REVIEW 2 major objections 6 minor 50 references
Distance-Higuchi Bounds on Inflationary Field Ranges and Lifetimes
T0 review · 2 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash
Pith's one-line read A quasi-de Sitter inflationary phase cannot outlive the distance–Higuchi wall, whose location is set by a light massive spin-2 tower and the generalized Higuchi bound.
desk verdict A clean conditional lifetime bound for quasi-de Sitter from the Distance Conjecture plus a spin-2 spectral assumption; weaker than TCC but honest about its load-bearing premise. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the distance–Higuchi wall: the hypersurface in field space where the exponentially light massive spin-2 state from the Distance-Conjecture tower falls to the generalized Higuchi bound $m_2^2 = (d-2)H^2(1-\epsilon_H)$, below which its helicity-zero mode becomes a ghost. The field-range constraint (22) carries the classical argument by balancing the exponential decrease of the tower mass against the decrease of $H$ during the roll, and the exact identity $T = \int d\phi/(H\sqrt{(d-2)\epsilon_H})$ then converts the allowed field range into a duration. For very flat potentials the argument switches to a stochastic description of the long-wavelength field, with a Brownian noise amplitude $A_d H^{d-1}$ and a Fokker–Planck equation whose reflection principle supplies the first-passage time for an order-one fraction of branches to cross the wall.
What would settle it
A concrete falsifier would be a consistent quantum-gravity construction with an infinite-distance field direction whose lightest tower contains no spin-2 member, or with curvature couplings that push the spin-2 unitarity threshold far below $(d-2)H^2(1-\epsilon_H)$, and in which a quasi-de Sitter phase driven by a flat potential lasts parametrically longer than $H^{-(d-1)} \ln^2(1/H)$ while remaining ghost-free.
Extended reading notes
Core claim
The central claim is Eq. (87): for quasi-de Sitter inflation in $d$ spacetime dimensions driven by a nearly flat scalar potential $V(\phi)$, the duration satisfies $\tau_{\rm inf} \lesssim \min\{ \ln(1/H)\, \sqrt{V}/|V'|,\, V^{-(d-1)/2}\, \ln^2(1/H) \}$ in reduced Planck units, up to dimension-dependent order-one coefficients. The first entry comes from classical slow-roll traversal of the finite field range allowed before a massive spin-2 state descending from the light tower violates the generalized Higuchi bound; the second comes from quantum diffusion, which makes an order-one fraction of coarse-grained branches hit the same wall on a timescale $H^{-(d-1)} \ln^2(1/H)$. The fixed statistical confidence qualification matters: in the stochastic regime no finite time kills every branch, but for any fixed $\delta$ the time by which a $\delta$ fraction of branches have crossed the wall is bounded by the displayed formula, with $\delta$ affecting only an order-one prefactor. The two bounds exchange dominance at an extremely small slope, so together they close the loophole in which the classical traversal time diverges as the potential flattens.
Load-bearing premise
The load-bearing premise is that the tower of states that becomes exponentially light at large field distance contains a massive spin-2 state whose mass falls at least as fast as $m \lesssim M_{\rm pl} e^{-\alpha \Delta\phi}$ with $\alpha \ge 1/\sqrt{d-2}$; the paper states that this is automatic for Kaluza–Klein graviton towers but does not follow from the Distance Conjecture alone.
Editorial extensions
If this is right
- For ordinary slow-roll potentials, the field-range bound translates into at most $N \lesssim \epsilon_V^{-1/2} \ln(M_{\rm pl}/(\sqrt{d-2}\, H))$ e-folds, so the classical duration diverges only as the potential is flattened.
- For ultra-flat potentials where classical motion freezes, quantum diffusion bounds the duration by $H^{-(d-1)} \ln^2(1/H)$ and the number of e-folds by $H^{-(d-2)} \ln^2(1/H)$, for any fixed fraction $\delta$ of branches allowed to cross the wall.
- The classical and stochastic bounds cross at $\sqrt{\epsilon_V} \lesssim H^{d-2}/(K_{d,\delta} B_0)$, meaning quantum diffusion does not tighten ordinary slow-roll bounds but precisely closes the flat-potential loophole.
- In four-dimensional single-field slow-roll inflation, the classical bound yields $H \lesssim 1.6\times 10^{14}$ GeV and tensor-to-scalar ratio $r \lesssim 0.41$, weaker than current observational limits but derived from minimal quantum-gravity input.
- The bound applies at every point in field space, not only in asymptotic limits, and covers cosmologies that settle into a metastable de Sitter phase.
Reading between the lines
- If the spin-2 spectral assumption holds, the result implies that along any field direction that makes the tower light, eternal inflation in a fixed quasi-de Sitter vacuum would be limited to the stochastic timescale unless the field bends away from that direction.
- The stochastic bound's quantile structure suggests that changing the confidence level from, say, 50 percent to 99 percent shifts the numerical prefactor but leaves the parametric $H^{-(d-1)} \ln^2(1/H)$ scaling intact, so the bound is insensitive to how strictly one defines the healthy fraction.
- A model-builder could try to evade the bound by giving the massive spin-2 state non-minimal couplings that raise its effective mass above the generalized Higuchi threshold, a direction the paper notes only through order-one curvature-coupling caveats.
- In $d=4$ the classical bound $H \lesssim 1.6\times 10^{14}$ GeV could in principle be probed by future cosmic-variance-limited tensor-mode searches, while the stochastic bound is too weak for CMB observables unless the potential is extraordinarily flat.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper derives upper bounds on the duration of quasi-de Sitter inflationary phases in d>2 spacetime dimensions by combining the sharpened Distance Conjecture with the generalized Higuchi bound. Under the explicitly stated spectral assumption that the relevant infinite-distance tower contains a massive spin-2 state whose mass falls at least as fast as e^{-αΔφ} with α ≥ 1/√(d−2), the authors establish a finite 'distance-Higuchi wall' for the inflaton field excursion (Eqs. (14), (22), (28)). Combining this wall with the classical rolling speed yields a classical lifetime bound τ_cl ≲ H^{-1}ε_V^{-1/2} ln(1/H) (Eq. (36)), while for ultra-flat potentials a stochastic first-passage calculation gives a quantile-based quantum bound τ_q ≲ H^{-(d−1)} ln^2(1/H) (Eq. (72)). The final bound is the minimum of the two (Eq. (87)). The paper carefully distinguishes the finite first-passage quantile from the infinite mean crossing time (Eqs. (78)-(79)) and explicitly lists the assumptions and limitations of the argument.
Significance. If the stated assumptions hold, the result is a genuinely bottom-up lifespan bound for quasi-de Sitter inflation that closes the ultra-flat-potential loophole: even when classical drift is negligible, stochastic diffusion drives an order-one fraction of branches across the distance-Higuchi wall within a finite time polynomial in H^{-1}. The derivation is self-contained and conservative, using only the sharpened Distance Conjecture, a transparent spectral premise, and standard stochastic-inflation tools. The paper is honest about the conditional nature of the theorem and about the fact that the bound is weaker than the TCC; it also notes that its numerical implications (H ≲ 1.6×10^14 GeV, r ≲ 0.41) are weaker than current observational constraints. The main strength is the conceptual mechanism and the clean first-passage treatment, not a phenomenological sharpening.
major comments (2)
- [Sec. 2, after Eq. (9); Abstract; Sec. 5, Eq. (87)] The central claim (Eq. (87)) and the abstract's statement that 'a universe cannot live longer' are conditional on the spectral assumption introduced after Eq. (9): the tower that becomes exponentially light at large field distance must contain a massive spin-2 state whose mass falls at least as fast as m ≤ M_pl e^{-αΔφ} with α ≥ 1/√(d−2). As the authors correctly note, the Distance Conjecture (10) alone does not fix the spin content, and the spin-2 property is automatic for Kaluza-Klein graviton towers but not for every tower. Since Eqs. (14), (22), (28), (36), (60), (72), and (87) all rely on this premise, I ask that the abstract and the statement of the main result explicitly say 'assuming the spin-2 spectral assumption stated in Sec. 2' rather than presenting the bound as unconditional. The concluding paragraphs already include this qualification, but the front matter does not.
- [Sec. 4, Eqs. (69)-(72)] The quantum lifetime bound is formulated as an ensemble-average statement: for a fixed fraction δ, at most a fraction δ of stochastic branches may have crossed the wall by time T. This is the correct physical interpretation, and the paper explains it well. However, the abstract's phrase 'a universe cannot live longer' could be misread as a deterministic lifetime for a single universe. I recommend using the paper's own careful wording ('an order-one fraction of coarse-grained quantum branches remains healthy only up to time...') in the abstract as well, so that the quantile interpretation is visible from the outset.
minor comments (6)
- [Sec. 2, Eq. (9)] Equation (9) is dimensionally inconsistent as written: m^2(Δφ) ≤ M_pl e^{-αΔφ} has dimensions of mass on the right-hand side and mass^2 on the left-hand side. Since M_pl is kept symbolic in later logarithms, please write m^2(Δφ) ≤ M_pl^2 e^{-αΔφ} (or equivalently m(Δφ) ≤ M_pl e^{-αΔφ}) for clarity.
- [Abstract] The sentence 'This bound despite being weaker than the Trans-Planckian Censorship Conjecture, which has been argued for classical cosmologies...' is grammatically incomplete; please insert a verb, e.g., 'This bound, despite being weaker than the TCC... is powerful because...'.
- [Sec. 3, Eq. (46)] Equation (46) is presented as 'the following bound' but it omits the O(1) prefactor 4/(d−2) and the '-1' that appear later in the exact expression (47). Since the text immediately says that O(1) factors are not included, I suggest labeling (46) as a schematic/parametric estimate or adding 'up to O(1) factors' directly in the display.
- [Sec. 4, Eq. (58)] The notation (δϕ)^2 for the variance ⟨ϕ^2⟩ is potentially confusing because δϕ is used elsewhere for a field displacement. Using Var(ϕ) or ⟨ϕ^2⟩ would be clearer.
- [Sec. 4, Eq. (72) and Eq. (77)] The text says 'for every fixed order-one δ' but δ is a fraction in (0,1); consider writing 'for every fixed δ ∈ (0,1)' to avoid the impression that δ itself is order-one in magnitude.
- [Sec. 4, paragraph after Eq. (62)] The heuristic random-walk argument leading to (53) is helpful, but it would benefit from an explicit statement that the steps are statistically independent on timescales of order H^{-1}, which is what justifies the √n scaling rather than coherent n scaling.
Circularity Check
No significant circularity: the lifetime bound is a consequence of stated quantum-gravity assumptions, not one of those assumptions; self-citations to TCC are comparative only.
full rationale
The paper's derivation is a conditional chain: assume the sharpened Distance Conjecture (Eq. (10)) and the explicitly stated additional spectral assumption that a spin-2 tower member falls at least as fast as m ≤ Mpl e^{-αΔφ} with α ≥ 1/sqrt(d-2) (Eq. (9), with the limitation acknowledged in the text immediately after), combine with the generalized Higuchi bound (Eq. (18)) to obtain field-excursion bounds (Eqs. (22), (14), (29)), and then convert field range into duration via classical scalar velocity (Eqs. (30), (36), (45)) and stochastic diffusion first-passage statistics (Eqs. (62), (67), (72)). Eq. (87) is a mathematical consequence of these stated inputs, not one of the inputs; the spin-2 spectral assumption does not already contain the lifetime bound. The paper is transparent that the spin-2 assumption is not implied by the Distance Conjecture alone, so this is an honest conditional result rather than a hidden circular premise. Self-citations to Bedroya's TCC papers [11,12,18,20] appear in the introduction and in comparison remarks; they are not used to prove any step, and the paper's bound is explicitly weaker than the TCC, so the central claim is not borrowed from a self-cited theorem. There is no fitted parameter renamed as a prediction, and no equation reduces to another by definition. The only mild concern is the presence of several self-citations for context, but they are not load-bearing.
Assumptions & free parameters
free parameters (2)
- delta (allowed violation fraction) =
not fitted; user-chosen order-one quantile
- O(1) numerical coefficients in lifetime bounds =
undetermined
assumptions (5)
- domain assumption Sharpened Distance Conjecture: the lightest tower exponent satisfies alpha >= 1/sqrt(d-2).
- domain assumption The relevant tower contains a massive spin-2 state whose mass falls at least as fast as m <= Mpl e^{-alpha Delta-phi}.
- domain assumption Generalized Higuchi bound on FLRW: m_2^2 > (d-2) H^2 (1 - epsilon_H).
- standard math Bunch-Davies vacuum for a free massless canonical scalar in de Sitter space.
- standard math Reflection principle and Brownian time-change theorem for first-passage problems.
Cite this review
Pith. "Pith review of Distance-Higuchi Bounds on Inflationary Field Ranges and Lifetimes." pith.science (2026). https://pith.science/paper/SY25QTJW
@misc{pith2026260811086,
author = {Pith},
title = {Pith review of: Distance-Higuchi Bounds on Inflationary Field Ranges and Lifetimes},
year = {2026},
howpublished = {\url{https://pith.science/paper/SY25QTJW}},
note = {Machine review of arXiv:2608.11086}
}
abstract
We show that quasi-de Sitter inflation driven by a nearly flat scalar potential has a finite polynomial lifespan dictated by the interplay between the swampland Distance Conjecture and the generalized Higuchi bound. By analyzing classical scalar rolling and quantum stochastic diffusion, we demonstrate that for any arbitrarily high but fixed statistical confidence, a universe cannot live longer than $\sim \min\left\{\ln(\frac{1}{H})\frac{\sqrt V}{V'},V^{-\frac{d-1}{2}}\ln^2(\frac{1}{H})\right\}$ in reduced Planck units while remaining Higuchi-consistent, where $H$ is the Hubble parameter, $V$ is the scalar potential, $d$ is the number of spacetime dimensions, and prime denotes derivative with respect to the scalar field. This bound despite being weaker than the Trans-Planckian Censorship Conjecture, which has been argued for classical cosmologies that flow to the asymptotic of the field space without tunneling, is powerful given its minimal quantum gravity input and applicability to all points in the moduli space.
Reference graph
Works this paper leans on
-
[36]
Stochastic Survival near Swampland Boundaries
O. Guleryuz, “Stochastic Survival near Swampland Boundaries,” arXiv:2606.08244
-
[1]
The String landscape and the swampland,
C. Vafa, “The String landscape and the swampland,” arXiv:hep-th/0509212
-
[2]
The Swampland: Introduction and Review,
E. Palti, “The Swampland: Introduction and Review,” Fortsch. Phys.67(2019) 1900037; arXiv:1903.06239
arXiv 2019
-
[3]
Lectures on the Swamp- land Program in String Compactifications,
M. van Beest, J. Calderón-Infante, D. Mirfendereski and I. Valenzuela, “Lectures on the Swamp- land Program in String Compactifications,” Phys. Rept.989(2022) 1; arXiv:2102.01111
arXiv 2022
-
[4]
Lectures on the string landscape and the Swampland,
N. B. Agmon, A. Bedroya, M. J. Kang and C. Vafa, “Lectures on the string landscape and the Swampland,” arXiv:2212.06187
-
[5]
Dark energy from string theory: an introductory review,
D. Andriot, “Dark energy from string theory: an introductory review,” arXiv:2603.25797
-
[6]
Breaking Free from the Swampland of Impossible Universes through the DESI Portal,
L. A. Anchordoqui and D. Lüst, “Breaking Free from the Swampland of Impossible Universes through the DESI Portal,” Universe12(2026) 216; arXiv:2605.10476
arXiv 2026
-
[7]
On the Geometry of the String Landscape and the Swampland,
H. Ooguri and C. Vafa, “On the Geometry of the String Landscape and the Swampland,” Nucl. Phys. B766(2007) 21; arXiv:hep-th/0605264
arXiv 2007
Show all 50 references
-
[8]
Sharpening the Distance Conjecture in Diverse Dimensions,
M. Etheredge, B. Heidenreich, S. Kaya, Y. Qiu, and T. Rudelius, “Sharpening the Distance Conjecture in Diverse Dimensions,” JHEP12(2022) 114; arXiv:2206.04063
2022 arXiv
-
[9]
De Sitter Space and the Swampland,
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, “De Sitter Space and the Swampland,” arXiv:1806.08362. 18
-
[10]
Distance and de Sitter Conjectures on the Swampland,
H. Ooguri, E. Palti, G. Shiu and C. Vafa, “Distance and de Sitter Conjectures on the Swampland,” Phys. Lett. B788(2019) 180; arXiv:1810.05506
2019 arXiv
-
[11]
Trans-Planckian Censorship and the Swampland,
A. Bedroya and C. Vafa, “Trans-Planckian Censorship and the Swampland,” JHEP09(2020) 123; arXiv:1909.11063
2020 arXiv
-
[12]
Trans-Planckian Censorship and Inflationary Cosmology,
A. Bedroya, R. Brandenberger, M. Loverde and C. Vafa, “Trans-Planckian Censorship and Inflationary Cosmology,” Phys. Rev. D101(2020) 103502 ; arXiv:1909.11106
2020 arXiv
-
[13]
The web of swampland conjectures and the TCC bound,
D. Andriot, N. Cribiori and D. Erkinger, “The web of swampland conjectures and the TCC bound,” JHEP07(2020) 162; arXiv:2004.00030
2020 arXiv
-
[14]
Asymptotic scalar field cosmology in string theory,
T. Rudelius, “Asymptotic scalar field cosmology in string theory,” JHEP10(2022) 018; arXiv:2208.08989
2022 arXiv
-
[15]
(Quasi-) de Sitter solutions across dimensions and the TCC bound,
D. Andriot and L. Horer, “(Quasi-) de Sitter solutions across dimensions and the TCC bound,” JHEP01(2023) 020; arXiv:2208.14462
2023 arXiv
-
[16]
Trans-Planckian censorship conjecture from the swampland distance conjecture,
S. Brahma, “Trans-Planckian censorship conjecture from the swampland distance conjecture,” Phys. Rev. D101(2020) 046013 ; arXiv:1910.12352
2020 arXiv
-
[17]
de Sitter Complementarity, TCC, and the Swampland,
A. Bedroya, “de Sitter Complementarity, TCC, and the Swampland,” LHEP2021(2021) 187; arXiv:2010.09760
2021 arXiv
-
[18]
Holographic origin of TCC and the distance conjecture,
A. Bedroya, “Holographic origin of TCC and the distance conjecture,” JHEP06(2024) 016; arXiv:2211.09128
2024 arXiv
-
[19]
Bounds on field range for slowly varying positive potentials,
D. van de Heisteeg, C. Vafa, M. Wiesner and D. H. Wu, “Bounds on field range for slowly varying positive potentials,” JHEP02(2024) 175; arXiv:2305.07701
2024 arXiv
-
[20]
TCC in the interior of moduli space and its implications for the string landscape and cosmology,
A. Bedroya, Q. Lu and P. J. Steinhardt, “TCC in the interior of moduli space and its implications for the string landscape and cosmology,” JHEP08(2025) 007; arXiv:2407.08793
2025 arXiv
-
[21]
Is the Superstring Weakly Coupled?,
M. Dine and N. Seiberg, “Is the Superstring Weakly Coupled?,” Phys. Lett. B162(1985) 299
1985
-
[22]
Supergravity description of field theories on curved manifolds and a no go theorem,
J. M. Maldacena and C. Nuñez, “Supergravity description of field theories on curved manifolds and a no go theorem,” Int. J. Mod. Phys. A16(2001) 822; arXiv:hep-th/0007018
2001 arXiv
-
[23]
On classical de Sitter solutions and parametric control,
D. Andriot and F. Ruehle, “On classical de Sitter solutions and parametric control,” JHEP06 (2024) 101; arXiv:2403.07065
2024 arXiv
-
[24]
Cosmological Event Horizons, Thermodynamics, and Particle Creation,
G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Creation,”Phys. Rev. D15(1977) 2738. 19
1977
-
[25]
Disturbing Implications of a Cosmological Constant,
L. Dyson, M. Kleban, and L. Susskind, “Disturbing Implications of a Cosmological Constant,” JHEP10(2002) 011; arXiv:hep-th/0208013
2002 arXiv
-
[26]
Emergent strings from infinite distance limits,
S. J. Lee, W. Lerche and T. Weigand, “Emergent strings from infinite distance limits,” JHEP02 (2022) 190; arXiv:1910.01135
2022 arXiv
-
[27]
A Spin-2 Conjecture on the Swampland,
D. Klaewer, D. Lüst, and E. Palti, “A Spin-2 Conjecture on the Swampland,”Fortschr. Phys.67 (2019) 1800102; arXiv:1811.07908
2019 arXiv
-
[28]
Forbidden Mass Range for Spin-2 Field Theory in de Sitter Space-time,
A. Higuchi, “Forbidden Mass Range for Spin-2 Field Theory in de Sitter Space-time,” Nucl. Phys. B282(1987) 397
1987
-
[29]
Massive Symmetric Tensor Field in Space-times with a Positive Cosmological Constant,
A. Higuchi, “Massive Symmetric Tensor Field in Space-times with a Positive Cosmological Constant,” Nucl. Phys. B325(1989) 745
1989
-
[30]
Partial Masslessness of Higher Spins in (A)dS,
S. Deser and A. Waldron, “Partial Masslessness of Higher Spins in (A)dS,” Nucl. Phys. B607 (2001) 577; arXiv:hep-th/0103198
2001 arXiv
-
[31]
A Note on String Excitations and the Higuchi Bound,
D. Lüst and E. Palti, “A Note on String Excitations and the Higuchi Bound,” Phys. Lett. B799 (2019) 135067 ; arXiv:1907.04161
2019 arXiv
-
[32]
Inflation, Higher Spins and the Swampland,
M. Scalisi, “Inflation, Higher Spins and the Swampland,” Phys. Lett. B808(2020) 135683; arXiv:1912.04283
2020 arXiv
-
[33]
R2-inflation derived from 4d strings, the role of the dilaton, and turning the Swampland into a mirage,
I. Antoniadis, D. V. Nanopoulos and K. A. Olive, “R2-inflation derived from 4d strings, the role of the dilaton, and turning the Swampland into a mirage,” JHEP06(2025) 155; arXiv:2410.16541
2025 arXiv
-
[34]
Cosmological Stability Bound in Massive Gravity and Bigravity,
M. Fasiello and A. J. Tolley, “Cosmological Stability Bound in Massive Gravity and Bigravity,” JCAP12(2013) 002; arXiv:1308.1647
2013 arXiv
-
[35]
Higuchi Bound on Slow Roll Inflation and the Swampland,
M. Lüben and D. Lüst, “Higuchi Bound on Slow Roll Inflation and the Swampland,” JHEP09 (2020) 055; arXiv:2003.10494
2020 arXiv
-
[37]
Pauli–Fierz Gravitons on Friedmann–Robertson–Walker Background,
L. Grisa and L. Sorbo, “Pauli–Fierz Gravitons on Friedmann–Robertson–Walker Background,” Phys. Lett. B686(2010) 273; arXiv:0905.3391
2010 arXiv
-
[38]
Cosmological Gravitational Particle Production of Massive Spin-2 Particles,
E. W. Kolb, S. Ling, A. J. Long, and R. A. Rosen, “Cosmological Gravitational Particle Production of Massive Spin-2 Particles,” JHEP05(2023) 181; arXiv:2302.04390
2023 arXiv
-
[39]
Improved estimates of cosmological perturbations,
N. C. Tsamis and R. P. Woodard, “Improved estimates of cosmological perturbations,” Phys. Rev. D69(2004) 084005; arXiv:astro-ph/0307463. 20
2004 arXiv
-
[40]
Horizon crossing and inflation with large eta,
W. H. Kinney, “Horizon crossing and inflation with large eta,” Phys. Rev. D72(2005) 023515; arXiv:gr-qc/0503017
2005 arXiv
-
[41]
Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,
P. A. R. Adeet al.[BICEP and Keck], “Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,” Phys. Rev. Lett.127(2021) 151301; arXiv:2110.00483
2021
-
[42]
Improved limits on the tensor-to-scalar ratio using BICEP and Planck data,
M. Tristramet al., “Improved limits on the tensor-to-scalar ratio using BICEP and Planck data,” Phys. Rev. D105(2022) 083524 ; arXiv:2112.07961
2022 arXiv
-
[43]
Power-Law Inflation,
F. Lucchin and S. Matarrese, “Power-Law Inflation,” Phys. Rev. D32(1985) 1316
1985
-
[44]
Scalar Fields in Cosmology with an Exponential Potential,
J. J. Halliwell, “Scalar Fields in Cosmology with an Exponential Potential,” Phys. Lett. B185 (1987) 341
1987
-
[45]
Restoration of Spontaneously Broken Continuous Symmetries in de Sitter Space-Time,
B. Ratra, “Restoration of Spontaneously Broken Continuous Symmetries in de Sitter Space-Time,” Phys. Rev. D31(1985) 1931
1985
-
[46]
Note on initial conditions for small-field inflation,
I. Antoniadis, A. Chatrabhuti, H. Isono and S. Sypsas, “Note on initial conditions for small-field inflation,” Phys. Rev. D102(2020) 103510; arXiv:2008.02494
2020 arXiv
-
[47]
Equilibrium State of a Self-Interacting Scalar Field in the de Sitter Background,
A. A. Starobinsky and J. Yokoyama, “Equilibrium State of a Self-Interacting Scalar Field in the de Sitter Background,” Phys. Rev. D50(1994) 6357; arXiv:astro-ph/9407016
1994 arXiv
-
[48]
Correlation Functions in Stochastic Inflation,
V. Vennin and A. A. Starobinsky, “Correlation Functions in Stochastic Inflation,” Eur. Phys. J. C75(2015) 413; arXiv:1506.04732
2015 arXiv
-
[49]
Stochastic Inflation Beyond Slow Roll,
C. Pattison, V. Vennin, H. Assadullahi, and D. Wands, “Stochastic Inflation Beyond Slow Roll,” JCAP07(2019) 031; arXiv:1905.06300
2019 arXiv
-
[50]
Power Spectrum in Stochastic Inflation,
K. Ando and V. Vennin, “Power Spectrum in Stochastic Inflation,” JCAP04(2021) 057; arXiv:2012.02031. 21
2021 arXiv
Reviewed August 12, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.