models that galaxy formation occurs too late to be viable; combining COBE with sufficiently early galaxy formation or the large-scale flows leads to $n_s >0.6$, or $f > 0.3 M_{Pl}$ as well. For extended and power law inflation models, this constraint is even tighter, $n_s > 0.7$; combined with other bounds on large bubbles in extended inflation, this leaves little room for most extended models.

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.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.46 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.84 · 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.

A pseudo-Nambu-Goldstone boson, with a potential of the form $V(\phi) = \Lambda^4[1 \pm \cos(\phi/f)], naturally gives rise to inflation if $f \sim M_{Pl}$ and $\Lambda \sim M_{GUT}$. We show how this can arise in technicolor-like and superstring models, and work out an explicit string example in the context of multiple gaugino condensation models. We study the cosmology of this model in detail, and find that sufficient reheating to ensure that baryogenesis can take place requires $f > 0.3 M_{Pl}$. The primordial density fluctuation spectrum generated is a non-scale-invariant power law, $P(k) \propto k^{n_s}$, with $n_s \simeq 1 - (M^2_{Pl}/8\pi f^2)$, leading to more power on large length scales than the $n_s = 1$ Harrison-Zeldovich spectrum. The standard CDM model with $0 \la n_s \la 0.6-0.7$ could in principle explain the large-scale clustering observed in the APM and IRAS galaxy surveys as well as large-scale flows, but the COBE microwave anisotropy implies such low amplitudes (or high bias factors, $b>2$) for these CDM models that galaxy formation occurs too late to be viable; combining COBE with sufficiently early galaxy formation or the large-scale flows leads to $n_s >0.6$, or $f > 0.3 M_{Pl}$ as well. For extended and power law inflation models, this constraint is even tighter, $n_s > 0.7$; combined with other bounds on large bubbles in extended inflation, this leaves little room for most extended models.

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 pseudo-Nambu-Goldstone boson, with a potential of the form $V(\phi) = \Lambda^4[1 \pm \cos(\phi/f)], naturally gives rise to inflation if $f \sim M_{Pl}$ and $\Lambda \sim M_{GUT}$.	background 0.78	0.14	0.09	asserted 0.92
s1	We show how this can arise in technicolor-like and superstring models, and work out an explicit string example in the context of multiple gaugino condensation models.	contribution 0.92	0.92	0.05	asserted 1.00
s2	We study the cosmology of this model in detail, and find that sufficient reheating to ensure that baryogenesis can take place requires $f > 0.3 M_{Pl}$.	result 0.99	0.95	0.12	asserted 1.00
s3	The primordial density fluctuation spectrum generated is a non-scale-invariant power law, $P(k) \propto k^{n_s}$, with $n_s \simeq 1 - (M^2_{Pl}/8\pi f^2)$, leading to more power on large length scales than the $n_s = 1$ Harrison-Zeldovich spectrum.	result 1.00	0.83	0.17	asserted 1.00
s4	The standard CDM model with $0 \la n_s \la 0.6-0.7$ could in principle explain the large-scale clustering observed in the APM and IRAS galaxy surveys as well as large-scale flows, but the COBE microwave anisotropy implies such low amplitudes (or high bias factors, $b>2$) for these CDM models that galaxy formation occurs too late to be viable; combining COBE with sufficiently early galaxy formation or the large-scale flows leads to $n_s >0.6$, or $f > 0.3 M_{Pl}$ as well.	result 0.73	0.43	0.30	hedged possibility 0.78
s5	For extended and power law inflation models, this constraint is even tighter, $n_s > 0.7$; combined with other bounds on large bubbles in extended inflation, this leaves little room for most extended models.	result 0.66	0.55	0.18	asserted 0.96

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.86.

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

Figures

**Figure 1.** Plot of various field values and parameters vs. f/MPl. The upper curves show that our estimate φ2/f (eq.3.5) for the value of the field at the end of the SR epoch (dotted) is very close to our numerical result φend/f for when inflation ends (solid); the middle (dotted) curve shows log(φ max 1 /f), the largest initial value of the field consistent with 60 e-folds of inflation; the lower (dashed) curve shows the density perturbation constraint (3.23) on the scale Λ [plotted as log(Λ/MPl)], assuming the bias parameter bg = 1

**Figure 2.** Results of the numerical integration of the scalar and gravitational equations of motion. The number of inflation e-folds N(φ1) of the scale factor is shown as a function of the initial value of the scalar field, φ1, for different values of the fundamental mass scale, f/MPl = 0.05, 0.07, 0.1, 0.2, and 0.5

**Figure 5.** The range (with ‘1 sigma error bars’) of the amplitude parameter σ8 for a standard CDM model in the limit that ΩB = 0 as a function of the power law slope ns, using the constraint from the rms fluctuations on 10o in COBE’s DMR experiment. Both the theoretical variance and the quoted experimental error are included in the error bars, which are in total about ±20%. The values of σ8 drop by a further ∼ 15% when ΩB ∼ 0.06 is used rather than the zero used here. If 41

**Figure 6.** Comparison of the DMR 53A + B × 90A + B cross correlation function with the quadrupole removed [37] with the theoretical predictions, including variance, for (a) ns = 1 and (b) ns = 0.4 spectra. The σ8 amplitudes shown have been set by requiring the angular power spectrum to reproduce the rms fluctuations on 10o . Clearly, although the data is somewhat better fit by the ns = 1 rather than the ns = 0.4 model, one cannot strongly distinguish between the 2 models on the basis of shape alone. The experimental errors plus theoretical variance in the quadrupole amplitude are sufficiently…

**Figure 7.** The linear rms fluctuations averaged over spherical regions of radius RTH are plotted as a function of the mass M ≈ 1012.4 (RTH/ h −1Mpc)3 M⊙, for CDM models with ns = 0.4, 0.6, 0.8, and 1 (with ns increasing as one moves vertically up the figure). The error bars show the 1 sigma range in spectrum normalization as a result of DMR and cosmic variance errors in σT (10o ). Although Fig.3(a) shows that ns < 1 spectra have more power on large scales and less on small scales than ns = 1 models with the same σ8, when σ8(ns) determined from COBE is used, the amplitude for ns < 1 is less on…

**Figure 8.** In (a), we show the number density of collapsed objects with 3D virial velocity in excess of v for the CDM model with spectral index ns = 0.8 and for the value of the amplitude parameter σ8 = 0.7 (indicated by the DMR σT (10o ) data for this model). The densities are shown as a function of redshift z, with z decreasing as one moves to the right in the figure. The velocities in the hierarchical peaks method [55] used for this computation could be larger by an amount given by the error bar labelled by ‘v range’; these error bars are explicitly put on the z = 0 curve. The number…

Showing 7 of the paper's 8 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/9207245 by the authors.

References

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A. R. Liddle and D. Wands, Mon. Not. R. astr. Soc. 253, 637 (1991). 40 FIGURE CAPTIONS Figure 1: Plot of various ﬁeld values and parameters vs. f/MPl . The upper curves show that our estimate φ2/f (eq.3.5) for the value of the ﬁeld at the end of the SR epoch (do tted) is very close to our numerical result φend/f for when inﬂation ends (solid); the middle ...

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Showing 60 of 63 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 63 Pith citations

Extra-dimensional Origins of Chemical Potentials at the Cosmological Collider
hep-ph 2026-07 conditional novelty 7.0 of 10

A rolling 5D gauge-field inflaton acts as an extra-dimensional electric field, creating charged and neutral KK particles far heavier than H and yielding observable oscillatory signatures.
Kinetic Gauge Friction in Natural Inflation
astro-ph.CO 2024-11 conditional novelty 7.0 of 10

Kinetic gauge friction can sustain natural inflation with sub-Planckian f, and a Chern-Simons term stabilizes the perturbations, yielding CMB-compatible spectra.
The strong backreaction regime in axion inflation
astro-ph.CO 2023-03 conditional novelty 7.0 of 10

Fully inhomogeneous lattice simulations of axion inflation through strong backreaction show extra efoldings growing with coupling, smoothed and broadened gauge spectra, and scale-dependent chirality loss.
Phenomenology of a Pseudo-Scalar Inflaton: Naturally Large Nongaussianity
astro-ph.CO 2011-02 accept novelty 7.0 of 10

Coupling a pseudo-scalar inflaton to gauge fields via phi F F-tilde produces large, nearly equilateral nongaussianity in the cosmic microwave background, with a distinctive combination of large tensor-to-scalar ratio ...
Racetrack Inflation
hep-th 2004-06 conditional novelty 7.0 of 10

A modified racetrack superpotential with KKLT volume stabilization yields a saddle point between two degenerate minima flat enough for eternal topological inflation, with the Kähler-modulus axion as the inflaton.

Show 55 more citing papers

Extranatural Inflation
hep-th 2003-01 accept novelty 7.0 of 10

A five-dimensional gauge field's extra component, protected by locality from quantum gravity corrections, can drive inflation with a red spectrum (n about 0.96) and gravitational waves (r about 0.11).
Primordial black holes and gravitational waves from aligned axion inflation
astro-ph.CO 2026-10 conditional novelty 6.0 of 10

A two-axion inflation model produces a small-scale curvature spike during a metastable-to-stable transition, yielding asteroid-mass primordial black holes and millihertz-to-decihertz gravitational waves.
Galaxy Clusters Selected via the Sunyaev-Zel'dovich Effect in 5 year data from the SPT-3G Main Survey
astro-ph.CO 2026-07 unverdicted novelty 6.0 of 10

A catalog of 7190 confirmed galaxy clusters from 5-year SPT-3G SZ observations spanning masses 7.9e13 to 1.6e15 solar masses and redshifts 0.037 to >2.
Post-inflationary enhancement of adiabatic perturbations in modular cosmology
astro-ph.CO 2025-07 conditional novelty 6.0 of 10

In modular inflation models, entropic perturbations frozen during inflation are converted into curvature perturbations after inflation, producing an enhanced power spectrum while preserving the spectral index ns.
Axion USR Inflation
astro-ph.CO 2025-07 conditional novelty 6.0 of 10

In axion inflation with an intermediate ultra-slow-roll phase, the instability parameter collapses at the start of USR, terminating gauge production and yielding a two-peak power spectrum with P_R ∝ k^m, m>4.
Pure Chromo-Natural Inflation: Signatures of Particle Production from Weak to Strong Backreaction
astro-ph.CO 2025-04 conditional novelty 6.0 of 10

Pure chromo-natural inflation unavoidably transitions from weak to strong backreaction, producing a chiral three-peak gravitational wave spectrum and a scalar peak that can form primordial black holes.
On the slope of curvature power spectrum in non-attractor inflation
astro-ph.CO 2019-12 conditional novelty 6.0 of 10

Extending a gradient-expansion method to higher order, the authors show the primordial curvature spectrum in non-attractor inflation can grow with spectral index up to 8 after a dip, then relax to about 3 near its peak.
Magnetogenesis from axion inflation
astro-ph.CO 2016-06 conditional novelty 6.0 of 10

Nonlinear lattice simulations of axion inflation with large Chern-Simons coupling to hypercharge yield a present-day field of about 10^-13 G at roughly 10 pc correlation length, near blazar bounds.
Fermion production during and after axion inflation
hep-ph 2015-08 accept novelty 6.0 of 10

A derivative coupling to a rolling axion biases gravitational fermion production toward one helicity during inflation and yields a net left-right number-density asymmetry after inflation for a range of fermion masses ...
Parity-violating CMB correlators with non-decaying statistical anisotropy
astro-ph.CO 2015-05 conditional novelty 6.0 of 10

Coupling the inflaton to a vector field with a non-decaying background generates a parity-odd, direction-dependent bispectrum with fixed coefficients 2:-3:1, and Planck data then bound the vector energy density below ...
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. XX. Constraints on inflation
astro-ph.CO 2015-02 accept novelty 6.0 of 10

Full-mission Planck data give a scalar spectral index ns = 0.9655 +/- 0.0062 and a tensor-to-scalar bound r < 0.11, disfavouring phi-squared and natural inflation relative to R-squared inflation.
Drifting Oscillations in Axion Monodromy
hep-th 2014-12 conditional novelty 6.0 of 10

Axion monodromy inflation predicts oscillations in the primordial power spectrum whose period drifts measurably across the CMB's e-folds at high frequency, so searches must include drift parameters.
Parity-violating and anisotropic correlations in pseudoscalar inflation
astro-ph.CO 2014-11 conditional novelty 6.0 of 10

Coupling a pseudoscalar inflaton to a vector field with a small coherent background generates CMB two-point correlations between different multipoles that violate both parity and statistical isotropy.
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.
Universal Constraints on Axions from Inflation
hep-ph 2014-09 conditional novelty 6.0 of 10

The axial coupling between a rolling axion and a gauge field generates curvature perturbations with the same xi-dependent strength whether the axion drives inflation or is a spectator, so observational bounds on xi ca...
The Powers of Monodromy
hep-th 2014-05 conditional novelty 6.0 of 10

Compactifying type IIB string theory on products of Riemann surfaces with a B-field axion and an F1 flux coupling yields monomial inflaton potentials with p = 2/3, 4/3, 2, and 3, because the inflaton energy shifts a c...
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 ...
Towards Universal Axion Inflation and Reheating in String Theory
hep-th 2014-04 conditional novelty 6.0 of 10

Two type IIB large-volume-scenario models use the universal axion as inflaton, one with an instanton-generated cosine potential and one with a flux-generated quadratic potential, and both reheat mainly into Standard M...
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...
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 ...
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.
Axion Inflation in Type II String Theory
hep-th 2007-10 conditional novelty 6.0 of 10

Axions from vanishing two-cycles in type IIB compactifications can have near-Planckian decay constants after string world-sheet corrections, potentially enabling multi-field inflation with tensor-to-scalar ratio up to 0.14.
Axionic Inflation from Large Volume Flux Compactifications
hep-th 2006-03 conditional novelty 6.0 of 10

A single-field axionic inflation model in large volume flux compactifications yields a red spectrum compatible with WMAP3 when the eta parameter is set by the gauge group size.
Inflating in a Better Racetrack
hep-th 2006-03 conditional novelty 6.0 of 10

An explicit type IIB compactification with two Kahler moduli can support racetrack inflation driven by a linear combination of axions, matching the COBE spectrum with n_s approximately 0.95.
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.
Exploring the Primordial Power Spectrum with Dark-Age 21 cm fluctuations
astro-ph.CO 2026-09 conditional novelty 5.0 of 10

Dark Ages 21 cm power-spectrum forecasts could constrain the spectral index runnings α_s and β_s roughly an order of magnitude tighter than Planck, enabling discrimination among inflation models degenerate in n_s and r.
Corrections to inflationary models induced by non-minimal coupling between scalar field and curvature
gr-qc 2026-07 conditional novelty 5.0 of 10

Power-law non-minimal coupling F=(H/λ)^{2n} deforms inflationary potentials, shifts r and n_S while preserving n_T=-r/8 and GR-like reheating, enabling r(1-n_S) classification of models against Planck/ACT data.
Comparative study of the strong backreaction regime in axion inflation: the effect of the potential
astro-ph.CO 2025-05 conditional novelty 5.0 of 10

In lattice simulations of axion inflation, the strong-backreaction stage that lengthens inflation occurs for all seven tested potentials, but its duration varies strongly with the potential.
QCD Axion on Hilltop by a Phase Shift of $\pi$
hep-ph 2019-08 conditional novelty 5.0 of 10

A heavy axion inflaton can shift the QCD axion potential by π, placing the QCD axion at the hilltop and allowing f_a ≳ 3×10^9 GeV to explain all dark matter.
ALP inflation and Big Bang on Earth
hep-ph 2019-03 accept novelty 5.0 of 10

Hilltop axion inflation fixes the inflaton mass at about one millionth of its decay constant, bringing the inflaton within reach of the SHiP beam-dump experiment if the inflation scale is low.
Lattice formulation of axion inflation. Application to preheating
astro-ph.CO 2018-12 accept novelty 5.0 of 10

A lattice discretization that keeps gauge and shift symmetry exact on the grid is used to map preheating after axion inflation, finding a threshold coupling near 1/Lambda = 9.5/m_pl that separates failed from near-com...
Baryon Asymmetry and Gravitational Waves from Pseudoscalar Inflation
hep-ph 2017-07 conditional novelty 5.0 of 10

Requiring the observed baryon asymmetry fixes the axion-hypercharge coupling to about 3×10^17 GeV, which in turn predicts a gravitational wave peak at MHz frequencies too high for current detectors.
Gauss-Bonnet Chern-Simons gravitational wave leptogenesis
hep-th 2017-02 conditional novelty 5.0 of 10

A Gauss-Bonnet coupling to the inflaton exponentially amplifies sub-horizon gravitational waves and enhances gravitational-anomaly leptogenesis, matching the observed baryon asymmetry for a UV cutoff near 10^14-16 GeV.
The ALP miracle: unified inflaton and dark matter
hep-ph 2017-02 conditional novelty 5.0 of 10

One axion-like particle with mass of order 0.01 eV and photon coupling of order 10^-11 GeV^-1 can simultaneously drive inflation, reheat the universe, and account for dark matter.
Exploring Cosmic Origins with CORE: Inflation
astro-ph.CO 2016-12 conditional novelty 5.0 of 10

Forecasts indicate a CMB polarization satellite with 1.7 microkelvin-arcmin sensitivity and 5 arcmin resolution would measure the tensor-to-scalar ratio to about 2e-4 and the scalar tilt to 0.0014, enough to separate ...
Impact of neutrino properties on the estimation of inflationary parameters from current and future observations
astro-ph.CO 2016-10 accept novelty 5.0 of 10

Realistic neutrino masses and hierarchies shift the inferred scalar spectral index by less than one sigma in current data, but the common zero-mass cutoff and nonstandard radiation content can bias inflationary contours.
Inflation from Broken Scale Invariance
hep-th 2014-06 conditional novelty 5.0 of 10

Spontaneously broken global scale invariance supplies a shift symmetry that protects the inflaton potential, reproducing Starobinsky-like and axion-like large-field inflation from small explicit breaking by nearly mar...
Towards large r from [p,q]-inflation
hep-th 2014-03 conditional novelty 5.0 of 10

[p,q] 7-branes in type IIB can induce a quadratic axion potential that, at probe level, gives chaotic-inflation observables with r about 0.14, but only by breaking supersymmetry explicitly during inflation.
Perturbations in Chromo-Natural Inflation
hep-th 2013-05 conditional novelty 5.0 of 10

Chromo-Natural Inflation generates a chiral, exponentially enhanced gravitational wave spectrum and, in its original form, cannot fit the Planck tilt and tensor-to-scalar ratio at the same time.
Observational Constraints on Gauge Field Production in Axion Inflation
astro-ph.CO 2012-03 conditional novelty 5.0 of 10

Fitting the inverse-decay power spectrum of axion inflation to WMAP7 plus ACT data gives the strongest current bound, xi_star < 2.15 at 95% CL, tighter than the bispectrum or mu-distortion bounds.
Gauge Field Production in Axion Inflation: Consequences for Monodromy, non-Gaussianity in the CMB, and Gravitational Waves at Interferometers
astro-ph.CO 2011-10 conditional novelty 5.0 of 10

Backreaction from gauge fields produced during axion inflation extends inflation by about 10 e-foldings and enhances the gravitational wave signal enough to be potentially visible at Advanced LIGO/VIRGO.
Non-Gaussianity from Curvatons Revisited
astro-ph.CO 2011-07 conditional novelty 5.0 of 10

For curvatons with non-quadratic potentials, the non-uniform onset of oscillation can drive large non-Gaussianity of either sign, and hilltop pseudo-Nambu-Goldstone curvatons predict 10 <~ f_NL <~ 30.
Duality Invariance of Cosmological Perturbation Spectra
gr-qc 1998-09 conditional novelty 5.0 of 10

A two-parameter transformation of the cosmological scale factor leaves the spectral index of scalar and tensor perturbations unchanged, relating slow-roll inflation to far-from-slow-roll and collapsing cosmologies.
A multi-axion model of inflation and dark matter
hep-ph 2026-07 reject novelty 4.0 of 10

A 300-mode Kaluza-Klein axion tower is proposed as a unified inflaton and dark-matter sector, but the lightest state's quoted lifetime contradicts the paper's own decay-rate formula.
Primordial blackholes from Gauss-Bonnet-corrected single field inflation
astro-ph.CO 2021-08 conditional novelty 4.0 of 10

Coupling the inflaton to the Gauss-Bonnet term creates a balance point where ultra-slow-roll inflation amplifies curvature perturbations enough to seed primordial black holes, with hand-tuned parameters giving either ...
Gravitational Waves from First-Order Phase Transition in a Simple Axion-Like Particle Model
hep-ph 2019-05 conditional novelty 4.0 of 10

A singlet complex scalar coupled to the Higgs can break its global U(1) in a first-order transition, generating gravitational waves that future detectors could use to probe axion decay constants from 10^3 to 10^8 GeV.
Rescuing Quartic and Natural Inflation in the Palatini Formalism
gr-qc 2018-12 conditional novelty 4.0 of 10

In the Palatini formulation, an R² term reshapes the Einstein-frame potential of minimally coupled quartic and natural inflation into a plateau, bringing their predicted spectral index and tensor-to-scalar ratio withi...
The ALP miracle revisited
hep-ph 2017-10 conditional novelty 4.0 of 10

A single axion-like particle with mass 0.01 to 1 eV and photon coupling of order 10^-11 GeV^-1 can plausibly drive inflation and account for dark matter, a window testable by next-generation axion experiments.
Inflation in $f(R,\phi)$-theories and mimetic gravity scenario
gr-qc 2015-04 conditional novelty 4.0 of 10

A scalar field coupled to f(R) gravity can drive inflation, exit gracefully, and match Planck's spectral index, with dark matter emerging as an integration constant in the mimetic extension.
Aligned Natural Inflation: Monodromies of two Axions
hep-th 2014-04 conditional novelty 4.0 of 10

Aligning two axion potentials produces an effective decay constant larger than the Planck mass from sub-Planckian inputs, giving a natural-inflation trajectory consistent with a large tensor-to-scalar ratio.
Axion inflation with gauge field production and primordial black holes
astro-ph.CO 2013-12 conditional novelty 4.0 of 10

Axion inflation with a gauge-field coupling predicts a large small-scale curvature spectrum; matching the resulting primordial black hole abundance to existing limits bounds the coupling at xi < 1.8 (quadratic potenti...
Physics potential of the International Axion Observatory (IAXO)
hep-ph 2019-04 conditional novelty 3.0 of 10

The paper argues that a large-scale solar axion helioscope would reach sensitivity to QCD axions and axion-like particles across the meV-to-eV mass range, covering several independent cosmological and astrophysical mo...
Clusters of primordial black holes
astro-ph.CO 2018-07 conditional novelty 3.0 of 10

Primordial black holes born in clusters, not spread uniformly, could survive existing abundance constraints and account for dark matter, early quasars, LIGO mergers, and unidentified gamma-ray sources, according to th...
CMB-S4 Science Book, First Edition
astro-ph.CO 2016-10 accept novelty 3.0 of 10

A community science book sets CMB-S4 targets: detect or bound primordial gravitational waves at r < 0.002, measure the neutrino mass sum near 15 meV, and pin the light-relic density to sigma(Neff) around 0.027.

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Said that the shape of its potential near the edge of the minimum is locally reminiscent of this paper's natural inflation potential involving a pseudo-Goldstone boson, except that both θ and τ must be simultaneously considered.

Preheating After Modular Inflation (2009) (same authors) · 0.96 · paraphrased: the licence does not allow quoting

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Such scenarios are multi-spectator generalizations of the rolling axion models of [ref] and of spectator chromonatural inflation (SCNI) models [ref] , themselves related to natural inflation [ref] .

Gravitational Axiverse Spectroscopy: Seeing the Forest for the Axions · Introduction · 0.87
Although string theory restricts the range of the original axion period in the first place, it then recycles a single axion via monodromy, providing a simple generalization of [ref] with its own distinctive predictions.

Gravity Waves and Linear Inflation from Axion Monodromy · Introduction: Axion Recycling · 0.97
In this paper, we will introduce and explore a two-field model that we unimaginatively dub “Generalized Natural Inflation” (GNI), a well-motivated generalization or “UV-completion” of the influential Natural Inflation (NI) scenario [ref] .

Non-Gaussianities in a two-field generalization of Natural Inflation · Introduction. · 0.97

Compares with it 4 papers

The shape of the potential near the edge of the minimum is locally reminiscent of the the racetrack inflation potential [ref] , as well as the “natural inflation” potential involving a pseudo-Goldstone boson [ref] (except that in our case both $θ$ and $τ$ must be simultaneously considered).

Preheating After Modular Inflation · Roulette Inflation · 0.96
This is in stark contrast to the model building challenge of Natural Inflation [ref] , where one must engineer a super-Planckian decay constant (for example, by alignment [ref] ), in conflict with the Weak Gravity Conjecture [ref] .

Observable Chiral Gravitational Waves from Inflation in String Theory · Constraints on Model Parameters for a Consistent Realization · 0.91
The idea of using dissipative dynamics to slow the motion of the inflaton is qualitatively similar to warm inflation [ref] and also to the variant of natural inflation [ref] proposed recently by Anber & Sorbo [ref] . * Observable features in the primordial power spectrum, generated by particle production and IR cascading, offer a novel example of the non-decoupling of high scale physics in the Cosmic Microwave Background (CMB) [ref] .

Nongaussianity from Particle Production During Inflation · Inflationary Particle Production · 0.81

Cites it as background 86 papers

Natural inflation [ref] is one of the best motivated scenarios to describe the inflationary expansion in the early universe.

Aligned Natural Inflation: Monodromies of two Axions · Introduction · 0.98
In this work we are interested in two particular inflationary models: the Natural inflation (NI) [ref] , and the Coleman-Weinberg Inflation (CWI) [ref] .

Massive neutrino self-interactions and inflation · Introduction · 0.91
Natural inflation model was suggested [ref] (also [ref] ).

A Case Study of Small Field Inflationary Dynamics in the Einstein-Gauss Bonnet Framework in the Light of $GW170817$ · Introduction · 0.95

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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