Towards Inflation in String Theory

Andrei Linde; Juan Maldacena; Liam McAllister; Renata Kallosh; Sandip P. Trivedi; Shamit Kachru

REVIEW

Towards Inflation in String Theory

Shamit Kachru, Renata Kallosh, Andrei Linde, Juan Maldacena, Liam McAllister, Sandip P. Trivedi

High Energy Physics - Theory · Submitted 7 Aug 2003 · 47 references

Pith's verdict: Two results that mattered — the redshift-flattened warped potential and the moduli-induced eta problem — with the negative half resting on a superpotential the authors openly admit they don't know.

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arXiv IDhep-th/0308055 (version 2)

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CitationAndrei Linde, Juan Maldacena, Liam McAllister, Renata Kallosh, Sandip P. Trivedi, Shamit Kachru. "Towards Inflation in String Theory." arXiv:hep-th/0308055 (2003). https://pith.science/paper/R4OVLLSM

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Editor's note

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This one is worth your time for two separate reasons. First, it shows that a D3-brane moving in a Klebanov-Strassler throat gets an exponentially flat potential from the redshift at the tip: eq. (3.9) and (4.10), with (r0/R)^4 = exp(-8 pi K / 3 g_s M). That disposes of the old flat-space eta problem of Dvali-Tye without large brane separations or tuned initial conditions. Second, and more consequentially, it shows that KKLT-style volume stabilization gives the D3 position modulus m^2 = 2H^2, i.e. eta = 2/3, which rules out sustained slow roll. The derivation is short and checkable: (5.15) through (5.18), with the conformal-coupling reading (5.19) as an independent cross-check. The blunt observation that essentially all prior brane-inflation papers ignored moduli stabilization is correct, and it reset what people had to specify in a model. Appendix F is also real work: it quantifies the escape routes at roughly one part in a hundred rather than hand-waving them away. Where it is soft: the word generic in the abstract is established for W = W(rho). Kahler invariance (5.7) forces W to depend on phi, section 5.1 says that dependence is unknown, and Appendix F shows a term g(rho)(1 + delta phi^2) can move m^2 anywhere for delta of order one half. The authors say this themselves, so it is not a hidden flaw, but it does make the negative result conditional. The more robust leg is the scaling argument (5.9)-(5.10): any energy scaling as r^{-alpha} with stabilization fixing rho gives m^2 = alpha H^2 regardless of the detailed W. That still assumes no compensating phi-dependence in X(rho, phi), so the live question is whether string theory supplies that compensation generically or only in special corners. The paper flags it and does not settle it, which is the right call for a first pass, but a reader should not take generic as proved. Minor: (5.17) prints (1 - phi phibar/3)^2 where the expansion of (5.15) is (1 - phi phibar/3)^{-2}. The final (5.18) is right, so it is a typo. Who should read it: anyone working on string inflation or moduli stabilization. It set the agenda for the next decade of the subject. Recommendation: send it to referees. The computations are explicit, the limitations are stated, and the negative result is worth publishing even in conditional form.

Referee report

Significance

This is an important and timely negative result. It takes the recently constructed warped de Sitter vacua and asks the obvious next question, whether a mobile brane in the same throat inflates, and answers it with an explicit, checkable supergravity computation rather than a hand-waving estimate. The identification of the obstruction as the conformal coupling of the D3 modulus, Eq. (5.19), is a clean cross-check that makes the result credible independent of the details of the stabilizing superpotential. The paper is also careful to state what it does not know: the phi-dependence of W is flagged as unknown in Section 5.1, and Appendix F quantifies the fine-tuning that could evade the obstruction. The scenario of Section 3-4 and the eta = 2/3 obstruction have both been widely taken up, and the paper sets a clear agenda for subsequent work on moduli stabilization and brane inflation. The computations are explicit and reproducible from the stated inputs.

Major objections (3)

[Section 5.1, Eqs. (5.9)-(5.10) and (5.15)-(5.18)] The abstract's 'typically' rests on two arguments that are presented as independent but are closer than the text suggests. Eqs. (5.15)-(5.18) derive m_phi^2 = 2 H^2 for W = W(rho), and the paper correctly notes in Section 5.1 that Kahler invariance (5.7) requires W to depend on phi and that this dependence is unknown. The scaling argument (5.9)-(5.10) is then offered as support that does not rely on the detailed form of W, but it assumes X = X(rho) with no compensating phi-dependence in X(rho, phi), which is the same assumption in a different guise. The unresolved load-bearing question is therefore not whether W = W(rho) is wrong, but whether string theory generically realizes the compensating phi-dependence that Appendix F shows can tune m_phi^2 to zero. The paper flags this honestly, but the abstract and conclusion would be strengthened by tying 'typically' explicitly to the assumption that the energy source depends on rho alone.
[Section 5.1, Eq. (5.14) and the D/(2r)^2 term] The numerical value eta = 2/3 depends on the exponent alpha = 2 in the energy scaling V ~ r^{-alpha}: expanding V = V0 (1 - phi phibar/(2 rho))^{-alpha} gives m_phi^2 = alpha H^2, so alpha = 2 is what produces 2 H^2. The text asserts that the warped anti-D3 tension scales like (1/r^3) e^{4A} and that with e^{4A} ~ r exp(-8 pi K / 3 g_s M) this yields the D/(2r)^2 term, differing from the corresponding term in [7] by a factor of r. This scaling is load-bearing for the central number and should be shown explicitly rather than stated, since a different alpha would change eta and hence the strength of the obstruction.
[Appendix F, Eq. (F.8) and the following paragraph] The illustrative arithmetic does not check out. With beta = 1/2, the combination beta - 2 beta^2 vanishes identically, so Eq. (F.8) gives m_phi^2 = 2 H^2 for every value of |V_AdS|/V_dS, not the claimed variation from 2 H^2 to -2 H^2 over 0 < |V_AdS|/V_dS < 4. Reaching m_phi^2 = -2 H^2 requires (|V_AdS|/V_dS)(beta - 2 beta^2) = 2, and since beta - 2 beta^2 is maximized at 1/8 for beta = 1/4, this needs |V_AdS|/V_dS = 16, outside the quoted interval. Please correct either the value of beta or the interval. This matters because the 'one part in 100' fine-tuning quoted in footnote 1 and repeated in the conclusion is drawn from this example.

Minor objections (5)

[Section 5.1, Eq. (5.17)] The printed factor (1 - phi phibar/3)^2 should be (1 - phi phibar/3)^{-2}, as follows from the exponent -2 in Eq. (5.15). The final result (5.18) is correct, so this is a typographical slip, but as printed the intermediate step would give the wrong sign for the mass.
[Appendix A, Eq. (A.4)] The smeared negative term is introduced as 'a minimal modification' and justified as 'reasonable to assume' for approximately homogeneous transverse spaces. Since the conclusion (A.6), eta <= -2/3, is used to argue that flat-space brane inflation fails, the assumption deserves a sentence of justification or an explicit statement of the class of compactifications to which it applies.
[Section 5.1, literature remark] The sentence that 'essentially all papers on the subject ... have ignored the problem of moduli stabilization' is a strong claim about the literature. It would be better supported by naming a few representative references, or softened to 'most'.
[Section 3.2] The conformal coupling term T3 (1/2) r1^2 R is introduced and noted to give a large contribution to eta, with the resolution deferred to Section 5. A forward pointer at this point would help the reader understand that the flat potential of Eq. (3.9) is not yet the final answer.
[Section 2, Eq. (2.2)] The displayed expression appears to contain T3 cubed in the numerator; please check the power, since the corresponding term in Eq. (2.1) involves T3 squared.

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The paper

The paper claims

Warped brane inflation survives only if volume stabilization leaves the brane position light, a condition the paper argues is non-generic.

The reading

This paper asks whether brane–antibrane inflation can survive being embedded in a fully stabilized string compactification. Warping a throat makes the D3–anti-D3 potential exponentially flat, so the naive slow-roll parameters are tiny. But stabilizing the overall volume with a nonperturbative superpotential, as in the de Sitter constructions the authors build on, also makes the brane-position field feel the volume minimum; expanding the F-term potential around that minimum gives $m^2=2H^2$, i.e. $|eta|=2/3$, which is too steep for sixty e-foldings. The authors conclude that inflation is possible only under restrictive, non-generic choices: Kähler stabilization of the volume, special warping, or a finely tuned dependence of the superpotential on the brane position.

What carries the argument

The argument turns on two objects. First, the warped throat gives the D3–anti-D3 potential $V=2T_3|frac{r_0^4}{R^4}(1-|frac{1}{N}|frac{r_0^4}{r_1^4})$, whose redshift factor makes the inflaton potential exponentially flat. Second, the Kähler potential $K=-3|log(|rho+|bar|rho-k(|phi,|bar|phi))$ has a no-scale cancellation, so a constant superpotential leaves the brane modulus free; once a nonperturbative term $Ae^{-a|rho}$ stabilizes the volume, the same Kähler potential converts the volume minimum into a mass term $|frac{2}{3}|phi|bar|phi$ for the brane position. The mechanism carrying the paper is therefore the mixing of the volume modulus and the inflaton in the Kähler potential, not the brane–antibrane force itself.

Extended reading notes

Core claim

The central claim is negative but sharp. In the warped type IIB compactifications of [5] with the volume stabilized as in [7], the four-dimensional supergravity potential for the volume modulus $|rho$ and brane position $|phi$ has a no-scale Kähler potential $K=-3|log(|rho+|bar|rho-k(|phi,|bar|phi))$. Substituting a volume-stabilizing $W(|rho)$ and expanding about the de Sitter minimum gives $V|simeq V_0(1+|frac{2}{3}|phi|bar|phi)$, hence $m_|phi^2=2H^2$ and $|eta=2/3$. The authors identify this as the conformal coupling of a scalar in a spacetime with cosmological constant, and note that the same result could have been anticipated from the AdS/CFT dual of the warped throat. They then argue that only non-generic stabilization mechanisms or a finely tuned $|phi$-dependence of $W$ can cancel this mass.

Load-bearing premise

The derivation drops the brane-position dependence of the nonperturbative superpotential, even though Kähler invariance requires some, so the universal $m^2=2H^2$ holds only for the special case $W=W(|rho)$.

Editorial extensions

If this is right

Warped brane–antibrane inflation with KKLT-type superpotential volume stabilization predicts $|eta=2/3$ and cannot produce sixty e-foldings, so any working model must change the stabilization mechanism or introduce a compensating $|phi$-dependence in $W$.
If the volume is stabilized by corrections to the Kähler potential instead, the flat warped potential can survive, and the paper's Appendix C estimates then apply: $n_s|approx0.97$, a very small tensor-to-scalar ratio, and an inflation scale around $10^{14}$ GeV.
The inflaton-mass problem is general for any energy source scaling as $r^{-|alpha}$ with $|alpha>0$ once the volume is fixed, so it also constrains D$p$–D$|bar p$ and branes-at-angles models with induced D3 charge.
The fine-tuning needed to cancel the mass is about one part in 100, not extraordinary, and eternal inflation may make the rare inflating regions cosmologically relevant.
Warping exponentially suppresses the tension of cosmic strings produced at brane–antibrane annihilation, easing a separate observational problem for the exit from inflation.

Reading between the lines

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

The paper's 'generic' verdict is conditional on the unknown nonperturbative superpotential: a direct calculation of $W(|rho,|phi)$ in a global flux compactification would turn the one-percent fine-tuning estimate into a yes-or-no test of whether the compensating term can arise naturally.
If the inflaton mass is tied to the volume minimum, then stabilization mechanisms that fix the volume while leaving the brane position light should be observationally distinguishable through $n_s$ and the tensor-to-scalar ratio, giving a way to favor or exclude the surviving branch.
The conformal-mass result suggests a broader statement: whenever the brane modulus is dual to a conformal scalar in a warped throat, stabilizing the volume at positive vacuum energy will induce $m^2=2H^2$ unless the superpotential has a compensating dependence on the brane position.
Because the required tuning is only about one percent, a statistical count of flux choices could estimate what fraction of stabilized vacua admit slow roll, converting the authors' anthropic remark into a quantitative landscape question.

Original abstract

We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well-known difficulty of brane-antibrane scenarios. Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation models can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied. We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory.

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, 4,896 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.35 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well-known difficulty of brane-antibrane scenarios. Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation models can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied. We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory.

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	We investigate the embedding of brane inflation into stable compactifications of string theory.	contribution 0.98	0.90	0.02	asserted 0.68
s1	At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well-known difficulty of brane-antibrane scenarios.	background 0.85	0.13	0.02	hedged possibility 0.75
s2	Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation.	result 0.93	0.49	0.09	asserted 0.91
s3	We discuss the non-generic conditions under which this problem does not arise.	contribution 0.88	0.76	0.04	asserted 0.55
s4	We conclude that brane inflation models can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied.	result 0.81	0.81	0.91	asserted 0.95
s5	We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory.	interpretation 1.00	0.48	0.11	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 0.69 · evidence from argument 0.83.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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S sections
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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

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Cosmic F- and D-strings
hep-th 2003-12 accept novelty 8.0 of 10

Long-lived cosmic strings built from bound fundamental and Dirichlet strings can exist in brane-inflation models, with tensions near 10^-10 to 10^-9 in G-mu, inside the reach of planned gravitational-wave detectors.
A Ghost-Free dS/AdS Correspondence in $\mathcal{N}=1$ Supergravity
hep-th 2026-11 accept novelty 7.0 of 10

A reflection of the goldstino Kähler metric reverses the scalar potential pointwise, giving ghost-free partner N=1 supergravities with a sharp dS/AdS stability dictionary.
Catastrophic Inflation in the Axiverse
hep-th 2026-08 conditional novelty 7.0 of 10

String-theory axions in explicit Calabi-Yau compactifications can produce small-field slow-roll inflation via volume-tuned catastrophes, though no example yet matches both the observed tilt and amplitude of density pe...
Cosmic superstrings in large volume compactifications: PTAs, LISA and time-varying tension
astro-ph.CO 2025-04 conditional novelty 7.0 of 10

Cosmic superstrings with a time-varying tension in large-volume string compactifications generically predict a LISA-band spectral drop and a high-frequency f^4 boost, encoding the mass and decay of the volume modulus.

Show 55 more citing papers

Chiral global embedding of Fibre Inflation with $\overline{\rm D3}$ uplift
hep-th 2024-12 conditional novelty 7.0 of 10

Explicit construction of a chiral global embedding of Fibre Inflation with anti-D3 uplift on an h^{1,1}=4 K3-fibered Calabi-Yau, using magnetised D7-branes, a Whitney brane, and O3-planes at a conifold tip, with viabl...
Fayet-Iliopoulos terms in supergravity without gauged R-symmetry
hep-th 2017-12 conditional novelty 7.0 of 10

A new non-linear coupling of a vector multiplet to supergravity generates a D-term that breaks supersymmetry without gauging R-symmetry, yielding a positive uplift of the scalar potential.
Non-extremal Black Hole Microstates: Fuzzballs of Fire or Fuzzballs of Fuzz ?
hep-th 2012-08 conditional novelty 7.0 of 10

Placing metastable supertubes inside scaling supersymmetric microstate geometries yields horizonless solutions with the mass and charges of near-extremal black holes, whose throat lengths can be tuned to match, exceed...
D3-brane Potentials from Fluxes in AdS/CFT
hep-th 2010-01 conditional novelty 7.0 of 10

The D3-brane potential in a warped conifold receives its leading infrared term from the square of imaginary anti-self-dual flux, with the full spectrum of scaling dimensions classified and matched to the dual conforma...
On the Existence of Meta-stable Vacua in Klebanov-Strassler
hep-th 2009-12 conditional novelty 7.0 of 10

The unique linearized Klebanov-Strassler deformation consistent with smeared anti-D3 branes in the ultraviolet has a finite-action infrared singularity in the three-form fluxes, so the metastable vacuum exists only if...
Monodromy in the CMB: Gravity Waves and String Inflation
hep-th 2008-03 conditional novelty 7.0 of 10

Monodromy of a D4-brane on a Nil manifold yields a phi^(2/3) inflaton potential, predicting ns around 0.98 and r around 0.04, a testable gravitational-wave signature from string theory.
Towards an Explicit Model of D-brane Inflation
hep-th 2007-06 conditional novelty 7.0 of 10

For the Kuperstein D7 embedding, the full D3-brane inflaton potential including moduli-stabilization corrections can be fine-tuned to support slow-roll inflation near an inflection point, while ACR embeddings admit no...
On Tunnelling In Two-Throat Warped Reheating
hep-th 2006-02 conditional novelty 7.0 of 10

The self-consistent decay rate for KK modes transferring energy between two warped throats equals the standard plane-wave tunnelling rate, and the rate can be enhanced by modifying the UV geometry.
Dynamics of warped compactifications and the shape of the warped landscape
hep-th 2005-07 conditional novelty 7.0 of 10

A ten-dimensional formula for the potential of warped flux compactifications is derived, yielding a slope-dominance criterion for de Sitter vacua and a warping-corrected definition of holomorphic Kahler moduli.
Large-Volume Flux Compactifications: Moduli Spectrum and D3/D7 Soft Supersymmetry Breaking
hep-th 2005-05 conditional novelty 7.0 of 10

In Calabi-Yau flux vacua with exponentially large volume, moduli masses and D3/D7 soft supersymmetry-breaking terms follow a hierarchy set by inverse powers of the volume, dominated by the large Kahler modulus F-term.
Landscape, the Scale of SUSY Breaking, and Inflation
hep-th 2004-11 conditional novelty 7.0 of 10

In the simplest KKLT model the inflationary Hubble scale is bounded by the gravitino mass, but a racetrack superpotential with a supersymmetric Minkowski minimum decouples the two scales.
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.
DBI in the Sky
hep-th 2004-04 conditional novelty 7.0 of 10

DBI inflation predicts equilateral non-Gaussianity with |f_NL| of order 0.32 gamma squared, bounded below at an observable level, and favors large tensor modes.
Scalar Speed Limits and Cosmology: Acceleration from D-cceleration
hep-th 2003-10 conditional novelty 7.0 of 10

Causality in the dual AdS geometry imposes a speed limit on the N=4 SYM scalar moduli, and coupling that DBI-corrected field theory to gravity yields power-law inflation from an ordinary quadratic potential at subPlan...
Production of Primordial Black Holes in the Double D3-Brane - anti-D3-Brane Inflation Model
hep-th 2026-08 reject novelty 6.0 of 10

In a double D3-anti-D3 brane inflation model, Myers dielectric effect may turn D1-strings into neutral 3-branes seeding primordial black holes, but the mass distribution is not derived.
Gravitational Waves from Multiple Cosmic Superstrings and the Overshoot Problem
hep-th 2026-07 conditional novelty 6.0 of 10

A string-theory model with three cosmic superstring species solves the modulus overshoot problem via gravitational-wave friction and predicts a high-frequency multi-peaked stochastic gravitational-wave spectrum.
Unification of polynomial and exponential cosmological attractors
hep-th 2026-07 conditional novelty 6.0 of 10

Embedding polynomial attractor potentials within α-attractor geometry yields a unified model class that interpolates between exponential and polynomial inflationary predictions via a single parameter μ.
Massive Graviton Dark Matter from a Gapped Continuum
hep-th 2026-07 conditional novelty 6.0 of 10

Radiative corrections pull an isolated, long-lived massive graviton out of the gapped linear-dilaton continuum, giving a sub-MeV dark-matter candidate that can coexist with a holographic fluid component.
DeepInflation: an AI agent for research and model discovery of inflation
astro-ph.CO 2026-01 conditional novelty 6.0 of 10

An LLM agent with symbolic regression finds simple inflation potentials that match target CMB observables, but the outputs are fitted to the targets rather than independently predicted.
Perturbative K\"ahler Moduli Inflation
hep-th 2025-06 reject novelty 6.0 of 10

Two classes of slow-roll inflation potentials, V0(1+C1 φ^(2/3)) and V0(1-C2 φ^(-2/3)), are derived from perturbative Kähler moduli stabilization and give r below 10^-2 and 10^-8.
Superheavy Dark Matter from the String Theory Axiverse
hep-th 2025-04 conditional novelty 6.0 of 10

Heavy axions from a simple string-theory compactification can be produced in large numbers by gravitational particle production at the end of inflation and can account for all dark matter, provided they remain stable ...
Supermassive primordial black holes in multiverse: for nano-Hertz gravitational wave and high-redshift JWST galaxies
gr-qc 2023-06 conditional novelty 6.0 of 10

When the inflaton rolls past a neighboring vacuum during inflation, the nucleation rate of supercritical bubbles peaks, producing a peak in the primordial black hole mass spectrum that can reach 10^11 solar masses.
UV Shadows in EFTs: Accidental Symmetries, Robustness and No-Scale Supergravity
hep-th 2020-06 conditional novelty 6.0 of 10

Accidental scaling symmetries of ten-dimensional supergravity, combined with supersymmetry and axionic shifts, fix the all-orders form of the four-dimensional Kähler potential and explain why no-scale structure is ubi...
Constraining axion inflation with gravitational waves across 29 decades in frequency
astro-ph.CO 2019-09 conditional novelty 6.0 of 10

Gravitational waves from gauge preheating after axion inflation contribute enough to Neff that Planck data already gives the tightest bound on the inflaton-gauge coupling, and CMB-S4 would rule out efficient preheating.
de Sitter Vacua from Ten Dimensions
hep-th 2019-08 conditional novelty 6.0 of 10

Gaugino condensation on D7-branes plus anti-D3-branes produce a ten-dimensional stress-energy that exactly reproduces the KKLT four-dimensional scalar potential and curvature.
Gaugino condensation and small uplifts in KKLT
hep-th 2019-02 conditional novelty 6.0 of 10

KKLT's ten-dimensional tadpole is canceled by a non-local restoring-force term once supersymmetry breaks, and geometrically consistent warped uplifts are hard to engineer in generic Calabi-Yau compactifications.
The stochastic spectator
astro-ph.CO 2017-01 accept novelty 6.0 of 10

For a quadratic spectator during monomial inflation the de Sitter equilibrium never describes the field value at the end of inflation; the outcome instead depends on whether an early adiabatic phase erased the initial...
The Goldstino Brane, the Constrained Superfields and Matter in N=1 Supergravity
hep-th 2016-08 conditional novelty 6.0 of 10

The goldstino brane and constrained superfield descriptions of spontaneously broken N=1 supergravity with matter are shown to be equivalent, with the brane picture additionally producing a gravitino mass term and repr...
Global String Embeddings for the Nilpotent Goldstino
hep-th 2015-12 conditional novelty 6.0 of 10

Two explicit Calabi-Yau compactifications are built that embed the nilpotent Goldstino (an anti-D3-brane on an O3-plane at a warped conifold tip) globally, one via an F-theory construction and one by retrofitting an e...
String Theory Realizations of the Nilpotent Goldstino
hep-th 2015-07 accept novelty 6.0 of 10

A single anti-D3-brane on an O3-plane in a warped IIB throat has exactly one massless worldvolume fermion, matching the goldstino of a nilpotent chiral superfield.
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.
Emergence of Spontaneously Broken Supersymmetry on an Anti-D3-Brane in KKLT dS Vacua
hep-th 2014-11 conditional novelty 6.0 of 10

With an orientifold-compatible kappa-gauge, the anti-D3-brane's DBI and Wess-Zumino terms add to twice the Volkov-Akulov action while the D3-brane's cancel, giving the KKLT uplift a goldstino origin in flat space.
${\cal R}^2$ inflation from scale invariant supergravity and anomaly free superstrings with fluxes
hep-th 2014-09 conditional novelty 6.0 of 10

Scale-invariant R-squared supergravity, with the scale-breaking Einstein term generated by anomaly cancellation via an axion shift, yields Starobinsky-like inflation and can be embedded in string flux compactifications.
Cosmology with Nilpotent Superfields
hep-th 2014-08 conditional novelty 6.0 of 10

Imposing S squared equals zero on the goldstino chiral multiplet removes the sgoldstino scalar from a wide class of supergravity inflation and KKLT uplifting models, simplifying them and tying them to Volkov-Akulov an...
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...
DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios
hep-th 2012-09 accept novelty 6.0 of 10

The pseudo-conformal symmetry-breaking pattern can be realized by a DBI probe brane in an AdS bulk, giving subluminal perturbations and a geometric, shift-protected weight-zero field with a scale-invariant spectrum.
A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow Roll
astro-ph.CO 2012-07 conditional novelty 6.0 of 10

In an ensemble of six-field string inflation models, multifield and many-field corrections to the power spectrum are common, but in models matching the observed tilt they occur almost entirely on unobservably large scales.
The backreaction of anti-D3 branes on the Klebanov-Strassler geometry
hep-th 2011-06 conditional novelty 6.0 of 10

All fifteen integration constants of the linearized anti-D3 brane deformation of the Klebanov-Strassler geometry are fixed in terms of the antibrane number, leaving a UV rescaling mode whose field-theory interpretatio...
Universality in D-brane Inflation
astro-ph.CO 2011-03 conditional novelty 6.0 of 10

Across more than 70 million realizations of six-field D-brane inflation, the probability of N e-folds is a power law with exponent near 3, and observationally viable single-field cases require at least 120 e-folds and...
Axions as Quintessence in String Theory
hep-th 2010-11 conditional novelty 6.0 of 10

A 5-brane/anti-5-brane pair in warped throats of a IIB flux compactification can give an axion a linear potential flat enough to drive quintessence, with slow roll met when the axion sits near the Planck scale.
Oscillations in the CMB from Axion Monodromy Inflation
hep-th 2009-07 conditional novelty 6.0 of 10

Axion monodromy inflation produces a sinusoidally modulated scalar power spectrum whose amplitude and frequency can be bounded by CMB data, and detectable modulations arise in consistent string compactifications.
Gravitational Waves from Broken Cosmic Strings: The Bursts and the Beads
astro-ph.CO 2009-03 conditional novelty 6.0 of 10

A network of metastable cosmic strings that decays by monopole pair nucleation produces 1/f gravitational wave bursts and a scale-invariant stochastic background, detectable by Advanced LIGO for tensions down to G mu ...
Running Inflation in the Standard Model
hep-ph 2008-12 conditional novelty 6.0 of 10

Two-loop renormalization group running makes the inflationary spectral index rise from 0.968 toward 0.98 as the Higgs mass approaches the vacuum stability bound near 126 GeV.
Gravity Waves from Tachyonic Preheating after Hybrid Inflation
astro-ph 2008-12 conditional novelty 6.0 of 10

Gravitational waves from tachyonic preheating after hybrid inflation follow simple power laws in the model parameters, and reaching Advanced LIGO frequencies requires extremely small coupling constants.
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.
Generalized non-supersymmetric flux vacua
hep-th 2008-07 conditional novelty 6.0 of 10

A classification of non-supersymmetric type II flux vacua by which D-branes remain BPS, yielding no-scale Minkowski examples and new AdS4 solutions.
Volume Modulus Inflation and the Gravitino Mass Problem
hep-th 2008-06 conditional novelty 6.0 of 10

In large-volume string compactifications the inflation bound tightens to H < m_{3/2}^{3/2}, and a toy model shows a long post-inflationary runaway guided by a radiation tracker can still settle into a TeV-gravitino vacuum.
D-brane Deconstructions in IIB Orientifolds
hep-th 2008-05 accept novelty 6.0 of 10

The correct D3 charge, moduli count, and flux lattice dimension for singular D7-branes in IIB orientifolds are given by the topology of an auxiliary surface that resolves the double intersection with the O7-plane.
Dynamics of Warped Flux Compactifications
hep-th 2008-03 conditional novelty 6.0 of 10

Warp corrections to the four-dimensional effective action of type IIB flux compactifications leave kinetic terms diagonal in a warped KK basis and modify the complex structure Kähler potential relative to prior proposals.
Duality Cascade in Brane Inflation
hep-th 2008-02 conditional novelty 6.0 of 10

Steps in a warped throat from the Seiberg duality cascade would produce small power-spectrum glitches but potentially large, distinctive non-Gaussianity in brane inflation, giving a possible CMB probe of string theory.
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.
Inflationary Constraints on Type IIA String Theory
hep-th 2007-11 accept novelty 6.0 of 10

In type IIA Calabi-Yau compactifications with standard fluxes, D6-branes and O6-planes at large volume and weak coupling, the slow-roll parameter obeys epsilon >= 27/13 wherever the potential is positive, so inflation...
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.
Spinflation
hep-th 2007-09 conditional novelty 6.0 of 10

Angular momentum in DBI brane inflation buys a handful of extra e-foldings but does not resolve the tension between sufficient inflation and controllable backreaction in the Klebanov-Strassler throat.
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.

See all 140 Pith citations

How later papers used it

406 later papers cite it

Evidence: substantial. 360 of the citing papers share no author with it, and 32 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 771 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

4 later papers by other authors are listed below: 3 built on it and 1 cited it as support. 2 more papers by the same authors are listed: 1 used its method or tool and 1 compared its own results with it.

Builds on it 3 of 8 papers with this label

Considered a simple generalization of this paper by introducing multiple stacks of moduli-stabilizing D7-branes extending into the warped throat where the inflationary D3-brane resides.

Inflation on an Open Racetrack (2009) · 1.00 · paraphrased: the licence does not allow quoting
Considered a generalization of the KKLMMT model of this paper in which the uplifting has an a priori generic scaling.

Inflation at the Tip (2008) · 0.97 · paraphrased: the licence does not allow quoting
Showed as a byproduct that eternal inflation of stochastic type is possible in this paper's KKLMMT setup with multiple Klebanov-Strassler throats.

Disorder on the landscape (2008) · 0.83 · paraphrased: the licence does not allow quoting

Uses its method or tool 1 of 7 papers with this label · 1 by the same authors

By the same authors

Followed the strategy of this paper, which proposes a computation of the D3/D3bar potential in warped geometries.

Planck 2018 and Brane Inflation Revisited (2018) (same authors) · 0.99 · paraphrased: the licence does not allow quoting

Compares with it 1 of 20 papers with this label · 1 by the same authors

By the same authors

Checked its own linearized solution by comparison with this paper's calculation of the force between a well-separated brane/antibrane pair in a warped throat.

A Gravity Dual of Metastable Dynamical Supersymmetry Breaking (2008) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

Cites it as support 1 of 6 papers with this label

Noted that, unfortunately, this is generically the case, citing this paper.

Chasing Brane Inflation in String-Theory (2007) · 0.96 · paraphrased: the licence does not allow quoting

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391 arXiv papers cite this in 756 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 · 459 sentences without a confident label

Contests it 1 paper

The first idea for an uplift, due to Kachru, Pearson, and Verlinde (KPV) [ref] , proposes that $p$ anti-D3-branes at the bottom of a Klebanov-Strassler warped throat region can break supersymmetry, with[The denominator was given as $(T+T)^3$ in [ref] and corrected to $(T+T)^2$, which properly accounts for the warping, in [ref] : see the treatment in [ref] .] [equation] where [equation] Here $T_D3$ is the D3-brane tension, $y_IR$ is the location of the tip of the warped throat inside $X_6$, and $e^A(y)$ is the warp factor from [ref], evaluated in the Klebanov-Strassler solution [ref] .

Moduli Stabilization in String Theory · Supersymmetry breaking and de Sitter uplift · contest 0.74

Builds on it 8 papers

Thus, we consider a simple generalization of [ref] by introducing multiple stacks of moduli-stabilizing D7-branes with extent into the warped throat where the inflationary D3-brane resides.

Inflation on an Open Racetrack · Introduction and Summary · 1.00
After reviewing the basic KKL(MM)T model [ref] , we port it from type IIB to IIA in section [ref] [ref] .

Flux Compactifications, dS Vacua and the Swampland · Abstract · 0.82
This suggests the idea of redoing the analysis of KKLMMT [ref] for a generic uplifting, i.e. $D/U^b$ instead of $D/U^3$.

Inflation at the Tip · Radial stability · 0.91

Uses its method or tool 7 papers

* We followed the approach of [ref] which introduced warping to obtain a flat potential that can drive inflation with an interbrane separation that is correctly smaller than the size of the extra dimensions.

Back to the origins of brane-antibrane inflation · Conclusions · 0.86
For a non-perturbative superpotential of the form $W_np = A (1 - Δ(t_0) y_3^2 + …) e^-i a s ,$ where $t_0$ is the value of the complex structure fixed by the choice of fluxes, one can compute the F-term potential following a similar computation in Appendix F of [ref] (using the relation $is = ρ$ between our variable and the one employed there).

Update of D3/D7-Brane Inflation on K3 x T^2/Z_2 · New features of the model with stringy corrections · 0.81
We can use the same idea used in [ref] to calculate the potential between the D3 and the anti-D3 in the KS geometry.

Towards brane-antibrane inflation in type $II_A$: The holographic MQCD model · Adding the spiralling brane · 0.99

Uses its data or values 8 papers

According to the investigation in Appendix C of [ref] , the value of $n_s$ in the D-brane inflationary model with $V ∼1- (mϕ)^4$ in the small $m$ (small $r$) limit is given by n_s = 1-53 N_e .

Planck 2018 and Brane Inflation Revisited · Introduction · 0.89
We shall settle on the value $w _A = 10^-4$ advocated in [ref] and the value $w _S = 2 10^-14$ advocated in [ref] , which is larger than that adopted in warped models $e ^-kπr_C ≃4.2 10^-16$.

Warped modes in flux compactification of type II b supergravity on the conifold · Warped modes in early universe · 0.99
The exponent $α= 2$ for anti-branes located in a highly warped region, i.e. at the bottom of the throat [ref] .

Small cosmological signatures from multi-brane models · The potential · 0.87

Compares with it 20 papers

We then used this solution to compute the force exerted on a probe M2 brane placed in the anti–M2 backreacted supergravity background and we showed that it exactly agrees with the calculation à la KKLMMT [ref] in which one considers the anti–M2 brane as probing the backreacted geometry of M2 branes on the Stenzel background[ The agreement between the functional form of these two results has been derived in [ref] .

Metastable Vacua and the Backreacted Stenzel Geometry · Conclusions · 0.96
Furthermore, the leading large–distance behavior of the inflaton potential agrees with the one computed in [ref] .

On The Inflaton Potential From Antibranes in Warped Throats · Introduction and Motivation · 1.00
Instead, our results show that F-term axion monodromy constructions such as Higgs-otic inflation face the same challenges as the NS5-brane models of [ref] , and manifest in these models the well-known couplings of moving branes to nonperturbative superpotential terms that plague D3-brane inflation scenarios [ref] .

Monodromy Charge in D7-brane Inflation · Conclusions · 0.88

Cites it as support 4 papers

It is known that one can evade the Maldacena-Nunez theorem taking into account higher-order curvature corrections and negative tension O-planes [ref] , as stressed in [ref] .

The landscape, the swampland and the era of precision cosmology · Discussion and conclusions · 0.98
Unfortunately, this is generically the case [ref] .

Chasing Brane Inflation in String-Theory · Introduction · 0.96
Notice that, as shown in Ref. [ref] , if the separation between brane and antibrane is sufficiently large, the Coulomb potential does not depend on the angular coordinates.

Towards multi-field D-brane inflation in a warped throat · An explicit inflaton potential: Ouyang embedding case · 0.96

Cites it as background 204 papers

Despite their consequential applications in holographic QFT [ref] , string cosmology [ref] , and black hole physics [ref] , some aspects of these anti-branes configurations are not yet fully understood.

On matched asymptotic expansions of backreacting metastable anti-branes · Introduction · 0.97
Such anti-branes are part of the “staple diet” of string phenomenology and string cosmology constructions: they are a crucial ingredient in the KKLT construction of de Sitter space [ref] and in the KKLMMT model for string theory inflation [ref] .

On the Existence of Meta-stable Vacua in Klebanov-Strassler · Introduction · 0.96
In this paper we find robust predictions in a surprising place: warped D-brane inflation [ref] , a well-studied scenario for inflation in string theory in which six (or more) dynamical fields are governed by a scalar potential with hundreds of terms.

Universality in D-brane Inflation · Introduction · 0.82

Discussion

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