False Vacuum Inflation with Einstein Gravity

Andrew R Liddle; David H Lyth; David Wands; Edmund J Copeland; Ewan D Stewart

REVIEW

False Vacuum Inflation with Einstein Gravity

Edmund J Copeland, Andrew R Liddle, David H Lyth, Ewan D Stewart, David Wands

Astrophysics · Submitted 10 Jan 1994 · 66 references

Pith's verdict: The standard reference for hybrid inflation phenomenology; the parameter-space map and the corrected n ≲ 1.14 are the durable contributions, and the prompt-transition argument in §3.2 is the one place where the abstract outruns the body.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 5 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDastro-ph/9401011 (version 1)

Pith IDKRBYWXUV, Pith's permanent record of this paper and its review

CitationAndrew R Liddle, David H Lyth, David Wands, Edmund J Copeland, Ewan D Stewart. "False Vacuum Inflation with Einstein Gravity." arXiv:astro-ph/9401011 (1994). https://pith.science/paper/KRBYWXUV

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Worth your time, and worth citing. This is the paper that turned Linde's hybrid inflation into a worked-out phenomenological model: the full COBE-normalised parameter space with the two analytic branches and their merger (Fig. 1), the corrected upper bound on the tilt, and the first pass at defect production in the vacuum-dominated regime. The correction of n_max from the larger values quoted by Linde and by Mollerach-Matarrese-Lucchin to about 1.14 is the sharpest single result, and the argument is clean: they simply keep ε and the exponential in the normalisation that the others dropped. That is a real fix, not a quibble, and they make it without fuss. The superstring section is more speculative but it is the part people remember — tying n to δ_GS3/(2π²⟨S+S̄⟩) gives an observational handle on orbifold data, which is a genuinely interesting move even if the construction is a toy with acknowledged dilaton and moduli problems (they cite Brustein-Steinhardt and de Carlos et al. against themselves). Credit for that honesty. The soft spot is §3.2. The claim that inflation ends within a Hubble time of φ_inst is a reductio: assume slow-roll persists, show ψ reaches ψ_vac, show ε and |η| then blow up. It rests on a stated assumption that gradients are negligible, and the authors say outright that they cannot follow the actual dynamics. That is fine as far as it goes, but the abstract's 'reheating is prompt so the reheat temperature can't be far below 10¹¹ GeV' is stated more firmly than the body earns — the body's own hedge is that defect statistics in this regime are unresolved, and the thermalisation argument is order-of-magnitude. It does not touch the tilt result, which is φ-independent in vacuum domination, so the central claim survives. Minor: the abstract lists no limitations at all, while the body is candid about several; a reader skimming only the abstract gets a cleaner picture than the paper supports. Audience is inflationary cosmology and string phenomenology people; anyone working on blue tilts, defect-plus-inflation scenarios, or supergravity model building should read it. Send it out.

Referee report

Significance

This is the foundational systematic study of hybrid inflation, and it earns its place: the slow-roll algebra of Section 2 is clean and self-consistent, the parameter-space delineation in Figs. 1 and 2 is a genuinely useful piece of work, and the correction of the earlier claims of Refs. [5,7] that n could be substantially larger than 1.14 is well argued and important. The superstring section is the most distinctive contribution: Eq. (4.36) ties the scalar tilt directly to the Green-Schwarz coefficients δ_GSi and the dilaton expectation value, which is a falsifiable, essentially parameter-free link between a CMB observable and compactification data. The paper is also commendably explicit about what it has not established, which makes the assessment of the remaining gaps straightforward.

Major objections (3)

[Abstract vs. §3.2, Eqs. (3.9)–(3.15)] The abstract states as a result that 'reheating is prompt so the reheat temperature can't be far below 10^11 GeV' (abstract:s4), but §3.2 establishes this only through a reductio: slow-roll is assumed to persist for one Hubble time, Eqs. (3.10)–(3.13) then show |M_ψ| ≫ H and adiabaticity hold so ψ reaches ψ_vac, and Eqs. (3.14)–(3.15) then give ε, |η| ≫ 1, contradicting the premise. The authors themselves state that in the absence of the back-reaction simplifying feature 'it is not even possible to give a qualitative account of the evolution', and the argument carries the explicit technical assumption that spatial gradients of φ and ψ are negligible. The abstract's phrasing is therefore stronger than the body supports. Either the abstract should be qualified to indicate that prompt reheating follows under the fast-roll picture of §3.2, or §3.2 should be supplemented with an order-of-magnitude estimate of the gradient back-reaction that does not presuppose the conclusion.
[Abstract (abstract:s7) vs. §4.3] The headline particle-physics claim is that the small-inflaton-mass problem 'can be avoided in a natural way for a class of supergravity models which follow from orbifold compactification of superstrings'. Section 4.3 supports this with a toy superpotential, but the authors state plainly that 'we have not however demonstrated that such a superpotential exists', and they leave unaddressed the two post-inflation problems they themselves raise: S′ is likely left far from its minimum once V0 disappears, and the T_i (i ≠ 3) sit at e^{iπ/6} rather than near their vacuum values. Since these are precisely the issues that would decide whether the construction is 'truly realistic', the abstract's confidence is not matched by §4.3. The δ_GS3 = 0 case is also left dependent on the unspecified superpotential. I would ask that the abstract be softened to 'can be avoided in a class of orbifold models, subject to the caveats of §4.3', and that §4.3 state explicitly which of the dilaton and moduli problems are assumed away.
[§3.2–§3.3, Eq. (3.18)] The defect discussion is quantitative only up to an unknown initial correlation length. Section 3.3 writes ξ = ζH^{-1} and concedes that in the vacuum-dominated case 'all we can be sure of (for fast roll-down) is that ζ_vac ≤ 1', yet the monopole abundance Eq. (3.18) and the string-tension benchmark of §3.2 (μ ≲ 9 × 10^{-6} m_Pl, compared with the structure-formation range 2–4 × 10^{-6} m_Pl^2) both effectively assume ζ ≈ 1. The abstract's claim that defects 'can have significant effects' is therefore conditional on an uncomputed quantity, and the margin between the quoted bound and the favoured range is small enough that a factor of a few in ζ would change the conclusion. The authors should state the ζ-dependence of the string and monopole bounds explicitly, so that a reader can see how much of the 'significant effects' claim survives if ζ_vac ≪ 1.

Minor objections (5)

[§2.5, Eqs. (2.49)–(2.50)] The COBE normalisation throughout neglects tilt and the gravitational-wave contribution, which is acknowledged in footnote 5 and again at the end of §2.5, where R is said to reach tens of percent in the intermediate regime. This is harmless for the vacuum-dominated n ≤ 1.14 result, where ε ≪ η, but it means the intermediate-regime values plotted in Fig. 2 (including the dip to n ≈ 0.92) are not self-consistently normalised. A sentence in the Fig. 2 caption flagging which portion of the curve is affected would help.
[§2.2, Eq. (2.16)] The constant 62 in N(k) depends on the assumed reheat temperature, and the paper elsewhere argues that T_reh ranges from 10^11 to 10^16 GeV. The text notes that V^{1/4} ~ 10^11 GeV reduces 60 to about 50 and that the potential is slowly varying, but the quantitative effect on n (through the e^{60η} factor in Eq. (2.37)) is only estimated. A short explicit statement of ∂n/∂N at the upper end of the allowed mass range would make the robustness of n_max = 1.14 transparent.
[§1 and §2.4] The comparison with Refs. [5] and [7], whose larger values of n are attributed to extrapolating the vacuum-dominated regime beyond its validity and neglecting ε, is a substantive criticism of work that is listed as unpublished ('to appear', 'CERN preprint'). The published versions should be checked before the criticism is retained in this form, and the wording should make clear which version was compared.
[§2.4, Eq. (2.26) and following text] The chain of inequalities in Eq. (2.26) and the sentence 'The maximum value does depends on λ and λ′' contain a grammatical slip; the latter should read 'does depend'. Similarly, 'distiguishable' (§1), 'monoples' (§3), 'similiar' (§3.2), 'truely' and 'possibiities' (§4) should be corrected, and 'Mollerach' should be 'Møllerach' in the reference list.
[Figure 3 caption] The caption refers to 'M/mPL'; this should be m_Pl. The caption would also benefit from stating explicitly that trajectory (a) is horizontal because δ is constant while V^{1/4}/m_Pl falls, whereas trajectory (b) is near-vertical because V^{1/4}/m_Pl is approximately constant.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

A two-field false-vacuum inflation model can produce a slightly blue primordial spectrum and can be embedded naturally in supergravity from orbifold compactification of superstrings.

The reading

The paper asks whether inflation can be driven while a second scalar field sits in a false vacuum — a metastable state with nonzero energy density — and whether that arrangement is more natural than ordinary chaotic inflation. When the inflaton falls below a critical value, the false vacuum becomes unstable and the transition to the true vacuum ends inflation. In the regime where the false-vacuum energy dominates, the authors find that the primordial density ripples have a spectral index — the slope of the spectrum, with $1$ meaning scale-invariant — slightly above $1$, reaching about $1.14$ for couplings of order unity, and that the inflationary energy scale can lie between $10^{16}$ and $10^{11}$ GeV with prompt reheating. They also argue that the small inflaton mass required by inflation, the main obstacle for supergravity models, can be achieved naturally in a class of supergravity theories from orbifold compactification of superstrings, where the spectral index is tied to the orbifold's one-loop coefficient. Topological defects form almost inevitably when the false vacuum decays, and at the highest energy scales they can contribute to large-scale structure and the microwave background.

What carries the argument

The load-bearing mechanism is the false-vacuum trajectory: while $�phi^2>�lambda M^2/�lambda'$, the $�psi$ field is pinned at $�psi=0$ and its constant energy density $V_0=�lambda M^4/4$ dominates the potential, so $H$ is nearly constant and the inflaton rolls slowly. The instability at $�phi_{�rm inst}$ converts the false-vacuum energy into the true vacuum and ends inflation. The spectral prediction comes from the standard slow-roll formula $n-1=2�eta-6�epsilon$ evaluated 60 e-foldings before the end, with $�eta=m_{�rm Pl}^2 V''/(8�pi V)$; in the vacuum-dominated limit $�eta$ is independent of $�phi$ and fixed by COBE, which is why $n$ is slightly above $1$. The supergravity part uses the orbifold Kähler potential $K=-�ln Y-�sum_i�ln X_i$ with $X_i=T_i+�bar T_i-�sum_�alpha|�phi_{�alpha i}|^2$; the cancellation of the $X_3$ factor in the $F$-term potential keeps the inflaton mass below $H$ and makes $n$ depend on the one-loop coefficient $�delta_{GS3}$.

Extended reading notes

Core claim

The central claim is that false-vacuum-dominated two-field inflation is a viable and distinctive model. With the potential $V(�phi,�psi)=�frac14�lambda(�psi^2-M^2)^2+�frac12 m^2�phi^2+�frac12�lambda'�phi^2�psi^2$, inflation proceeds along $�psi=0$ until $�phi$ drops below $�phi_{�rm inst}^2=�lambda M^2/�lambda'$; the resulting instability ends inflation. In the vacuum-dominated regime the slow-roll parameters satisfy $�epsilon�ll�eta$, so the spectral index is $n-1=2�eta_{60}-6�epsilon_{60}>0$, with $�eta$ fixed by the COBE normalization; for unit couplings $n$ runs from essentially $1$ to about $1.14$, not the larger values previously suggested. The same potential can be realized in orbifold-compactified supergravity, where the $X_3$ factor that would generate an $O(H)$ mass for the inflaton cancels for one modulus direction and $n=1+�delta_{GS3}/(2�pi^2�langle S+�bar S�rangle)$, for example $n=1.06$ for $�delta_{GS3}=5$ and $�langle S+�bar S�rangle=4$. The inflationary energy scale can be as low as $10^{11}$ GeV, but reheating is prompt, so the reheat temperature is not far below that, and topological defects are almost inevitable.

Load-bearing premise

The load-bearing premise is that the phase transition ends inflation within about a Hubble time of $�phi=�phi_{�rm inst}$, which the authors establish by a contradiction argument that assumes slow roll continues for one Hubble time and that spatial gradients of both fields are negligible, without following the actual dynamics or the resulting defect statistics.

Editorial extensions

If this is right

The false-vacuum-dominated branch predicts a spectral index between $1$ and about $1.14$ for couplings of order unity, a blue tilt that differs from the red tilt typical of ordinary chaotic inflation.
The inflationary energy scale can be anywhere from $10^{16}$ down to $10^{11}$ GeV, but prompt reheating keeps the reheat temperature from falling far below $10^{11}$ GeV, which constrains gravitino production.
Topological defects — domain walls, strings, monopoles, or textures depending on the symmetry — form when the false vacuum decays, and at the upper energy scale they can contribute significantly to the microwave background and large-scale structure.
The model can be realized in global supersymmetry through an axion-like global $U(1)$ false vacuum, and in orbifold supergravity the spectral index is tied to the one-loop coefficient and the dilaton expectation.
A first-order version with bubble nucleation is subject to big-bubble constraints and generally requires $M�gtrsim 10^{13}$ GeV for unit couplings unless the couplings are tuned.

Reading between the lines

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

Because most working inflation models predict $n<1$, a precise measurement of the sign of the tilt is a cleaner discriminator for this branch than the amplitude of the ripples alone.
If the orbifold relation $n=1+�delta_{GS3}/(2�pi^2�langle S+�bar S�rangle)$ is taken seriously, the spectral index becomes a direct probe of the one-loop coefficient and the dilaton expectation during inflation, so a measured $n$ would constrain string compactification parameters.
The paper leaves the defect statistics of the vacuum-dominated transition unresolved; a numerical simulation of the reheating transition could turn the defect abundance into either a confirmation or an exclusion channel for the high-scale end of the model.

Original abstract

We investigate chaotic inflation models with two scalar fields, such that one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the inflaton field falls below some critical value, and a first or second order transition to the true vacuum ensues. Particular attention is paid to Linde's second-order `Hybrid Inflation'; with the false vacuum dominating, inflation differs from the usual true vacuum case both in its cosmology and in its relation to particle physics. The spectral index of the adiabatic density perturbation can be very close to 1, or it can be around ten percent higher. The energy scale at the end of inflation can be anywhere between $10^{16}$\,GeV and $10^{11}$\,GeV, though reheating is prompt so the reheat temperature can't be far below $10^{11}\,$GeV. Topological defects are almost inevitably produced at the end of inflation, and if the inflationary energy scale is near its upper limit they can have significant effects. Because false vacuum inflation occurs with the inflaton field far below the Planck scale, it is easier to implement in the context of supergravity than standard chaotic inflation. That the inflaton mass is small compared with the inflationary Hubble parameter is still a problem for generic supergravity theories, but remarkably this can be avoided in a natural way for a class of supergravity models which follow from orbifold compactification of superstrings. This opens up the prospect of a truly realistic, superstring

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, 7,111 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.72 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.67 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We investigate chaotic inflation models with two scalar fields, such that one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the inflaton field falls below some critical value, and a first or second order transition to the true vacuum ensues. Particular attention is paid to Linde's second-order `Hybrid Inflation'; with the false vacuum dominating, inflation differs from the usual true vacuum case both in its cosmology and in its relation to particle physics. The spectral index of the adiabatic density perturbation can be very close to 1, or it can be around ten percent higher. The energy scale at the end of inflation can be anywhere between $10^{16}$\,GeV and $10^{11}$\,GeV, though reheating is prompt so the reheat temperature can't be far below $10^{11}\,$GeV. Topological defects are almost inevitably produced at the end of inflation, and if the inflationary energy scale is near its upper limit they can have significant effects. Because false vacuum inflation occurs with the inflaton field far below the Planck scale, it is easier to implement in the context of supergravity than standard chaotic inflation. That the inflaton mass is small compared with the inflationary Hubble parameter is still a problem for generic supergravity theories, but remarkably this can be avoided in a natural way for a class of supergravity models which follow from orbifold compactification of superstrings. This opens up the prospect of a truly realistic, superstring

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 chaotic inflation models with two scalar fields, such that one field (the inflaton) rolls while the other is trapped in a false vacuum state.	contribution 0.92	0.70	0.05	asserted 0.95
s1	The false vacuum becomes unstable when the inflaton field falls below some critical value, and a first or second order transition to the true vacuum ensues.	method 0.39	0.27	0.08	asserted 0.99
s2	Particular attention is paid to Linde's second-order `Hybrid Inflation'; with the false vacuum dominating, inflation differs from the usual true vacuum case both in its cosmology and in its relation to particle physics.	contribution 0.67	0.32	0.12	asserted 0.98
s3	The spectral index of the adiabatic density perturbation can be very close to 1, or it can be around ten percent higher.	result 1.00	0.70	0.10	hedged possibility 0.74
s4	The energy scale at the end of inflation can be anywhere between $10^{16}$\,GeV and $10^{11}$\,GeV, though reheating is prompt so the reheat temperature can't be far below $10^{11}\,$GeV.	result 1.00	0.68	0.09	asserted 0.55
s5	Topological defects are almost inevitably produced at the end of inflation, and if the inflationary energy scale is near its upper limit they can have significant effects.	result 0.91	0.50	0.07	asserted 0.65
s6	Because false vacuum inflation occurs with the inflaton field far below the Planck scale, it is easier to implement in the context of supergravity than standard chaotic inflation.	interpretation 0.86	0.26	0.12	asserted 0.87
s7	That the inflaton mass is small compared with the inflationary Hubble parameter is still a problem for generic supergravity theories, but remarkably this can be avoided in a natural way for a class of supergravity models which follow from orbifold compactification of superstrings.	contribution 0.32	0.41	0.14	asserted 0.85
s8	This opens up the prospect of a truly realistic, superstring	interpretation 0.85	0.12	0.12	hedged possibility 0.74

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.68.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

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

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The solid line shows the locus of M and m which satisfy the COBE normalisation for λ = λ ′ = 1. The two analytic branches are clearly seen. The dot-dashed line indicates the analytic solution for the extreme vacuum dominated branch, as utilised by Linde [5]; the deviation of the exact solution from it is caused by the increasing significance of the exponential term in Eq. (2.37) which is included in the parametric analytic solution Eq. (2.36), as used in [7] and indicated here by the dotted line. The dotted line (hidden under the solid for most of its length) terminates when the…

**Figure 2.** The spectral index n is shown for the exact COBE normalised models of

Figures reproduced from arXiv:astro-ph/9401011 by the authors.

References

Works cited (66)

[1]

A. D. Linde, Phys. Lett. B129, 177 (1983); A. D. Linde, Particle Physics and Inﬂationary Cosmology , Harwood Academic, Switzerland (1990)

View on Pith 1983
[2]

A. Linde, Phys. Lett. B249, 18 (1990)

View on Pith 1990
[3]

F. C. Adams and K. Freese, Phys. Rev. D 43, 353 (1991)

View on Pith 1991
[4]

A. D. Linde, Phys. Lett. B259, 38 (1991)

View on Pith 1991
[5]

A. D. Linde, “Hybrid Inﬂation”, to appear, Phys. Rev. D 49, (Jan 15th, 1994)

View on Pith 1994
[6]

A. R. Liddle and D. H. Lyth, Phys. Rep. 231, 1 (1993)

View on Pith 1993
[7]

S. Mollerach, S. Matarrese and F. Lucchin, “Blue Perturb ation Spectra from Inﬂation”, CERN preprint, astro-ph/9309054 (1993)

View on Pith Pith review arXiv 1993
[8]

D. La and P. J. Steinhardt, Phys. Rev. Lett. 62, 376 (1989)

View on Pith 1989
[9]

P. J. Steinhardt and F. S. Accetta, Phys. Rev. Lett. 64, 2740 (1990); J. D. Barrow and K. Maeda, Nucl. Phys. B341, 294 (1990)

View on Pith 1990
[10]

L. Amendola, S. Capozziello, M. Litterio and F. Occhion ero, Phys. Rev. D 45, 417 (1992)

View on Pith 1992
[11]

L. A. Kofman and A. D. Linde, Nucl. Phys. B282, 555 (1987)

View on Pith 1987
[12]

E. T. Vishniac, K. A. Olive and D. Seckel, Nucl. Phys. B289, 717 (1987)

View on Pith 1987
[13]

L. A. Kofman and D. Yu. Pogosyan, Phys. Lett. B214, 508 (1988)

View on Pith 1988
[14]

J. Yokoyama, Phys. Lett. B212, 273 (1988); Phys. Rev. Lett. 63, 712 (1989)

View on Pith 1988
[15]

L. Kofman, G. R. Blumenthal, H. Hodges and J. R. Primack, Proceedings of the Workshop on LS Structure, Rio (1989), eds D W Latham and L N da Costa

View on Pith 1989
[16]

D. S. Salopek, J. R. Bond and J. M. Bardeen, Phys. Rev. D 40, 1753 (1989)

View on Pith 1989
[17]

D. H. Lyth, Phys. Lett. B246, 359 (1990)

View on Pith 1990
[18]

H. M. Hodges and J. R. Primack, Phys. Rev. D 43, 3155 (1991)

View on Pith 1991
[19]

M. Nagasawa and J. Yokoyama, Nucl. Phys. B370, 472 (1992)

View on Pith 1992
[20]

M. Kawashi and K. Sato, Phys. Lett. B189, 23 (1987)

View on Pith 1987
[21]

G. F. Smoot et al , Astrophys. J. Lett. 396, L1 (1992)

View on Pith 1992
[22]

E. L. Wright et al , “Comments on the Statistical Analysis of Excess Variance i n the COBE DMR Maps”, to appear, Astrophys. J. (1994)

View on Pith 1994
[23]

A. R. Liddle, “The Inﬂationary Energy Scale”, to appear , Phys. Rev. D 49 (Jan 15th, 1994)

View on Pith 1994
[24]

A. Linde, Phys. Lett. B284, 215 (1992)

View on Pith 1992
[25]

A. R. Liddle and D. H. Lyth, Phys. Lett. B291, 391 (1992)

View on Pith 1992
[26]

A. A. Starobinsky, Sov. Astron. Lett. 11, 133 (1985)

View on Pith 1985
[27]

T. W. B. Kibble, J. Phys. A9, 1387 (1976)

View on Pith 1976
[28]

D. H. Lyth, Phys. Lett. B147, 403 (1984); ibid B150, 465 (E) (1985). 33

View on Pith 1984
[29]

A. H Guth and S.-Y. Pi, Phys. Rev. D 32, 1899 (1985)

View on Pith 1985
[30]

A. D. Linde and D. H. Lyth, Phys. Lett. B246, 353 (1990)

View on Pith 1990
[31]

D. H. Lyth, Phys. Rev. D 45, 3394 (1992)

View on Pith 1992
[32]

D. H. Lyth and E. D. Stewart, Phys. Rev. D 46, 532 (1992)

View on Pith 1992
[33]

E. Copeland, D. Haws, S. Holbraad and R. Rivers, ‘The Sta tistical Properties of Strings. I Free Strings’, in ‘The Formation and Evolution of Cosmic Strings ’, eds G.Gibbons, S. Hawking and T. Vachaspati, (CUP 1990)

View on Pith 1990
[34]

A. Stebbins, Ann. N. Y. Acad. Sci. 688, 824 (1993)

View on Pith 1993
[35]

T. Vachaspati and A. Vilenkin, Phys. Rev. Lett. 67 1057 (1991)

View on Pith 1991
[36]

A. Albrecht and A. Stebbins, Phys. Rev. Lett. 69, 2615 (1992)

View on Pith 1992
[37]

M. Hindmarsh, “Small scale microwave background ﬂuctu ations from cosmic strings”, Cam- bridge preprint DAMTP-93-28, astro-ph/9307040 (1993)

View on Pith Pith review arXiv 1993
[38]

A. M. Laycock and A. R. Liddle, “Extended Inﬂation with a Curvature-Coupled Inﬂaton”, to appear, Phys. Rev. D 49 (Feb 15th, 1994)

View on Pith 1994
[39]

J. Preskill, Phys. Rev. Lett. 43, 1365 (1979)

View on Pith 1979
[40]

E. N. Parker, Ap. J. 160, 383 (1970). M. S. Turner, E. N. Parker and T. Bogdan, Phys. Rev. D 26, 1296 (1982)

View on Pith 1970
[41]

E. W. Kolb and M. S. Turner, The Early Universe , Addison Wesley (1990)

View on Pith 1990
[42]

For a review of supersymmetry and supergravity, see H. P . Nilles, Phys. Rep. 110, 1 (1984)

View on Pith 1984
[43]

J. E. Kim, Phys. Lett. B136, 378 (1984); J. E. Kim and H. P. Nilles, Phys. Lett. B138, 150 (1984); K. Rajagopal, M. S. Turner and F. Wilczek, Nucl. Phys. B358, 447 (1991); T. Goto and M. Yamaguchi, Phys. Lett. B276, 103 (1992)

View on Pith 1984
[44]

K. Freese, J. A. Frieman and A. V. Olinto, Phys. Rev. Lett . 65, 3233 (1990); F. C. Adams, J. R. Bond, K. Freese, J. A. Frieman and A. V. Olint o, Phys. Rev. D 47, 426 (1993)

View on Pith 1990
[45]

K. Olive, Phys. Rep. 190, 307 (1990)

View on Pith 1990
[46]

D. L¨ ust and C. Mu˜ noz, Phys. Lett.B279, 272 (1992)

View on Pith 1992
[47]

S. Ferrara, C. Kounnas and M. Porrati, Phys. Lett. B181, 263 (1986)

View on Pith 1986
[48]

J.-P. Derendinger, S. Ferrara, C. Kounnas and F. Zwirne r, Nucl. Phys. B372, 145 (1992)

View on Pith 1992
[49]

B. de Carlos, J. A. Casas and C. Mu˜ noz, Nucl. Phys. B399, 623 (1993)

View on Pith 1993
[50]

A. Brignole, L. E. Ib´ a˜ nez and C. Mu˜ noz, “Towards a The ory of Soft Terms for the Super- symmetric Standard Model”, Universidad Aut´ onoma de Madrid preprint FTUAM-26/93, hep- ph/9308271 (1993)

View on Pith 1993
[51]

M. Cvetiˇ c, A. Font, L. E. Ib´ a˜ nez, D. L¨ ust and F. Quevedo, Nucl. Phys. B361, 194 (1991). 34

View on Pith 1991
[52]

S. Ferrara, D. L¨ ust, A. Shapere and S. Theisen, Phys. Le tt. B225, 363 (1989); S. Ferrara, D. L¨ ust and S. Theisen, Phys. Lett. B233, 147 (1989)

View on Pith 1989
[53]

L. E. Ib´ a˜ nez and D. L¨ ust, Nucl. Phys.B382, 305 (1992)

View on Pith 1992
[54]

E. D. Stewart, in preparation

View on Pith
[55]

E. Witten, Phys. Lett. B155, 151 (1985)

View on Pith 1985
[56]

R. Brustein and P. J. Steinhardt, Phys. Lett. B302, 196 (1993)

View on Pith 1993
[57]

B. de Carlos, J. A. Casas, F. Quevedo and E. Roulet, “Mode l-Independent Properties and Cosmological Implications of the Dilaton and Moduli Sector s of 4-D Strings”, CERN preprint CERN-TH.6958/93, hep-ph/9308325 (1993)

View on Pith Pith review arXiv 1993
[58]

A. Font, L. E. Ib´ a˜ nez, D. L¨ ust and F. Quevedo, Phys. Lett. B249, 35 (1990)

View on Pith 1990
[59]

A. H. Guth, Phys. Rev. D 23, 347 (1981)

View on Pith 1981
[60]

A. H. Guth and E. J. Weinberg, Nucl. Phys. B212, 321 (1983)

View on Pith 1983
[61]

S. Coleman, Phys. Rev. D 15, 2929 (1977)

View on Pith 1977
[62]

F. C. Adams, Phys. Rev. D 48, 2800 (1993)

View on Pith 1993
[63]

E. J. Weinberg, Phys. Rev. D 40, 3950 (1989); A. R. Liddle and D. Wands, Phys. Rev. D 45, 2665 (1992); M. S. Turner, E. J. Weinberg and L. M. Widrow, Phys. Rev. D 46, 2384 (1992)

View on Pith 1989
[64]

A. R. Liddle and D. Wands, Mon. Not. Roy. astr. Soc. 253, 637 (1991)

View on Pith 1991
[65]

H. Nariai, Prog. Theor. Phys. 42, 544 (1969)

View on Pith 1969
[66]

K. Maeda, Phys. Rev. D 39, 3159 (1989). Figure Captions Figure 1 The solid line shows the locus of M and m which satisfy the COBE normalisation for λ = λ′ = 1. The two analytic branches are clearly seen. The dot-dashed l ine indicates the analytic solution for the extreme vacuum dominated branch, as utilised by Linde [5 ]; the deviation of the exact solut...

View on Pith Pith review arXiv 1989

Forward citations

Showing 60 of 77 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 77 Pith citations

Towards Inflation in String Theory
hep-th 2003-08 accept novelty 8.0 of 10

A warped throat produces a flat brane-antibrane inflaton potential, but superpotential stabilization of the compactification volume generically gives the inflaton m^2 = 2H^2 and ends slow roll.
Warm-Inflation: a software for first-principles integration of warm inflation power spectra
hep-ph 2026-10 accept novelty 7.0 of 10

A first-principles Mathematica code for integrating warm inflation power spectra using gauge-invariant perturbation equations and a noise autocorrelator that interpolates between quantum and classical regimes.
Resolving the Hubble Tension with New Early Dark Energy
astro-ph.CO 2020-06 conditional novelty 7.0 of 10

A triggered first-order phase transition in a dark sector before recombination lowers the sound horizon and yields H0 = 71.4 +/- 1.0 km/s/Mpc with the local prior, reducing the Hubble tension to 2.5 sigma without it.
New Early Dark Energy
astro-ph.CO 2019-10 conditional novelty 7.0 of 10

A first-order dark-sector phase transition before recombination supplies a short early dark energy burst that fits CMB, BAO, supernova and local H0 data better than ΛCDM, yielding H0 = 71.4 ± 1.0 km/s/Mpc.
Quantum diffusion during inflation and primordial black holes
hep-th 2017-07 conditional novelty 7.0 of 10

The full probability distribution of inflationary curvature perturbations is derived in both the classical and diffusion-dominated limits, and used to show that diffusion-dominated regions of the potential can last at...

Show 55 more citing papers

Fibre Inflation: Observable Gravity Waves from IIB String Compactifications
hep-th 2008-08 conditional novelty 7.0 of 10

A K3-fibre Kähler modulus in a large-volume type IIB compactification drives large-field inflation with a parameter-free relation r ≈ 6(ns-1)², predicting r ≈ 0.005 and ns ≈ 0.970.
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.
Extranatural Inflation
hep-th 2003-01 accept novelty 7.0 of 10

A five-dimensional gauge field's extra component, protected by locality from quantum gravity corrections, can drive inflation with a red spectrum (n about 0.96) and gravitational waves (r about 0.11).
Sneutrino Tribrid Inflation in Flipped $\mathbf{SU(5)}$: Confronting ACT DR6 and Planck Observations
hep-ph 2026-08 conditional novelty 6.0 of 10

A flipped SU(5) sneutrino tribrid inflation model with an independent cutoff scale matches the ACT DR6 and Planck n_s and predicts an observable tensor-to-scalar ratio plus non-thermal leptogenesis.
Axion isocurvature and the model-building problem of low-scale inflation
hep-ph 2026-07 conditional novelty 6.0 of 10

A light pre-inflationary QCD axion that is all the dark matter forces the inflationary Hubble scale below ~10^7–10^10 GeV and, for canonical slow-roll inflation, confines the inflaton to sub-10^-4 M_Pl of field motion...
Tunnelling out of Starobinsky inflation: Raising the spectral tilt
astro-ph.CO 2026-07 conditional novelty 6.0 of 10

A first-order phase-transition exit from a displaced Starobinsky branch truncates ~12 e-folds, shifting the spectral tilt from n_s≈0.965 to ≈0.973 at r≈2×10⁻³.
Superhorizon curvature perturbations in hybrid inflation revisited
astro-ph.CO 2026-06 unverdicted novelty 6.0 of 10

Hybrid inflation's waterfall tachyonic instability grows isocurvature modes that convert to curvature perturbations at the field-space turn, yielding a k^{3}-peaked spectrum with always-positive f_NL that enhances PBH...
Gravitational Dark Matter Production in Supergravity $\alpha$-Attractor Inflation
hep-ph 2024-11 conditional novelty 6.0 of 10

Supergravity corrections in α-attractor inflation suppress gravitational dark matter production and shift the required reheating temperature to 10^3-10^7 GeV.
Observing Invisible Axions with Gravitational Waves
hep-ph 2021-01 accept novelty 6.0 of 10

Global axion strings produce a gravitational wave spectrum enhanced at low frequencies by four powers of a large logarithm, making ultralight axions with decay constants above 10^14 GeV detectable by SKA and future in...
Probing the scale of grand unification with gravitational waves
hep-ph 2019-12 conditional novelty 6.0 of 10

The B-L phase transition near the grand unification scale, embedded in SO(10), produces metastable cosmic strings whose gravitational-wave background should be detectable by LIGO at design sensitivity.
Axion-Dilaton Destabilization and the Hubble Tension
astro-ph.CO 2019-04 conditional novelty 6.0 of 10

An interacting axion-dilaton system can generate an early dark energy phase that dilutes as a^-6 near recombination, offering a string-motivated realization of a proposed Hubble-tension fix.
Inflation from Nilpotent K\"ahler Corrections
hep-th 2016-09 conditional novelty 6.0 of 10

Kähler potential mixing between a nilpotent superfield and a bulk modulus can drive inflation and, in hyperbolic geometry, yields α-attractor predictions.
Multiple Fields in Stochastic Inflation
hep-th 2016-04 accept novelty 6.0 of 10

In multi-field stochastic inflation the number of fields is a critical parameter: above two fields the probability of exploring arbitrarily large field values is nonzero, and for plateau potentials the mean number of ...
Cosmological Attractors from $\alpha$-Scale Supergravity
hep-th 2015-03 accept novelty 6.0 of 10

A single chiral superfield with a logarithmic Kaehler potential of curvature set by alpha reproduces alpha-attractor inflation, with the Kaehler curvature controlling both the stability of the de Sitter plateau and th...
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.
Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies
astro-ph.CO 2015-01 conditional novelty 6.0 of 10

A mild waterfall phase of hybrid inflation produces a broad primordial black hole mass spectrum that can match the dark matter abundance and seed supermassive black holes, for a narrow window of potential parameters.
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...
Effective field theory approach to quasi-single field inflation and effects of heavy fields
hep-th 2012-11 conditional novelty 6.0 of 10

A general effective-field-theory action for quasi-single field inflation is constructed to third order, and used to compute the power spectrum and classify the squeezed-limit momentum dependence of scalar three-point ...
General dissipation coefficient in low-temperature warm inflation
hep-ph 2012-07 conditional novelty 6.0 of 10

On-shell mediator decays, though Boltzmann-suppressed, can dominate the dissipation coefficient in low-temperature supersymmetric warm inflation for small couplings, giving friction that grows as the coupling shrinks.
On the importance of heavy fields during inflation
hep-th 2012-01 conditional novelty 6.0 of 10

The single-field effective theory of a turning two-field inflationary trajectory stays accurate whenever the fractional rate of change of the turn's angular velocity is small compared with the heavy mode's effective mass.
Quasi-Single Field Inflation and Non-Gaussianities
hep-th 2009-11 accept novelty 6.0 of 10

A turning inflaton trajectory coupled to a Hubble-mass isocurvaton produces a continuous family of primordial bispectrum shapes interpolating between equilateral and local, with squeezed-limit scaling set by the isocu...
Gravitational waves from an early matter era
astro-ph.CO 2009-01 accept novelty 6.0 of 10

Density ripples in an early matter era source a gravitational-wave background enhanced by (k_dom/k_dec)^2 over naive estimates, but nonlinear growth caps the enhancement at roughly the inverse square root of the primo...
Ultraviolet Regularisation in de Sitter Space
hep-th 2006-04 conditional novelty 6.0 of 10

A re-derivation shows that ultraviolet regularization in de Sitter space can preserve de Sitter invariance, contrary to earlier claims of anomalous symmetry breaking.
Non-Gaussianities in two-field inflation
astro-ph 2006-03 accept novelty 6.0 of 10

In two-field inflation with a separable potential, the nonlinear parameter f_NL is slow-roll suppressed, and in double quadratic inflation it is of order 1/N, far below observational limits.
Hilltop Inflation
hep-ph 2005-02 conditional novelty 6.0 of 10

Hilltop inflation, starting near a potential maximum, is shown to be generic, to predict r < 0.002, and to arise naturally from F- and D-term models once Planck-suppressed terms are included.
Suppressing the lower Multipoles in the CMB Anisotropies
astro-ph 2003-03 conditional novelty 6.0 of 10

A short kinetic-dominated stage at the onset of the last 65 e-folds of inflation can cut off primordial power at horizon scales, and WMAP temperature data prefer such a cutoff at roughly two sigma, not decisively.
Running cosmological constant in light of recent CMB-BAO data
astro-ph.CO 2026-10 conditional novelty 5.0 of 10

A logarithmically corrected cosmological constant can drive inflation that fits CMB-plus-BAO data with a positive correction and CMB-only data with a regularized negative correction, depending on the size and sign of ...
Supersymmetric Hybrid Inflation with K\"{a}hler-Induced $\mathbf{R}$-Symmetry Breaking
hep-ph 2025-06 conditional novelty 5.0 of 10

Nonrenormalizable R-symmetry breaking in the Kahler potential can tune the spectral index of supersymmetric hybrid inflation into the ACT DR6 window while keeping tensor modes below 1e-5.
Higgs-like inflation under ACTivated mass
hep-ph 2025-05 conditional novelty 5.0 of 10

In metric Higgs-like inflation, a quadratic mass term in the Jordan frame raises the spectral index and can restore compatibility with the ACT+BK+Planck+DESI data.
How Accidental was Inflation?
hep-ph 2025-04 conditional novelty 5.0 of 10

A small, string-theoretically plausible deformation of the Starobinsky potential (lambda about 0.9999) fits the Planck plus ACT and DESI value of the spectral tilt better than the pure Starobinsky model, and introduce...
Curvature perturbations from vacuum transition during inflation
astro-ph.CO 2025-02 conditional novelty 5.0 of 10

Vacuum transitions during inflation, modulated by a light spectator field, can generate curvature perturbations with non-Gaussianity fNL ~ O(10) in a Higgs inflation setup.
Towards hybrid inflation with $n_s=1$ in light of Hubble tension and primordial gravitational waves
astro-ph.CO 2022-05 conditional novelty 5.0 of 10

Hybrid inflation ending in a waterfall instability can lift the scalar spectral index to ns = 1, reviving chaotic φ² inflation when combined with early dark energy.
New Early Dark Energy is compatible with current LSS data
astro-ph.CO 2020-08 conditional novelty 5.0 of 10

Adding full-shape LSS data to CMB, BAO and supernova measurements leaves the New Early Dark Energy fit essentially unchanged, with H0 = 71.2 +/- 1.0 and a roughly 4 sigma preference for a nonzero NEDE fraction.
QCD Axion on Hilltop by a Phase Shift of $\pi$
hep-ph 2019-08 conditional novelty 5.0 of 10

A heavy axion inflaton can shift the QCD axion potential by π, placing the QCD axion at the hilltop and allowing f_a ≳ 3×10^9 GeV to explain all dark matter.
Higgs as heavy-lifted physics during inflation
hep-ph 2018-12 conditional novelty 5.0 of 10

Strong Higgs-inflaton mixing during inflation lifts the effective Higgs mass scale to m_h/c_s, where c_s is the inflaton sound speed, extending the range of Higgs masses that produce observable non-analytic signals in...
The ALP miracle: unified inflaton and dark matter
hep-ph 2017-02 conditional novelty 5.0 of 10

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

Forecasts indicate a CMB polarization satellite with 1.7 microkelvin-arcmin sensitivity and 5 arcmin resolution would measure the tensor-to-scalar ratio to about 2e-4 and the scalar tilt to 0.0014, enough to separate ...
Calculations of Inflaton Decays and Reheating: with Applications to No-Scale Inflation Models
hep-ph 2015-05 accept novelty 5.0 of 10

Careful numerical and analytic treatment of the reheating equation of state in no-scale Starobinsky-like inflation yields N_* values that, compared with Planck 2015, constrain the inflaton decay rate to Gamma_phi/m > ...
Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
astro-ph.CO 2014-05 conditional novelty 5.0 of 10

Numerically integrating the stochastic inflaton dynamics reproduces the standard power spectrum in chaotic inflation and yields, for the first time, the full power spectrum through the hybrid inflation waterfall, incl...
A No-Scale Inflationary Model to Fit Them All
hep-ph 2014-05 conditional novelty 5.0 of 10

A single no-scale supergravity model with two fields reproduces both quadratic and Starobinsky-like inflation as limits of one angle, spanning tensor-to-scalar ratios from roughly 0.09 to 0.003 at n_s about 0.96.
Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity
hep-th 2013-07 conditional novelty 5.0 of 10

Four distinct superpotentials in SU(2,1)/SU(2)xU(1) no-scale supergravity each yield the Starobinsky R+R^2 inflationary potential once the companion field is stabilized, and multi-modulus variants shift the predicted ...
The Gravitational Wave Spectrum from Cosmological B-L Breaking
hep-ph 2013-05 conditional novelty 5.0 of 10

In a B-L hybrid inflation model, cosmic strings produce a gravitational wave background five to eight orders of magnitude above the inflationary one, with a spectral kink that encodes the reheating temperature.
Dissipative Effects on Reheating after Inflation
hep-ph 2012-12 conditional novelty 5.0 of 10

For a light inflaton with a large oscillation amplitude, dissipation into the thermal plasma it produces sets the reheating temperature, which can differ from the standard perturbative estimate by orders of magnitude.
CMB Imprints of a Pre-Inflationary Climbing Phase
hep-th 2012-02 conditional novelty 5.0 of 10

A string-motivated pre-inflationary climbing phase suppresses the scalar CMB power spectrum and mildly enhances the tensor spectrum at large angular scales, with oscillations superposed on both.
Poly-instanton Inflation
hep-th 2011-10 conditional novelty 5.0 of 10

Poly-instanton corrections to the type IIB superpotential can drive slow-roll inflation on a Kähler fibre modulus, predicting ns about 0.96 and r about 10^-5.
Induced gravitational wave background and primordial black holes
astro-ph.CO 2009-08 conditional novelty 5.0 of 10

Second-order density ripples source a gravitational wave background whose amplitude is bounded more tightly by primordial black hole abundance limits than by current LIGO data, with Advanced LIGO able to surpass the b...
Non-Gaussianity, Spectral Index and Tensor Modes in Mixed Inflaton and Curvaton Models
astro-ph 2008-02 accept novelty 5.0 of 10

In mixed inflaton-curvaton models, large non-Gaussianity can coexist with an acceptable spectral index and tensor-to-scalar ratio, and a consistency relation links the bispectrum and trispectrum when the curvaton stay...
Gravitational Wave Production At The End Of Inflation
astro-ph 2006-12 conditional novelty 5.0 of 10

Preheating after inflation generates a stochastic gravitational wave background whose amplitude is independent of the inflationary energy scale while its peak frequency scales inversely with it, reaching Omega_gw h^2 ...
Tachyonic Instability and Dynamics of Spontaneous Symmetry Breaking
hep-th 2001-06 accept novelty 5.0 of 10

Spontaneous symmetry breaking from a tachyonic (negative mass squared) potential completes within one oscillation of the field distribution, because the instability converts potential energy into colliding classical w...
Split supersymmetry and hybrid inflation in light of Atacama Cosmology Telescope DR6 data
hep-ph 2025-07 conditional novelty 4.0 of 10

An update of mu-term hybrid inflation shows that a tuned soft-SUSY parameter B makes the scalar spectral index match ACT DR6, with tensor-to-scalar ratio of order 10^-3 to 10^-2 and a 2 TeV wino dark matter candidate.
Waterfall phase in supersymmetric hybrid inflation
hep-ph 2025-07 conditional novelty 4.0 of 10

Waterfall-phase e-foldings in R-symmetric SUSY hybrid inflation can produce a PTA-compatible scalar-induced gravitational wave background and, in SU(5), dilute monopoles to observable levels.
Hybrid cosmological attractors
hep-th 2022-04 conditional novelty 4.0 of 10

Uplifting an α-attractor potential with a hybrid-inflation sector produces a second attractor with ns = 1, continuously interpolating to the standard 1 - 2/N as the uplift or critical field shrinks.
The zoo plot meets the swampland: mutual (in)consistency of single-field inflation, string conjectures, and cosmological data
astro-ph.CO 2018-08 conditional novelty 4.0 of 10

Planck and BICEP2/Keck data force the swampland conjectures' order-unity parameter c below about 0.1, in strong tension with the string-theory expectation that c is of order one.
Inflation and Alternatives with Blue Tensor Spectra
astro-ph.CO 2014-03 conditional novelty 4.0 of 10

Allowing a free tensor tilt in BICEP2 plus Planck data yields a mild preference for blue n_T, and the paper argues non-Gaussianity would then separate inflationary blue-tilt models from string gas cosmology.
COrE (Cosmic Origins Explorer) A White Paper
astro-ph.CO 2011-02 conditional novelty 4.0 of 10

A 15-band full-sky microwave polarimeter with 10 to 30 times Planck's sensitivity would detect primordial tensor modes at r = 0.001 at 3 sigma and measure the CMB lensing deflection to the cosmic variance limit, provi...

See all 77 Pith citations

How the literature uses it

189 arXiv papers cite this in 277 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 · 172 sentences without a confident label

Contests it 2 papers

The `classic' model of hybrid inflation [ref] predicts a blue spectrum of CMB perturbations that is now ruled out by observations [ref] .

On Hybrid Monodromy Inflation (Hic Sunt Dracones) · Introduction · contest 0.85
The main drawback of hybrid inflationary models was their prediction for the spectral index $n_s ≳1$ [ref] , value excluded by the Planck data [ref] .

Gravitational Waves and Primordial Black Holes from Supersymmetric Hybrid Inflation · Introduction · contest 0.83

Builds on it 2 papers

We focus on a variation of extended hybrid Inflationary potential [ref] , in which the potential along the rolling direction is replaced with an inflection point inflation potential [ref] V(ϕ,ψ) = V_0+1/2 m^2ϕ^2 - 4 A λ__3/3 ϕ^3 + λ__3^2 ϕ^4+ 1/4λψ^4-1/3γM ψ^3 +1/2 λ^' ϕ^2ψ^2+1/2 αM^2 ψ^2

Examining the end of inflation with primordial black holes mass distribution and gravitational waves · Double field inflation · 0.90
This is the same as the original hybrid inflation model considered in Refs. [ref] except that we have included the additional field, $σ$, coupled to the waterfall field, as proposed by Lyth [ref] .

Curvaton and the inhomogeneous end of inflation · Hybrid Inflation · 0.99

Uses its method or tool 1 paper

We shall use the percolation parameter [ref] [equation] to determine the time of the transition.

Curvature perturbations from vacuum transition during inflation · Setup · 0.94

Compares with it 5 papers

Note that, in our case, the leading SUGRA correction to the inflationary potential for minimal Kähler potential, which corresponds to the second term in the parenthesis of Eq. [ref], is the same as the one found in the first of Ref. [ref] , in the case of standard hybrid inflation and in Ref. [ref] , in the case of shifted and smooth hybrid inflation.

Phenomenology and Cosmology of Supersymmetric Grand Unified Theories · Supergravity corrections · 1.00
We observe that this result is essentially compatible with the Lyth bound [ref] .]

Higgs Inflation and the Refined dS Conjecture · Introduction · 0.97
The behavior is also somewhat analogous to hybrid inflation [ref] , although in our case, slow-roll inflation could persist long after the inflaton trajectory changes direction.

QCD Axion Hybrid Inflation · Introduction · 0.96

Cites it as support 1 paper

In supersymmetric models, generic supergravity correction can spoil the flatness of the inflaton potential during the inflation since it can induce a large mass correction for inflaton field [ref] .

Orbifold GUT inflation · Introduction · 0.96

Cites it as background 80 papers

Such a process is a crucial element of the hybrid inflationary scenario, introduced by Linde, in which inflation ends through a sudden instability [ref] .

Non-Gaussianity constrains hybrid inflation · Introduction · 0.95
Supersymmetric hybrid inflation comes in two variants, depending on whether the vacuum energy density during inflation is dominated by a nonzero F term [ref] or D term [ref] .

Unified Model of D-Term Inflation · Introduction · 0.99
In conventional hybrid inflation [ref] inflation ends abruptly by the waterfall transition.

Curvature perturbation and waterfall dynamics in hybrid inflation · Introduction · 0.91

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

A. D. Linde, Phys. Lett. B129, 177 (1983); A. D. Linde, Particle Physics and Inﬂationary Cosmology , Harwood Academic, Switzerland (1990)

View on Pith 1983

[2] [2]

A. Linde, Phys. Lett. B249, 18 (1990)

View on Pith 1990

[3] [3]

F. C. Adams and K. Freese, Phys. Rev. D 43, 353 (1991)

View on Pith 1991

[4] [4]

A. D. Linde, Phys. Lett. B259, 38 (1991)

View on Pith 1991

[5] [5]

A. D. Linde, “Hybrid Inﬂation”, to appear, Phys. Rev. D 49, (Jan 15th, 1994)

View on Pith 1994

[6] [6]

A. R. Liddle and D. H. Lyth, Phys. Rep. 231, 1 (1993)

View on Pith 1993

[7] [7]

S. Mollerach, S. Matarrese and F. Lucchin, “Blue Perturb ation Spectra from Inﬂation”, CERN preprint, astro-ph/9309054 (1993)

View on Pith Pith review arXiv 1993

[8] [8]

D. La and P. J. Steinhardt, Phys. Rev. Lett. 62, 376 (1989)

View on Pith 1989

[9] [9]

P. J. Steinhardt and F. S. Accetta, Phys. Rev. Lett. 64, 2740 (1990); J. D. Barrow and K. Maeda, Nucl. Phys. B341, 294 (1990)

View on Pith 1990

[10] [10]

L. Amendola, S. Capozziello, M. Litterio and F. Occhion ero, Phys. Rev. D 45, 417 (1992)

View on Pith 1992

[11] [11]

L. A. Kofman and A. D. Linde, Nucl. Phys. B282, 555 (1987)

View on Pith 1987

[12] [12]

E. T. Vishniac, K. A. Olive and D. Seckel, Nucl. Phys. B289, 717 (1987)

View on Pith 1987

[13] [13]

L. A. Kofman and D. Yu. Pogosyan, Phys. Lett. B214, 508 (1988)

View on Pith 1988

[14] [14]

J. Yokoyama, Phys. Lett. B212, 273 (1988); Phys. Rev. Lett. 63, 712 (1989)

View on Pith 1988

[15] [15]

L. Kofman, G. R. Blumenthal, H. Hodges and J. R. Primack, Proceedings of the Workshop on LS Structure, Rio (1989), eds D W Latham and L N da Costa

View on Pith 1989

[16] [16]

D. S. Salopek, J. R. Bond and J. M. Bardeen, Phys. Rev. D 40, 1753 (1989)

View on Pith 1989

[17] [17]

D. H. Lyth, Phys. Lett. B246, 359 (1990)

View on Pith 1990

[18] [18]

H. M. Hodges and J. R. Primack, Phys. Rev. D 43, 3155 (1991)

View on Pith 1991

[19] [19]

M. Nagasawa and J. Yokoyama, Nucl. Phys. B370, 472 (1992)

View on Pith 1992

[20] [20]

M. Kawashi and K. Sato, Phys. Lett. B189, 23 (1987)

View on Pith 1987

[21] [21]

G. F. Smoot et al , Astrophys. J. Lett. 396, L1 (1992)

View on Pith 1992

[22] [22]

E. L. Wright et al , “Comments on the Statistical Analysis of Excess Variance i n the COBE DMR Maps”, to appear, Astrophys. J. (1994)

View on Pith 1994

[23] [23]

A. R. Liddle, “The Inﬂationary Energy Scale”, to appear , Phys. Rev. D 49 (Jan 15th, 1994)

View on Pith 1994

[24] [24]

A. Linde, Phys. Lett. B284, 215 (1992)

View on Pith 1992

[25] [25]

A. R. Liddle and D. H. Lyth, Phys. Lett. B291, 391 (1992)

View on Pith 1992

[26] [26]

A. A. Starobinsky, Sov. Astron. Lett. 11, 133 (1985)

View on Pith 1985

[27] [27]

T. W. B. Kibble, J. Phys. A9, 1387 (1976)

View on Pith 1976

[28] [28]

D. H. Lyth, Phys. Lett. B147, 403 (1984); ibid B150, 465 (E) (1985). 33

View on Pith 1984

[29] [29]

A. H Guth and S.-Y. Pi, Phys. Rev. D 32, 1899 (1985)

View on Pith 1985

[30] [30]

A. D. Linde and D. H. Lyth, Phys. Lett. B246, 353 (1990)

View on Pith 1990

[31] [31]

D. H. Lyth, Phys. Rev. D 45, 3394 (1992)

View on Pith 1992

[32] [32]

D. H. Lyth and E. D. Stewart, Phys. Rev. D 46, 532 (1992)

View on Pith 1992

[33] [33]

E. Copeland, D. Haws, S. Holbraad and R. Rivers, ‘The Sta tistical Properties of Strings. I Free Strings’, in ‘The Formation and Evolution of Cosmic Strings ’, eds G.Gibbons, S. Hawking and T. Vachaspati, (CUP 1990)

View on Pith 1990

[34] [34]

A. Stebbins, Ann. N. Y. Acad. Sci. 688, 824 (1993)

View on Pith 1993

[35] [35]

T. Vachaspati and A. Vilenkin, Phys. Rev. Lett. 67 1057 (1991)

View on Pith 1991

[36] [36]

A. Albrecht and A. Stebbins, Phys. Rev. Lett. 69, 2615 (1992)

View on Pith 1992

[37] [37]

M. Hindmarsh, “Small scale microwave background ﬂuctu ations from cosmic strings”, Cam- bridge preprint DAMTP-93-28, astro-ph/9307040 (1993)

View on Pith Pith review arXiv 1993

[38] [38]

A. M. Laycock and A. R. Liddle, “Extended Inﬂation with a Curvature-Coupled Inﬂaton”, to appear, Phys. Rev. D 49 (Feb 15th, 1994)

View on Pith 1994

[39] [39]

J. Preskill, Phys. Rev. Lett. 43, 1365 (1979)

View on Pith 1979

[40] [40]

E. N. Parker, Ap. J. 160, 383 (1970). M. S. Turner, E. N. Parker and T. Bogdan, Phys. Rev. D 26, 1296 (1982)

View on Pith 1970

[41] [41]

E. W. Kolb and M. S. Turner, The Early Universe , Addison Wesley (1990)

View on Pith 1990

[42] [42]

For a review of supersymmetry and supergravity, see H. P . Nilles, Phys. Rep. 110, 1 (1984)

View on Pith 1984

[43] [43]

J. E. Kim, Phys. Lett. B136, 378 (1984); J. E. Kim and H. P. Nilles, Phys. Lett. B138, 150 (1984); K. Rajagopal, M. S. Turner and F. Wilczek, Nucl. Phys. B358, 447 (1991); T. Goto and M. Yamaguchi, Phys. Lett. B276, 103 (1992)

View on Pith 1984

[44] [44]

K. Freese, J. A. Frieman and A. V. Olinto, Phys. Rev. Lett . 65, 3233 (1990); F. C. Adams, J. R. Bond, K. Freese, J. A. Frieman and A. V. Olint o, Phys. Rev. D 47, 426 (1993)

View on Pith 1990

[45] [45]

K. Olive, Phys. Rep. 190, 307 (1990)

View on Pith 1990

[46] [46]

D. L¨ ust and C. Mu˜ noz, Phys. Lett.B279, 272 (1992)

View on Pith 1992

[47] [47]

S. Ferrara, C. Kounnas and M. Porrati, Phys. Lett. B181, 263 (1986)

View on Pith 1986

[48] [48]

J.-P. Derendinger, S. Ferrara, C. Kounnas and F. Zwirne r, Nucl. Phys. B372, 145 (1992)

View on Pith 1992

[49] [49]

B. de Carlos, J. A. Casas and C. Mu˜ noz, Nucl. Phys. B399, 623 (1993)

View on Pith 1993

[50] [50]

A. Brignole, L. E. Ib´ a˜ nez and C. Mu˜ noz, “Towards a The ory of Soft Terms for the Super- symmetric Standard Model”, Universidad Aut´ onoma de Madrid preprint FTUAM-26/93, hep- ph/9308271 (1993)

View on Pith 1993

[51] [51]

M. Cvetiˇ c, A. Font, L. E. Ib´ a˜ nez, D. L¨ ust and F. Quevedo, Nucl. Phys. B361, 194 (1991). 34

View on Pith 1991

[52] [52]

S. Ferrara, D. L¨ ust, A. Shapere and S. Theisen, Phys. Le tt. B225, 363 (1989); S. Ferrara, D. L¨ ust and S. Theisen, Phys. Lett. B233, 147 (1989)

View on Pith 1989

[53] [53]

L. E. Ib´ a˜ nez and D. L¨ ust, Nucl. Phys.B382, 305 (1992)

View on Pith 1992

[54] [54]

E. D. Stewart, in preparation

View on Pith

[55] [55]

E. Witten, Phys. Lett. B155, 151 (1985)

View on Pith 1985

[56] [56]

R. Brustein and P. J. Steinhardt, Phys. Lett. B302, 196 (1993)

View on Pith 1993

[57] [57]

B. de Carlos, J. A. Casas, F. Quevedo and E. Roulet, “Mode l-Independent Properties and Cosmological Implications of the Dilaton and Moduli Sector s of 4-D Strings”, CERN preprint CERN-TH.6958/93, hep-ph/9308325 (1993)

View on Pith Pith review arXiv 1993

[58] [58]

A. Font, L. E. Ib´ a˜ nez, D. L¨ ust and F. Quevedo, Phys. Lett. B249, 35 (1990)

View on Pith 1990

[59] [59]

A. H. Guth, Phys. Rev. D 23, 347 (1981)

View on Pith 1981

[60] [60]

A. H. Guth and E. J. Weinberg, Nucl. Phys. B212, 321 (1983)

View on Pith 1983

[61] [61]

S. Coleman, Phys. Rev. D 15, 2929 (1977)

View on Pith 1977

[62] [62]

F. C. Adams, Phys. Rev. D 48, 2800 (1993)

View on Pith 1993

[63] [63]

E. J. Weinberg, Phys. Rev. D 40, 3950 (1989); A. R. Liddle and D. Wands, Phys. Rev. D 45, 2665 (1992); M. S. Turner, E. J. Weinberg and L. M. Widrow, Phys. Rev. D 46, 2384 (1992)

View on Pith 1989

[64] [64]

A. R. Liddle and D. Wands, Mon. Not. Roy. astr. Soc. 253, 637 (1991)

View on Pith 1991

[65] [65]

H. Nariai, Prog. Theor. Phys. 42, 544 (1969)

View on Pith 1969

[66] [66]

K. Maeda, Phys. Rev. D 39, 3159 (1989). Figure Captions Figure 1 The solid line shows the locus of M and m which satisfy the COBE normalisation for λ = λ′ = 1. The two analytic branches are clearly seen. The dot-dashed l ine indicates the analytic solution for the extreme vacuum dominated branch, as utilised by Linde [5 ]; the deviation of the exact solut...

View on Pith Pith review arXiv 1989