Analysis of inflationary models in higher-dimensional uniform inflation

Takuya Hirose

REVIEW 2 major objections 4 minor 2 cited by

Analysis of inflationary models in higher-dimensional uniform inflation

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims that uniformly expanding extra dimensions during inflation are ruled out by Planck 2018 data except for a single extra dimension, and only in narrow model windows.

desk verdict The general-D formulas are clean, but the D=1 survivor points sit in the b0k << 1 branch the paper assumes away, so the headline exception is likely an artifact. read the letter →

arxiv 2501.13581 v1 pith:7G77NF75 submitted 2025-01-23 hep-ph astro-ph.COhep-th

Takuya Hirose This is my paper · ORCID

classification hep-phastro-ph.COhep-th

keywords higher-dimensionaluniforminflationextradimensionscosmologicalperturbationsspectralindextensor-scalarratioKaluza-KleinmodesPlanck2018inflationarymodels

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether the extra dimensions of a higher-dimensional universe could have expanded at the same rate as our three space dimensions during inflation and still be compatible with the Planck 2018 measurements of the primordial power spectrum. It computes the cosmological perturbation spectra in $D+4$ dimensions and derives the slow-roll predictions $n_s = 1 - (D+6)\epsilon_V + 2\eta_V$ and $r = 8(D+2)\epsilon_V$ in the $b_0 k \gg 1$ limit. Five representative potentials are then tested against the Planck 2018 $n_s$--$r$ contours: chaotic inflation, natural inflation, quartic hilltop inflation, inflation with spontaneously broken SUSY, and $R^2$ inflation. The paper's conclusion is that uniform expansion is strongly disfavored for $D\ge 2$, while $D=1$ survives only in narrow windows. If correct, this is a direct cosmological argument against more than one uniformly expanding extra dimension during inflation.

What carries the argument

The machinery is a $(D+4)$-dimensional cosmological perturbation calculation about a background whose scale factors satisfy $a(t)=b(t)=e^{Ht}$, so the extra dimensions and ordinary space inflate in step. From the perturbed Einstein equations the paper builds two master variables, $\Theta$ and $\Omega$, linear combinations of the comoving curvature perturbation $R$ and the extra-dimension metric perturbation $\Xi$; these obey Mukhanov-Sasaki-type mode equations whose solutions give the scalar power spectrum. The tensor perturbation follows the same master equation, and the sum over Kaluza-Klein modes is encoded in the function $S_\nu((b_0 k)^2)$, evaluated in the two limits $b_0 k \ll 1$ and $b_0 k \gg 1$. The $b_0 k \gg 1$ limit yields the headline formulas $n_s = 1 - (D+6)\epsilon_V + 2\eta_V$ and $r = 8(D+2)\epsilon_V$, which carry the model-by-model comparison with Planck, with $\epsilon_V$ and $\eta_V$ the potential slow-roll parameters defined with a $(D+2)$ prefactor.

What would settle it

Compute the product $b_0 k_*$ at the Planck pivot scale $k_* = 0.002\ \mathrm{Mpc}^{-1}$ for each claimed viable model and $D$, using the paper's own relation between $b_0$, $M_*$, and $N_*$ (Eq. (2.14)). If any viable case has $b_0 k_*$ not much larger than 1, the asymptotic formulas for $n_s$ and $r$ fail and the $D=1$ exception must be re-derived from the full $S_\nu$ sums.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the spectral index and the tensor-to-scalar ratio become dimension-dependent when extra dimensions expand at the same rate as ordinary space. In the branch $b_0 k \gg 1$, the results are $n_s = 1 - (D+6)\epsilon_V + 2\eta_V$ and $r = 8(D+2)\epsilon_V$. The factor $(D+2)$ in $r$ means higher-dimensional models produce more tensor perturbations at fixed slow-roll parameters, and the extra $D\epsilon_V$ term in $n_s$ moves the tilt away from scale invariance. Applying these formulas to the five potentials and comparing with the Planck 2018 contours, the paper finds that chaotic inflation with $n\ge2$, natural inflation, quartic hilltop inflation, spontaneously broken SUSY inflation, and $R^2$ inflation are excluded for $D\ge2$; only $D=1$ remains viable in limited cases (chaotic $n=1$, and natural or quartic hilltop with $N_*>60$). The conclusion is that uniform expansion of extra dimensions is not desirable except possibly for one extra dimension.

Load-bearing premise

The load-bearing premise is that the observed CMB modes lie in the $b_0 k \gg 1$ branch; in the opposite branch $b_0 k \ll 1$ the spectral index picks up an extra $-D$ term and even $D=1$ would sit far outside the Planck window, but the paper does not prove the pivot scale satisfies $b_0 k \gg 1$ for every $D$.

Editorial extensions

If this is right

For $D\ge2$, none of the five potentials analyzed sits inside the Planck 2018 95% allowed region once uniform expansion is imposed.
$D=1$ survives only in narrow parameter windows: chaotic inflation with $n=1$ near $r\approx0.10$, and natural or quartic hilltop inflation with e-folds $N_*>60$.
The tensor-scalar ratio is enhanced by the factor $(D+2)$, so higher-dimensional uniform inflation generically predicts stronger B-mode signals than four-dimensional inflation at the same slow-roll parameters.
$R^2$ inflation, the best fit in four dimensions, is excluded for every $D\ge1$ because the $D$-dimensional corrections drive $n_s$ below and $r$ above the Planck window.
In the $b_0 k \ll 1$ branch the spectral index contains an additional $-D$ term, so scale invariance is destroyed for $D\ge1$; the viable $D=1$ conclusion rests entirely on the $b_0 k \gg 1$ branch.

Reading between the lines

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

Beyond the paper: the choice of branch $b_0 k \gg 1$ is assumed, not demonstrated. If the CMB pivot scale for a given $D$ actually lies in the $b_0 k \ll 1$ regime, the spectral index gains a $-D$ term and even $D=1$ would be far outside the Planck window.
Beyond the paper: the $D$-dependent tensor enhancement means future B-mode measurements could discriminate uniform higher-dimensional inflation from ordinary four-dimensional inflation before spectral-index analysis does: a detection of $r$ above the four-dimensional prediction with matching $n_s$ would point to $D\ge1$.
Beyond the paper: the analysis assumes a single inflaton and neglects radion stabilization during and after inflation; if stabilization backreacts on the perturbation equations, the derived $n_s$ and $r$ could be modified, and the paper itself flags this as future work.
Beyond the paper: the same method could be applied to extranatural inflation and moduli inflation, where the inflaton lives in the extra dimensions, and those models might evade the present bounds.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's the short version. The paper's new content is a general-D perturbation calculation for uniform higher-dimensional inflation: it reproduces the D=0 and D=1 limits, gives clean formulas ns = 1 - (D+6)ε + 2η and r = 8(D+2)ε in the b0k >> 1 regime, and applies them to five models. That's a useful, self-consistent piece of work, and the qualitative exclusion of D ≥ 2 is likely robust.

The problem is the branch choice. The paper asserts, 'Hereafter, we assume the b0k >> 1 case' without checking whether the CMB modes satisfy it. Using the paper's own relation bend = b0 e^{N*} and the dark-dimension benchmark bend ~ 10 μm with H ~ 10^13 GeV, the dimensionless ratio at horizon exit is b0k = bend H e^{-N*}. For N* = 60 that's ~10^-2, for N* = 70 it's ~10^-7—both deep in the b0k << 1 branch, where ns = 1 - (D+6)ε + 2η - D. For D=1 that gives ns ≈ -0.03, wildly outside Planck. The natural-inflation and quartic-hilltop D=1 survivors at 60 < N* ≤ 70 are exactly the points in the wrong branch, and the chaotic n=1 N*=60 point too. Only the N*=50 chaotic point might be in the b0k >> 1 branch, and it's borderline excluded. So the 'one extra dimension is viable' conclusion rests on an unstated, violated assumption. The D≥2 exclusions stand either way, but the interesting part of the abstract doesn't.

The radion is also treated without a stabilization mechanism; the paper says so explicitly. That's a genuine gap, but addressable. The finite list of five models is a minor caveat, and the author acknowledges it.

Who should read this? People working on the dark-dimension scenario and higher-dimensional inflation. The formalism is worth knowing; the interpretation is not. The paper deserves a serious referee—the calculation is non-trivial and the flaw is fixable. The author needs to either justify b0k >> 1 for the CMB scale or recompute the D=1 points in the correct branch. If the exception disappears, the paper becomes a less flashy but still valid exclusion of uniform expansion for D ≥ 2. I'd accept it for review with a request to address the branch issue head-on.

Referee Report

2 major / 4 minor

Summary. This paper analyzes (D+4)-dimensional uniform inflation, in which D compact extra dimensions expand at the same rate as the three non-compact spatial dimensions during inflation. The author derives the scalar and tensor power spectra from the perturbed Einstein equations, obtains the spectral index n_s and tensor-to-scalar ratio r in the two asymptotic regimes b0k << 1 and b0k >> 1, and then tests five inflationary models against Planck 2018 contours. The central quantitative results are n_s = 1 - (D+6)εV + 2ηV and r = 8(D+2)εV in the b0k >> 1 branch, and n_s = 1 - D - (D+6)εV + 2ηV in the b0k << 1 branch. The paper concludes that uniform expansion of the extra dimensions is disfavored by Planck data except possibly for D=1, where natural inflation and quartic hilltop inflation can survive at 60 < N* <= 70.

Significance. If the derivation and branch selection are correct, the paper would provide a useful constraint on higher-dimensional inflationary scenarios and on the dark-dimension proposal, since it would single out one extra dimension as the only viable case. The manuscript has genuine strengths: the perturbation calculation is carried out in full (D+4)-dimensional Einstein equations; the D=0 four-dimensional limit and the D=1 five-dimensional limit of Ref. [20] are reproduced; the formulas for n_s and r are derived rather than fitted; and the five model comparisons are internally consistent and transparent. The significance of the conclusion is, however, conditional on the b0k >> 1 branch being the physically relevant regime for the CMB pivot modes, and this is precisely the point that the manuscript assumes rather than demonstrates.

major comments (2)

[Section 3.6, Eqs. (3.58)-(3.60); Figs. 1-3] The statement 'Hereafter, we assume the b0k ≫ 1 case' is not a harmless choice. Equation (3.58) shows that in the b0k << 1 branch the spectral index is n_s = 1 - D - (D+6)εV + 2ηV, so for D=1 it differs from the b0k >> 1 prediction in Eq. (3.59) by an additive -1. Therefore the D=1 viable points in Figs. 2(a) and 3(a) (natural and quartic hilltop at 60 < N* <= 70) and the N*=60 chaotic n=1 point in Fig. 1 all depend entirely on the assumed branch. Moreover, the branch is not merely unproven: using the paper's own benchmark b0 ~ 10^-25 μm for D=1 and N*=60 (given after Eq. (2.14)) together with the pivot scale k* = 0.002 Mpc^-1 gives b0 k* ~ 10^-57, which is deep in the b0k << 1 regime. The author should either state explicitly the normalization or physical interpretation that would place the CMB pivot in the b0k >> 1 branch, or recompute all model predictions with Eq. (3.58) and revise the conclusions accordingly.
[Section 2.2, after Eq. (2.14); Section 3.1] The identification of b_end with the present-day extra-dimensional size and the use of Eq. (2.14) to estimate b0 presuppose that the radion is stabilized after inflation without changing the scale-factor history or the branch of the CMB modes. The manuscript explicitly states that radion stabilization is beyond its scope and refers to [20], so this is a stated limitation rather than an internal inconsistency. However, the b0k estimate that underlies the branch selection is load-bearing for the D=1 conclusion. A quantitative discussion of the stabilization scale and its backreaction is needed to justify treating b_end ~ 10 μm as the endpoint of uniform expansion, especially because the perturbed metric contains the radion-like variable Ξ whose dynamics is used in constructing the curvature perturbation but is never given a mass or potential.

minor comments (4)

[Section 4.3, Eqs. (4.16), (4.19), (4.20)] The quantity N_i is used in the slow-roll parameters and in n_s and r for quartic hilltop inflation, but it is never defined; the text only defines N in Eq. (4.18). Please define N_i and state its relation to the e-fold number N_* used in Fig. 3, since the model predictions cannot be reproduced without this identification.
[Section 2.1 and Table 1] There are several typographical and presentation issues: 'metic' should be 'metric' in Section 2.1, the table heading reads 'T able 1', and the subsection heading contains a duplicated 'constraint'. The tables should also be explicitly referenced by number in the text.
[Sections 3.1 and 3.3, Eqs. (3.3), (3.18)-(3.22)] The gauge transformation of Ξ in Eq. (3.3) and the construction of the variables Θ and Ω in Eqs. (3.18)-(3.22) are compressed; providing the intermediate algebra in an appendix would make the derivation substantially easier to verify.
[Section 4.1, Eq. (4.6)] The claim that the n=1 chaotic inflation results reduce to the dotted-line relation r ≃ -8 n_s + 8(1 - 1/N*) is stated without derivation; a one-line derivation would make the connection transparent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the perturbation spectra are derived from the Einstein equations and compared against external Planck 2018 contours; the b0k >> 1 branch choice is an unproven regime assumption, not a fitted input.

full rationale

The paper's central results, ns = 1 - (D+6)epsilon_V + 2 eta_V and r = 8(D+2)epsilon_V in the b0k >> 1 limit, are obtained by solving the perturbed Einstein equations with slow-roll approximations and standard Bunch-Davis initial conditions. The five model predictions are then compared with external Planck 2018 data, so the conclusion is not encoded in the input. The only potentially troubling step is the assertion in Section 3.6 that 'Hereafter, we assume the b0k >> 1 case' because the b0k << 1 branch gives ns far from one. This is a regime choice, not a fit of a parameter to the target conclusion, and it does not make the predicted ns-r values equivalent to the assumption by construction. Whether the CMB pivot scale actually satisfies b0k >> 1 for D=1 is a legitimate physical-regime concern, but it is a correctness risk, not circularity. Self-citations are not load-bearing: the cited five-dimensional perturbation formalism is external, and the paper's own reference [43] is unrelated to the main derivation.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central ns/r formulas are derived from Einstein equations and are fully self-contained; the free parameters listed are the physically motivated inputs (e-fold range and initial radius) that the model comparisons scan over. The axioms are the standard perturbation-theory assumptions plus the uniform-expansion ansatz. No new entities are introduced.

free parameters (2)

N* (number of e-folds) = 50, 60, 70
Chosen by hand over the CMB-relevant range; the D=1 allowed window for natural and hilltop inflation appears only for 60 < N* ≤ 70, so N* is load-bearing for the exception.
b0 (initial radius of extra dimensions) = e.g., b0^-1 ~ 10^15 GeV for D=1
Sets the KK scale and determines which branch (b0k <<1 or >>1) applies to CMB modes; the branch choice is central to the conclusion.

assumptions (6)

domain assumption The extra dimensions and three non-compact dimensions share the same scale factor during inflation (a(t)=b(t)=e^{Ht}).
This defines uniform inflation; from Eq. (2.2).
domain assumption The extra-dimensional space is a symmetric D-torus S^1×...×S^1 with equal radii.
Used for the KK mode sum Sν and the Fourier expansion (3.15).
domain assumption Perturbations start in the Bunch-Davis vacuum.
Used to fix the positive-frequency mode functions in (3.32).
domain assumption The CMB modes are in the b0k >> 1 regime.
Assumed in Section 3.6 after showing the b0k << 1 branch has ns far from 1; load-bearing for the D=1 exception.
domain assumption Radion stabilization after inflation does not affect the perturbation spectra computed during inflation.
Stated in Section 2.2; the radion potential during inflation is not modeled.
domain assumption The five potentials are taken over from four-dimensional phenomenology unchanged.
For the SUSY model this is explicitly called 'for simplicity' in Section 5.

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Pith. "Pith review of Analysis of inflationary models in higher-dimensional uniform inflation." pith.science (2026). https://pith.science/paper/7G77NF75

@misc{pith2026250113581,
  author       = {Pith},
  title        = {Pith review of: Analysis of inflationary models in higher-dimensional uniform inflation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7G77NF75}},
  note         = {Machine review of arXiv:2501.13581}
}

abstract

We consider higher-dimensional uniform inflation, in which the extra dimensions expand at the same rate as three-dimensional non-compact space during inflation. We compute the cosmological perturbation in $D+4$ dimensions and derive the spectral index $n_s$ and the tensor-scalar ratio $r$. We analyze five inflationary models: chaotic inflation, natural inflation, quartic hilltop inflation, inflation with spontaneously broken SUSY, and $R^2$ inflation. By combining the results from these models with the Planck 2018 constraints, we discuss that it is not desirable for the extra-dimensional space to expand at the same rate as the three-dimensional non-compact space, except for the case of one extra dimension.

Figures

Figures reproduced from arXiv: 2501.13581 by the authors.

**Figure 1.** Chaotic inflation with n = 1. Small and large red circles represent N∗ = 50 and N∗ = 60, respectively. ns-r plot is taken from [7]. 4.2 Natural inflation The idea of natural inflation [28,29] is that the inflaton is regarded as pseudo Nambu Goldstone boson. In this model, the potential has V (ϕ) = V0 1 + cos ϕ f , (4.7) where f is a spontaneous breaking scale. Calculating the slow-roll parameters, one has ϵ =… view at source ↗

**Figure 2.** Natural inflation with D = 1, 2. Our results represent purple lines. ns-r plot is taken from [7]. We show the results of natural inflation with D = 1, 2 in [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗

**Figure 3.** Quartic hilltop inflation with D = 1, 2. Our results represent green lines. ns-r plot is taken from [7]. We show the results of quartic hilltop inflation with D = 1, 2 in [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

TransPlanckian Censorship on Dark Dimension Inflation
hep-th 2026-07 conditional novelty 6.0 of 10

TransPlanckian Censorship forces dark-dimension inflation into a narrow one-dimension window with a pre-inflationary phase and suppresses tensor modes to r < 10^-10.
Inflation with a Growing Fifth Dimension
hep-th 2025-12 conditional novelty 6.0 of 10

Inflation from a UV-brane inflaton in a warped 5D bulk with an IR brane predicts a blue-tilted low-k scalar spectrum and oscillating tensor features because the early adiabatic modes come from the radion.

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Works this paper leans on

48 extracted references · 16 canonical work pages · cited by 2 Pith papers

[20]

Cosmological perturbations from five-dimensional inflation,

I. Antoniadis, J. Cunat, and A. Guillen, “Cosmological perturbations from five-dimensional inflation,” JHEP 05 (2024) 290 [arXiv:2311.17680]

arXiv 2024
[1]

The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,

A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23 (1981) 347–356

1981
[2]

Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions,

V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, “Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions,” Phys. Rept. 215 (1992) 203–333. 23

work page 1992
[3]

Inflation and the theory of cosmological perturbations,

A. Riotto, “Inflation and the theory of cosmological perturbations,” ICTP Lect. Notes Ser. 14 (2003) 317–413 [hep-ph/0210162]

arXiv 2003
[4]

Inflation,

D. Baumann, “Inflation,” Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small (2011) 523–686 [arXiv:0907.5424]

arXiv 2011
[5]

Lectures on inflation and cosmological perturbations,

D. Langlois, “Lectures on inflation and cosmological perturbations,” Lect. Notes Phys. 800 (2010) 1–57 [arXiv:1001.5259]

arXiv 2010
[6]

Encyclopædia Inflationaris: Opiparous Edition,

J. Martin, C. Ringeval, and V. Vennin, “Encyclopædia Inflationaris: Opiparous Edition,” Phys. Dark Univ. 5-6 (2014) 75–235 [arXiv:1303.3787]

arXiv 2014
[7]

Planck 2018 results. VI. Cosmological parameters,

Planck Collaboration, “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys. 641 (2020) A6 [arXiv:1807.06209]. [Erratum: Astron.Astrophys. 652, C4 (2021)]

arXiv 2020

Show all 48 references

[8]

Planck 2018 results. X. Constraints on inflation,

Planck Collaboration, “Planck 2018 results. X. Constraints on inflation,” Astron. Astrophys. 641 (2020) A10 [arXiv:1807.06211]

2020 arXiv
[9]

Aspects of the dark dimension in cosmology,

L. A. Anchordoqui, I. Antoniadis, and D. Lust, “Aspects of the dark dimension in cosmology,” Phys. Rev. D 107 (2023) 083530 [arXiv:2212.08527]

2023 arXiv
[10]

Large extra dimensions from higher-dimensional inflation,

L. A. Anchordoqui and I. Antoniadis, “Large extra dimensions from higher-dimensional inflation,” Phys. Rev. D 109 (2024) 103508 [arXiv:2310.20282]

2024 arXiv
[11]

The Hierarchy problem and new dimensions at a millimeter,

N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “The Hierarchy problem and new dimensions at a millimeter,” Phys. Lett. B 429 (1998) 263–272 [hep-ph/9803315]

1998 arXiv
[12]

New dimensions at a millimeter to a Fermi and superstrings at a TeV,

I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “New dimensions at a millimeter to a Fermi and superstrings at a TeV,” Phys. Lett. B 436 (1998) 257–263 [hep-ph/9804398]

1998 arXiv
[13]

Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity,

N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity,” Phys. Rev. D 59 (1999) 086004 [hep-ph/9807344]

1999 arXiv
[14]

Rapid asymmetric inflation and early cosmology in theories with submillimeter dimensions,

N. Arkani-Hamed, S. Dimopoulos, N. Kaloper, and J. March-Russell, “Rapid asymmetric inflation and early cosmology in theories with submillimeter dimensions,” Nucl. Phys. B 567 (2000) 189–228 [hep-ph/9903224]

2000 arXiv
[15]

Inflation from extra dimensions,

J. M. Cline, “Inflation from extra dimensions,” AIP Conf. Proc. 488 (1999) 64–71 [hep-ph/9904495]

1999 arXiv
[16]

Inflation in the five-dimensional universe with an orbifold extra dimension,

T. Nihei, “Inflation in the five-dimensional universe with an orbifold extra dimension,” Phys. Lett. B 465 (1999) 81–85 [hep-ph/9905487]. 24

1999 arXiv
[17]

The dark dimension and the Swampland,

M. Montero, C. Vafa, and I. Valenzuela, “The dark dimension and the Swampland,” JHEP 02 (2023) 022 [arXiv:2205.12293]

2023 arXiv
[18]

AdS and the Swampland,

D. L¨ ust, E. Palti, and C. Vafa, “AdS and the Swampland,” Phys. Lett. B 797 (2019) 134867 [arXiv:1906.05225]

2019 arXiv
[19]

Primordial Power Spectrum of Five Dimensional Uniform Inflation

L. A. Anchordoqui and I. Antoniadis, “Primordial Power Spectrum of Five Dimensional Uniform Inflation.” arXiv:2412.19213
[21]

New Test of the Gravitational 1 /r2 Law at Separations down to 52 µm,

J. G. Lee, E. G. Adelberger, T. S. Cook, S. M. Fleischer, and B. R. Heckel, “New Test of the Gravitational 1 /r2 Law at Separations down to 52 µm,” Phys. Rev. Lett. 124 (2020) 101101 [arXiv:2002.11761]

2020 arXiv
[22]

Supernova and neutron star limits on large extra dimensions reexamined,

S. Hannestad and G. G. Raffelt, “Supernova and neutron star limits on large extra dimensions reexamined,” Phys. Rev. D 67 (2003) 125008 [hep-ph/0304029]. [Erratum: Phys.Rev.D 69, 029901 (2004)]

2003 arXiv
[23]

Search for new phenomena in events with an energetic jet and missing transverse momentum in pp collisions at √s =13 TeV with the ATLAS detector,

ATLAS Collaboration, “Search for new phenomena in events with an energetic jet and missing transverse momentum in pp collisions at √s =13 TeV with the ATLAS detector,” Phys. Rev. D 103 (2021) 112006 [arXiv:2102.10874]

2021 arXiv
[24]

Cosmological perturbations in brane world theories: Formalism,

C. van de Bruck, M. Dorca, R. H. Brandenberger, and A. Lukas, “Cosmological perturbations in brane world theories: Formalism,” Phys. Rev. D 62 (2000) 123515 [hep-th/0005032]

2000 arXiv
[25]

General perturbations in D+1 standard and brane cosmology revisited,

Z. Delf ´ ın, R. Cordero, T. Matos, and M. A. Garc ´ ıa-Aspeitia, “General perturbations in D+1 standard and brane cosmology revisited,” Int. J. Mod. Phys. A 39 (2024) 2450040 [arXiv:2302.01338]

2024 arXiv
[26]

Adiabatic and entropy perturbations from inflation,

C. Gordon, D. Wands, B. A. Bassett, and R. Maartens, “Adiabatic and entropy perturbations from inflation,” Phys. Rev. D 63 (2000) 023506 [astro-ph/0009131]

2000 arXiv
[27]

Chaotic Inflation,

A. D. Linde, “Chaotic Inflation,” Phys. Lett. B 129 (1983) 177–181

1983
[28]

Natural inflation with pseudo - Nambu-Goldstone bosons,

K. Freese, J. A. Frieman, and A. V. Olinto, “Natural inflation with pseudo - Nambu-Goldstone bosons,” Phys. Rev. Lett. 65 (1990) 3233–3236

1990
[29]

Natural Inflation: Status after WMAP 3-year data,

C. Savage, K. Freese, and W. H. Kinney, “Natural Inflation: Status after WMAP 3-year data,” Phys. Rev. D 74 (2006) 123511 [hep-ph/0609144]

2006 arXiv
[30]

A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,

A. D. Linde, “A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,” Phys. Lett. B 108 (1982) 389–393

1982
[31]

Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,

A. Albrecht and P. J. Steinhardt, “Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,” Phys. Rev. Lett. 48 (1982) 1220–1223. 25

1982
[32]

Hilltop inflation,

L. Boubekeur and D. H. Lyth, “Hilltop inflation,” JCAP 07 (2005) 010 [hep-ph/0502047]

2005 arXiv
[33]

An analytic treatment of quartic hilltop inflation,

K. Dimopoulos, “An analytic treatment of quartic hilltop inflation,” Phys. Lett. B 809 (2020) 135688 [arXiv:2006.06029]

2020 arXiv
[34]

Large scale structure and supersymmetric inflation without fine tuning,

G. R. Dvali, Q. Shafi, and R. K. Schaefer, “Large scale structure and supersymmetric inflation without fine tuning,” Phys. Rev. Lett. 73 (1994) 1886–1889 [hep-ph/9406319]

1994 arXiv
[35]

A New Type of Isotropic Cosmological Models Without Singularity,

A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,” Phys. Lett. B 91 (1980) 99–102

1980
[36]

R + αRn Inflation in higher-dimensional Space-times,

S. P. Otero, F. G. Pedro, and C. Wieck, “ R + αRn Inflation in higher-dimensional Space-times,” JHEP 05 (2017) 058 [arXiv:1702.08311]

2017 arXiv
[37]

Extra natural inflation,

N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, “Extra natural inflation,” Phys. Rev. Lett. 90 (2003) 221302 [hep-th/0301218]

2003 arXiv
[38]

Pseudonatural inflation,

N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, “Pseudonatural inflation,” JCAP 07 (2003) 003 [hep-th/0302034]

2003 arXiv
[39]

Inflaton versus Curvaton in Higher Dimensional Gauge Theories,

T. Inami, Y. Koyama, C.-M. Lin, and S. Minakami, “Inflaton versus Curvaton in Higher Dimensional Gauge Theories,” Prog. Theor. Phys. 125 (2011) 345–358 [arXiv:1004.5477]

2011 arXiv
[40]

Radion stabilization in the presence of a Wilson line phase,

Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Radion stabilization in the presence of a Wilson line phase,” PTEP 2014 (2014) 073B04 [arXiv:1404.5125]

2014 arXiv
[41]

Large field inflation models from higher-dimensional gauge theories,

K. Furuuchi and Y. Koyama, “Large field inflation models from higher-dimensional gauge theories,” JCAP 02 (2015) 031 [arXiv:1407.1951]

2015 arXiv
[42]

Inflation from radion gauge-Higgs potential at Planck scale,

Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Inflation from radion gauge-Higgs potential at Planck scale,” PTEP 2015 (2015) 093B03 [arXiv:1504.06905]

2015 arXiv
[43]

Extranatural flux inflation,

T. Hirose and N. Maru, “Extranatural flux inflation,” JHEP 09 (2021) 124 [arXiv:2105.11782]

2021 arXiv
[44]

Kahler moduli inflation,

J. P. Conlon and F. Quevedo, “Kahler moduli inflation,” JHEP 01 (2006) 146 [hep-th/0509012]

2006 arXiv
[45]

Models of Modular Inflation and Their Phenomenological Consequences,

I. Ben-Dayan, R. Brustein, and S. P. de Alwis, “Models of Modular Inflation and Their Phenomenological Consequences,” JCAP 07 (2008) 011 [arXiv:0802.3160]

2008 arXiv
[46]

Modular invariant inflation,

T. Kobayashi, D. Nitta, and Y. Urakawa, “Modular invariant inflation,” JCAP 08 (2016) 014 [arXiv:1604.02995]

2016 arXiv
[47]

Moduli inflation from modular flavor symmetries,

Y. Abe, T. Higaki, F. Kaneko, T. Kobayashi, and H. Otsuka, “Moduli inflation from modular flavor symmetries,” JHEP 06 (2023) 187 [arXiv:2303.02947]. 26

2023 arXiv
[48]

Modular invariant slow roll inflation,

G.-J. Ding, S.-Y. Jiang, and W. Zhao, “Modular invariant slow roll inflation,” JCAP 10 (2024) 016 [arXiv:2405.06497]. 27

2024 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [20]

Cosmological perturbations from five-dimensional inflation,

I. Antoniadis, J. Cunat, and A. Guillen, “Cosmological perturbations from five-dimensional inflation,” JHEP 05 (2024) 290 [arXiv:2311.17680]

arXiv 2024

[2] [1]

The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,

A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23 (1981) 347–356

1981

[3] [2]

Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions,

V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, “Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions,” Phys. Rept. 215 (1992) 203–333. 23

work page 1992

[4] [3]

Inflation and the theory of cosmological perturbations,

A. Riotto, “Inflation and the theory of cosmological perturbations,” ICTP Lect. Notes Ser. 14 (2003) 317–413 [hep-ph/0210162]

arXiv 2003

[5] [4]

Inflation,

D. Baumann, “Inflation,” Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small (2011) 523–686 [arXiv:0907.5424]

arXiv 2011

[6] [5]

Lectures on inflation and cosmological perturbations,

D. Langlois, “Lectures on inflation and cosmological perturbations,” Lect. Notes Phys. 800 (2010) 1–57 [arXiv:1001.5259]

arXiv 2010

[7] [6]

Encyclopædia Inflationaris: Opiparous Edition,

J. Martin, C. Ringeval, and V. Vennin, “Encyclopædia Inflationaris: Opiparous Edition,” Phys. Dark Univ. 5-6 (2014) 75–235 [arXiv:1303.3787]

arXiv 2014

[8] [7]

Planck 2018 results. VI. Cosmological parameters,

Planck Collaboration, “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys. 641 (2020) A6 [arXiv:1807.06209]. [Erratum: Astron.Astrophys. 652, C4 (2021)]

arXiv 2020