Dynamics of Symmetry Breaking and Tachyonic Preheating

Andrei Linde; Gary Felder; Igor Tkachev; Juan Garcia-Bellido; Lev Kofman; Patrick B. Greene

REVIEW

Dynamics of Symmetry Breaking and Tachyonic Preheating

Gary Felder, Juan Garcia-Bellido, Patrick B. Greene, Lev Kofman, Andrei Linde, Igor Tkachev

High Energy Physics - Phenomenology · Submitted 13 Dec 2000 · 22 references

Pith's verdict: The letter that named tachyonic preheating: the single-oscillation claim holds up qualitatively, but the technical backing sits in a companion paper still in preparation.

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 · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/0012142 (version 1)

Pith IDAPTRQX7V, Pith's permanent record of this paper and its review

CitationAndrei Linde, Gary Felder, Igor Tkachev, Juan Garcia-Bellido, Lev Kofman, Patrick B. Greene. "Dynamics of Symmetry Breaking and Tachyonic Preheating." arXiv:hep-ph/0012142 (2000). https://pith.science/paper/APTRQX7V

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

Short version: this is the letter that named tachyonic preheating, and the headline claim — symmetry breaking in these models finishes in a single oscillation, so the homogeneous stage of hybrid reheating essentially doesn't happen — is well argued and, for a letter, adequately supported. It's a standard citation for good reason and it deserves to be one. What's actually new is the reframing. Symmetry breaking here is a nonperturbative, gradient-energy-dominated process, not a perturbative roll with small corrections. The paper makes the case that Hartree and 1/N treatments miss defect production and rescattering, and that the domain structure is leading order rather than a correction. The analytic estimates are clean and internally consistent: the growth time t* ~ (1/2m) ln(pi^2/lambda) in Eq. (3) is robust and only logarithmically sensitive to the initial spectrum, and the cubic-model seed estimate in Eq. (5) is sensible. The lattice movies aren't decoration; they show the percolation picture directly. The authors are also honest that their own 1998 paper already covered the g^2 >> lambda limit. Soft spots, in order of weight. First, the technical backing — lattice parameters, the renormalization subtraction for the cubic model, error analysis — all lives in ref. [12], listed as in preparation. That's the main reason this reads as a letter announcing a program rather than closing it. Second, the figures are qualitative histograms with no error bars and no lattice-spacing scan. On the stress-test point about the cubic model: it's the sharpest concern, but I'd temper it. The bubble seeding comes from the tail of the coarse-grained IR field, whose variance is set by modes below the tachyonic scale and by box volume, not by the UV lattice spacing; the tail probability is exponentially suppressed in (dphi/dphi_rms)^2 regardless of cutoff. So the qualitative picture should survive. What isn't shown is a lattice-spacing scan, and the renormalization subtraction is exactly where a cutoff dependence would enter. Worth asking for, not a refutation. Also, the F-term conclusion doesn't rest on the cubic toy alone — they ran F-term and D-term lattices directly. Who should read it: anyone working on reheating, hybrid inflation, or defect formation, plus the DCC crowd. Send it to referees; the companion paper is where the real scrutiny belongs.

Referee report

Significance

If the central claim holds, it displaces the parametric-resonance picture of hybrid reheating with a fast spinodal mechanism and promotes domain structure and gradient energy to leading-order features of symmetry breaking rather than perturbative corrections. The paper's strengths are real and should be named: the analytic estimates in Eqs. (2), (3) and (5) are internally consistent and give a clear, physically transparent criterion for single-oscillation completion; the lattice treatment goes beyond Hartree/1-N methods in a regime where those methods are known to fail; the visual presentation (probability distributions plus the four submitted animations) makes the dynamics checkable by eye; and the extension to F-term and D-term hybrid models yields a concrete, in-principle falsifiable statement about the duration of the homogeneous oscillation stage. The identification of the cubic potential (Eq. 4) as the effective potential along the F-term trajectory is a genuinely useful structural observation.

Major objections (3)

[Sec. II.B, Eq. (5) and Figs. 4-5] The cubic model is the prototype for the F-term hybrid-inflation claim in Sec. III, and its dynamics is seeded differently from the quadratic case: because m^2(phi) = -2*lambda*v*phi + 3*lambda*phi^2 vanishes at phi = 0, there is no fixed tachyonic mass, and the instability must grow out of the initial fluctuation spectrum. The manuscript itself states that fluctuations 'a few times greater than (5)' grow faster and 'may therefore have greater impact,' and that 'low probability fluctuations with delta-phi >> delta-phi_rms correspond to peaks of the initial Gaussian distribution.' The abundance and amplitude of those peaks are controlled by the far UV tail of the initial spectrum, i.e. by the lattice cutoff and the choice of initial vacuum distribution, yet no lattice-spacing variation, box-size variation, or initial-spectrum variation is reported for this model. The renormalization subtraction (the induced lambda*v*phi*<phi^2> term) is acknowledged but its implementation is not shown. Because Sec. III identifies the cubic potential with the F-term trajectory (g^2 = 2*lambda), the 'typically tachyonic, single oscillation' conclusion for F-term models inherits this sensitivity. A short convergence check would settle the point: repeat the cubic-model runs at two lattice spacings (or two UV cutoffs of the initial spectrum) and report whether the time to reach <phi^2> ~ v^2 and the fraction of volume in bubbles are stable. If they are, the concern is closed and the F-term claim is on firm ground.
[Sec. III, Eq. (6)] The simulations switch on the tachyonic mass at t = 0 with vacuum initial conditions, i.e. an instantaneous quench. In hybrid inflation the transition is not instantaneous: phi rolls through phi_c = M/g with finite velocity, and the effective tachyonic mass m_sigma^2 = g^2*phi^2 - lambda*v^2 grows only as phi moves below phi_c. The manuscript acknowledges in the penultimate paragraph of Sec. III that 'there may exist some particular versions of hybrid inflation in which tachyonic preheating is inefficient, e.g. because of fast motion of the field phi near the bifurcation point,' but gives no quantitative criterion separating the fast-quench regime from the slow-roll-through regime. A criterion would be valuable and is within reach: for instance, the ratio of the rolling velocity |phi-dot|/phi_c to the growth rate m_sigma at the point where the instability sets in, or equivalently the number of e-folds of tachyonic growth available before the trajectory reaches the flat part near the minimum. Even an estimate of the parameter range over which the single-oscillation result survives, or a single lattice run with a nonzero initial phi-dot, would substantially strengthen the 'typically' in the abstract.
[Figs. 1, 3, 5, 6 and Ref. [12]] The central claim is quantitative ('within a single oscillation'), but the evidence presented in the letter is a set of probability histograms with no quoted lattice spacing, box size, initial-spectrum cutoff, or statistical uncertainty, and the technical details, including the renormalization procedure, are deferred to Ref. [12], which is listed as 'in preparation.' A letter may legitimately defer details, but the specific numbers that would let a reader judge convergence are exactly the ones deferred. At minimum the letter should state the lattice spacing and physical box size in units of m^{-1} (or v), confirm that the 128^3 and 256^3 runs agree on the time at which the distribution settles at |phi| ~ v, and state how the initial fluctuation spectrum is truncated. This is a modest addition and would make the headline number auditable rather than illustrative.

Minor objections (7)

[Sec. II.A, Eq. (2)] The mode-function normalization 1/sqrt(2k) exp(-ikt + i k.x) should be stated as a box or continuum convention, since the overall amplitude of <delta-phi^2> and hence the numerical coefficient inside the logarithm in t_* depends on it. The text notes that t_* depends only logarithmically on the initial distribution, which mitigates this, but the convention should still be explicit.
[Sec. II.B] The statement that fluctuations grow 'until the amplitude of delta-phi becomes comparable to 2v/3' would read better with the one-line justification: m_eff^2 = -2*lambda*v*phi + 3*lambda*phi^2 vanishes at phi = 2v/3. As written the reader must reconstruct this.
[Figs. 1, 3, 5, 6 captions] The time labels (t = 0, 8, 10, 13, 14, 19 in Fig. 1; t = 0, 40, 44, 48, 50, 70 in Fig. 5) are not given units. Please state in each caption that time is in units of m^{-1} (or the appropriate scale for that model), and state the lattice size used for each figure.
[Fig. 6] The caption refers to motion along the ellipse g^2*phi^2 + lambda*sigma^2 = g^2*phi_c^2, but sigma is complex in this model. Please clarify whether sigma in the ellipse denotes |sigma| and whether the plotted distribution is over phi and |sigma| or over phi and one component.
[References] Several reference entries need correction: Ref. [14] should read 'Bastero-Gil' rather than 'Bastelo-Gil'; Ref. [20] should read 'Van Proeyen' rather than 'Van Proyen'; and the first author affiliation gives 'Stanford, CA 9 4305' where '94305' is intended.
[Sec. II.A, paragraph 3] Typo: 'until its becomes O(v)' should read 'until it becomes O(v)'.
[Submission / supplementary files] The four animations (1.gif-4.gif) are cited as part of the submission and hosted at a Stanford URL. Please confirm whether they will be archived with the published version, since a URL alone is not a durable reference.

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

The paper

The paper claims

Symmetry breaking may complete within a single oscillation of the field, not through a long slow roll toward the minimum.

The reading

The paper revisits the textbook story of spontaneous symmetry breaking — a field sitting at an unstable maximum with a negative mass squared, then rolling down to a new minimum — and argues that the process is far faster and more violent than perturbation theory suggests. Using three-dimensional lattice simulations of the classical field, the authors show that the exponentially growing long-wavelength modes reach the size of the symmetry-breaking scale $v$ within a time $t_*$ that depends only logarithmically on the coupling, and that the resulting gradient energy of the domain structure is comparable to the entire initial potential energy $V(0)$. The practical consequence is that the field distribution settles near $|v|$ after a single oscillation, so the usual picture of many slow oscillations about the minimum does not apply. The authors then apply this to hybrid inflation, where inflation ends at a bifurcation point and the triggering field is unstable: they argue that preheating there is typically tachyonic rather than parametric-resonant, so the stage of coherent oscillation of the inflaton fields ends after one oscillation. If that is right, the standard treatment of reheating in hybrid models — resonant particle production over many oscillations — is describing the wrong mechanism.

What carries the argument

The load-bearing mechanism is the spinodal (tachyonic) instability combined with a classical-statistical lattice treatment of the field. Because the growing modes acquire occupation numbers $n_k ∼ π^2/λ ≫ 1$, the quantum state is legitimately replaced by an ensemble of classical waves obeying the relativistic wave equation on a $128^3$ or $256^3$ grid, evolved with the LATTICEEASY code. The argument turns on two estimates that make the effect leading-order rather than a correction: the growth time $t_* ∼ (1/2m)ln(π^2/λ)$, which is only logarithmically sensitive to the initial fluctuation spectrum, and the gradient energy of the resulting domain structure, $∼ k^2δφ^2 = O(m^4/λ)$, which matches the initial potential energy and therefore blocks any coherent return to the symmetric state. In the cubic model the same role is played by the field-dependent mass $m^2_{eff}(φ) = -2λvφ + 3λφ^2$, which vanishes at $φ = 0$ and makes the onset of instability depend on rare peaks of the initial distribution, giving the bubble-like growth seen in the simulations.

Extended reading notes

Core claim

The central claim is that spontaneous symmetry breaking driven by a suddenly imposed tachyonic mass is a one-oscillation event. For the quadratic model $V(φ) = -m^2φ^2/2 + λφ^4/4$, the authors estimate that all modes with $k < m$ grow until $t_* ≈ (1/2m)ln(π^2/λ)$, at which point their occupation numbers are $n_k ∼ π^2/λ ≫ 1$ and the field has broken into domains of size only logarithmically larger than $m^{-1}$. Because the domain walls carry gradient energy of order $m^4/λ$ — the same order as the initial false-vacuum energy $V(0) = m^4/4λ$ — the field cannot return coherently to $φ = 0$, and the simulations show the probability distribution $P(φ,t)$ collapsing onto the two minima after the first oscillation. For the cubic model $V = -λvφ^3/3 + λφ^4/4 + λv^4/12$, the growth is more like bubble formation seeded by rare high peaks of the initial Gaussian fluctuations, but the outcome is the same: relaxation to the minimum within one oscillation. Applied to hybrid inflation, $V(φ,σ) = λ(σ^2-v^2)^2/4 + g^2φ^2σ^2/2 + m^2φ^2/2$, the authors report lattice runs for the non-supersymmetric model and for SUSY-motivated F-term and D-term variants showing that the homogeneous fields are destroyed by backreaction of the tachyonic fluctuations after a single oscillation, so preheating in hybrid inflation is generically tachyonic.

Load-bearing premise

The result rests on treating the quantum field as an ensemble of classical waves on a lattice with a sharp switch-on of the negative mass squared at $t = 0$, and on the one-oscillation outcome being independent of the lattice cutoff and of the renormalization subtraction — a procedure the paper states is needed for the cubic model but defers to a longer paper still in preparation.

Editorial extensions

If this is right

Preheating in hybrid inflation should be modelled as spinodal decay of the homogeneous fields rather than as broad parametric resonance, which changes the predicted spectrum and occupation numbers of produced particles.
The stage of coherent oscillations of the inflaton fields in hybrid models ends after a single oscillation, so scenarios that rely on many oscillations to build up resonant occupation numbers need re-examination.
Because a large fraction of $V(0)$ goes into gradient energy and domain structure, topological defects such as cosmic strings (for a complex $σ$) are produced as a leading-order outcome of the transition, not as a rare by-product.
Gravitino production in hybrid inflation should be computed from scattering of the classical waves generated by tachyonic preheating, not from decays of a coherently oscillating condensate.
The same one-oscillation picture is proposed for the formation of disoriented chiral condensates in heavy-ion collisions, where a rapidly cooled plasma suddenly finds itself on an unstable side of its effective potential.

Reading between the lines

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

If the mechanism is as generic as claimed, the relevant dividing line between 'tachyonic' and 'resonant' reheating is the ratio of the quench rate to the tachyonic growth rate $m$; a smooth, slow change of sign of the effective mass should interpolate between the two pictures, which is a testable statement about intermediate regimes.
The logarithmic dependence of $t_*$ on $λ$ suggests the one-oscillation outcome is robust to the details of the initial fluctuation spectrum, but it also implies the outcome is sensitive to the initial dispersion in a way that a different vacuum choice could shift.
Since gradient energy at the level of $V(0)$ is produced, the transition is a candidate source of a stochastic gravitational-wave background from the resulting field inhomogeneities, an observable the paper does not discuss.

Original abstract

We reconsider the old problem of the dynamics of spontaneous symmetry breaking using 3d lattice simulations, and develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential. As an application of this theory we consider preheating in the hybrid inflation scenario, including SUSY-motivated F-term and D-term inflationary models. We show that preheating in hybrid inflation is typically tachyonic and the stage of oscillations of a homogeneous component of the scalar fields driving inflation ends after a single oscillation. Our results may also be relevant for the theory of the formation of disoriented chiral condensates in heavy ion collisions.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,338 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.31 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We reconsider the old problem of the dynamics of spontaneous symmetry breaking using 3d lattice simulations, and develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential. As an application of this theory we consider preheating in the hybrid inflation scenario, including SUSY-motivated F-term and D-term inflationary models. We show that preheating in hybrid inflation is typically tachyonic and the stage of oscillations of a homogeneous component of the scalar fields driving inflation ends after a single oscillation. Our results may also be relevant for the theory of the formation of disoriented chiral condensates in heavy ion collisions.

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 reconsider the old problem of the dynamics of spontaneous symmetry breaking using 3d lattice simulations, and develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field.	contribution 0.99	0.94	0.24	asserted 0.99
s1	Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential.	result 0.93	0.72	0.43	asserted 0.96
s2	As an application of this theory we consider preheating in the hybrid inflation scenario, including SUSY-motivated F-term and D-term inflationary models.	contribution 0.98	0.76	0.06	asserted 0.66
s3	We show that preheating in hybrid inflation is typically tachyonic and the stage of oscillations of a homogeneous component of the scalar fields driving inflation ends after a single oscillation.	result 1.00	0.93	0.38	asserted 1.00
s4	Our results may also be relevant for the theory of the formation of disoriented chiral condensates in heavy ion collisions.	interpretation 0.95	0.20	0.03	hedged possibility 1.00

What kind of paper the classifier reports this is: simulation study 0.73 · evidence from simulation or computation 1.00.

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.** FIG. 1. The process of symmetry breaking in the model

**Figure 2.** FIG. 2. Growth of quantum fluctuations in the process of

**Figure 3.** FIG. 3. The process of symmetry breaking in the model

**Figure 4.** FIG. 4. Fast growth of the peaks of the distribution of the

**Figure 5.** FIG. 5. Histograms describing the process of symmetry

**Figure 6.** FIG. 6. The process of symmetry breaking in the hybrid

Figures reproduced from arXiv:hep-ph/0012142 by the authors.

References

Works cited (22)

[12]

G. Felder, J. Garc ´ ıa-Bellido, P. B. Greene, L. Kofman, A.D. Linde, and I. Tkachev, in preparation

View on Pith
[1]

D.A. Kirzhnits, JETP Lett. 15, 529 (1972); D.A. Kirzh- 6 nits and A.D. Linde, Phys. Lett. 42B, 471 (1972); Sov. Phys. JETP 40, 628 (1974); S. Weinberg, Phys. Rev. D9, 3320 (1974); L. Dolan and R. Jackiw, Phys. Rev. D9, 3357 (1974)

View on Pith 1972
[2]

D. A. Kirzhnits and A. D. Linde, Ann. Phys. 101, 195 (1976)

View on Pith 1976
[3]

A. A. Anselm and M. G. Ryskin, Phys. Lett. B266, (1991) 482; J. D. Bjorken, K. L. Kowalski and C. C. Tay- lor, SLAC Report No. SLAC-PUB-6109; K. Rajagopal and F. Wilczek, Nucl. Phys. B399, 395 (1993) and B404, 577 (1993); D. Boyanovsky, H. J. de Vega and R. Holman, Phys. Rev. D51, (1995) 734

View on Pith 1991
[4]

A. Linde, Phys. Lett. B259, 38 (1991); Phys. Rev. D49, 748 (1994)

View on Pith 1991
[5]

J. Garc ´ ıa-Bellido and A. Linde, Phys. Rev. D57 6065 (1998)

View on Pith 1998
[6]

L. A. Kofman, A. D. Linde and A. A. Starobinsky, Phys. Rev. Lett. 73, 3195 (1994); Phys. Rev. D 56, 3258 (1997)

View on Pith 1994
[7]

B. R. Greene, T. Prokopec and T. G. Roos, Phys. Rev. D56, 6484 (1997) [hep-ph/9705357]

View on Pith Pith review arXiv 1997
[8]

G. Felder, L. Kofman and A. Linde, Phys. Rev. D59, 123523 (1999) [hep-ph/9812289]

View on Pith Pith review arXiv 1999
[9]

D. Boyanovsky, M. D’Attanasio, H. J. de Vega, R. Holman, and D.S. Lee, Phys. Rev. D52, 6805 (1995); D. Boyanovsky, H. J. de Vega, and R. Holman, hep- ph/9903534

View on Pith 1995
[10]

S. Khlebnikov and I. I. Tkachev, Phys. Rev. Lett. 77, 219 (1996); Phys. Rev. Lett. 79, 1607 (1997); Phys. Rev. D56, 653 (1997)

View on Pith 1996
[11]

G. Felder and I. Tkachev, “LATTICEEASY: A program for lattice simulations of scalar ﬁelds in an expanding universe,” hep-ph/0011159

View on Pith Pith review arXiv
[13]

E.J. Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart, and D. Wands, Phys. Rev. D49 (1994) 6410

View on Pith 1994
[14]

M. Bastelo-Gil, S. King, and J. Sanderson, Phys. Rev. D60, 103517 (1999)

View on Pith 1999
[15]

J. Bardeen, J.R. Bond, N. Kaiser and A. Szalay, Astro- phys. J. 304, 15 (1986)

View on Pith 1986
[16]

A. D. Linde, Nucl. Phys. B216, 421 (1983); A.D.Linde, Particle Physics and Inﬂationary Cosmology (Harwood, Chur, Switzerland,1990)

View on Pith 1983
[17]

A. Linde, Nucl. Phys. B372, 421 (1992) [hep- th/9110037]

View on Pith 1992
[18]

P. Binetruy and G. Dvali, Phys. Lett. B388, 241 (1996); E. Halyo, Phys. Lett. B387, 43 (1996) [hep-ph/9606423]

View on Pith Pith review arXiv 1996
[19]

G. Felder and L. Kofman, “The development of equilib- rium after preheating,” hep-ph/0011160

View on Pith Pith review arXiv
[20]

R. Kallosh, L. Kofman, A. Linde and A. Van Proyen, Phys. Rev. D61, 103503 (2000) [hep-th/9907124]; Class. Quant. Grav. 17, 4269 (2000) [hep-th/0006179]

View on Pith Pith review arXiv 2000
[21]

G. F. Giudice, I. Tkachev and A. Riotto, JHEP 9908, 009 (1999) [hep-ph/9907510]; JHEP 9911, 036 (1999) [hep-ph/9911302]

View on Pith Pith review arXiv 1999
[22]

J. Garc ´ ıa-Bellido, D. Grigoriev, A. Kusenko and M. Sha - poshnikov, Phys. Rev. D60, 123504 (1999). 7 This figure "1.gif" is available in "gif" format from: http://arxiv.org/ps/hep-ph/0012142v1 This figure "2.gif" is available in "gif" format from: http://arxiv.org/ps/hep-ph/0012142v1 This figure "3.gif" is available in "gif" format from: http://arxiv.o...

View on Pith Pith review arXiv 1999

Forward citations

Showing 60 of 71 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 71 Pith citations

Cosmological implications for hairy black holes via spontaneous symmetry breaking: Are Hairy Black Holes Primordial?
gr-qc 2026-09 conditional novelty 7.0 of 10

In Einstein-Scalar-Gauss-Bonnet gravity, cosmological constraints force any viable hairy black hole to be an ultralight primordial black hole with mass around a few grams.
Can the universe be matter-dominated after a supercooled first-order phase transition?
hep-ph 2026-07 conditional novelty 7.0 of 10

After a supercooled first-order phase transition, the scalar field's equation of state is set by the bubble-wall Lorentz factor γ*, and matter domination is delayed until a/a* ≃ γ* in the free-streaming limit.
Feebly-Interacting Peccei-Quinn Model
hep-ph 2024-12 conditional novelty 7.0 of 10

A feebly-interacting PQ scalar with large wave-function renormalization can generate a large axion decay constant while keeping all mass scales near the TeV scale, predicting a light PQ Higgs and new dark matter scenarios.
Theory and Numerics of Gravitational Waves from Preheating after Inflation
astro-ph 2007-07 accept novelty 7.0 of 10

Gravitational waves from preheating after inflation peak at a frequency and amplitude set by the characteristic size of the field fragments, with hybrid models potentially detectable.
The Inflationary Brane-Antibrane Universe
hep-th 2001-05 conditional novelty 7.0 of 10

Brane-antibrane motion near a symmetric point of a compact torus gives a quartic potential flat enough for 60 e-folds, with spectral index n-1 = -3/N and a compactification scale near 10^12 GeV.

Show 55 more citing papers

Gravitational Waves from New Inflation
hep-ph 2026-10 conditional novelty 6.0 of 10

The authors compute the complete gravitational-wave spectrum predicted by new inflation, including preheating, primordial tensor modes, bremsstrahlung, and inflaton-particle scattering, over a wide parameter range.
Bumpy inflation from explosive particle production
astro-ph.CO 2026-08 conditional novelty 6.0 of 10

A spectator field that briefly turns massless during inflation generates a bump in the effective inflaton potential, and the bump can boost the curvature power spectrum on small scales by roughly eight orders of magnitude.
Gravitational waves from self-resonance during reheating with a quantum-corrected inflaton potential
hep-ph 2026-07 conditional novelty 6.0 of 10

A Coleman-Weinberg correction that cancels the inflaton's quadratic term at the potential minimum triggers quartic self-resonance and a peaked GW background at 10^8-10^10 Hz; a negative quadratic term instead gives a ...
PBHs and GWs from Scaling Monopoles
hep-ph 2026-06 unverdicted novelty 6.0 of 10

Scaling monopoles generate PBHs via stochastic overdensities and GWs with correlated spectra, potentially with magnetically charged PBHs as a signature if the scaling ends via gauge boson mass.
Memoirs of the curvaton: non-perturbative non-Gaussianity and supermassive primordial black holes
astro-ph.CO 2026-06 unverdicted novelty 6.0 of 10

Curvaton self-interactions in non-quadratic potentials produce a local non-Gaussian map that enables supermassive primordial black hole formation at peak amplitudes of order 10^{-5} while remaining consistent with μ-d...
Tachyonic particle production: quantum 2PI formalism with momentum exchanging collisions
hep-ph 2026-06 unverdicted novelty 6.0 of 10

Presents a self-consistent reduction of non-local next-to-leading-order 2PI equations to local quantum kinetic equations that incorporate momentum exchange during tachyonic instabilities.
Torsion induced current-scalaron coupling in Einstein-Cartan gravity
hep-ph 2025-07 conditional novelty 6.0 of 10

In Einstein-Cartan gravity, torsion-current couplings induce scalaron-current and scalaron Chern-Simons interactions, with explicit decay constants and a classification of their asymptotic behavior.
Potential Surge Preheating: enhanced resonance from potential features
astro-ph.CO 2024-12 conditional novelty 6.0 of 10

Localized Gaussian features added to the quadratic inflaton potential near its minimum enhance preheating and can drive the equation of state to a radiation-like value, leaving distinctive gravitational wave and Neff ...
Non-equilibrium dynamics of Goldstone excitation from holography
hep-ph 2024-12 conditional novelty 6.0 of 10

Holographic simulations with dynamical pions show a prethermalization stage at non-critical temperatures and a fitted k^2 t scaling, claimed as evidence for a non-thermal fixed point.
Light Dark Matter from Inflaton Decay
hep-ph 2020-11 conditional novelty 6.0 of 10

Inflaton decay produces dark matter colder than the plasma when the reheat temperature exceeds the inflaton mass, reopening sub-keV dark matter and giving isocurvature-free QCD axions.
Large Density Perturbations from Reheating to Standard Model particles due to the Dynamics of the Higgs Boson during Inflation
hep-ph 2020-09 conditional novelty 6.0 of 10

A spectator Higgs field with quantum fluctuations imprints Hubble-patch-dependent masses on inflaton decay products, generating curvature perturbations that exceed CMB bounds for most couplings to heavy SM states.
The art of simulating the early Universe -- Part I
astro-ph.CO 2020-06 conditional novelty 6.0 of 10

The paper supplies explicit, symplectic, arbitrary-even-order lattice integrators for scalar, U(1) and SU(N) gauge fields in an expanding background, including self-consistent expansion, with gauge constraints preserv...
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.
Preheating in Palatini Higgs inflation
hep-ph 2019-02 conditional novelty 6.0 of 10

Palatini Higgs inflation reheats through tachyonic Higgs production that depletes the inflaton condensate in less than one e-fold, unlike the metric case where gauge bosons dominate.
Non-minimal gravitational reheating during kination
gr-qc 2018-03 conditional novelty 6.0 of 10

A spectator scalar field, non-minimally coupled to gravity, is displaced by a tachyonic instability during kination and later decays, reheating the universe at a temperature set by the model's masses and couplings.
Gravitational wave production from preheating: parameter dependence
astro-ph.CO 2017-07 conditional novelty 6.0 of 10

The authors provide power-law fits, calibrated on lattice simulations over 0.4 < q < 5000 (quartic inflaton) and 6000 < q < 10^6 (quadratic inflaton), for the peak frequency and amplitude of the gravitational-wave bac...
Baryon asymmetry from primordial black holes
hep-ph 2016-10 conditional novelty 6.0 of 10

A curvature-coupled CP-violating operator makes evaporating primordial black holes radiate more leptons than antileptons, potentially producing the observed baryon asymmetry.
Combined Preheating on the lattice with applications to Higgs inflation
astro-ph.CO 2016-04 conditional novelty 6.0 of 10

In 3+1 lattice simulations of a simplified Higgs inflation model, gauge boson decays into fermions delay parametric resonance yet leave fermions holding about 96 percent of the total energy density after 400 inflaton ...
Geometrical Destabilization of Inflation
astro-ph.CO 2015-10 conditional novelty 6.0 of 10

The curvature of the inflationary field space can render heavy scalar fields tachyonic during inflation, ending inflation early and modifying observable predictions.
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.
The Kinematics of Cosmic Reheating
hep-ph 2013-05 accept novelty 6.0 of 10

Thermal masses do not generically cap the reheating temperature: depending on plasma interactions they can block, permit, or open new dissipation channels, and fermion channels can dominate at high temperature despite...
Gravitational Waves from Oscillon Preheating
astro-ph.CO 2013-04 conditional novelty 6.0 of 10

Lattice simulations of axion monodromy preheating show that forming oscillons imprint their harmonic structure as multiple peaks and troughs on the stochastic gravitational wave spectrum, while fully formed oscillons ...
Natural Cold Baryogenesis from Strongly Interacting Electroweak Symmetry Breaking
hep-ph 2011-04 conditional novelty 6.0 of 10

Cold electroweak baryogenesis can plausibly arise from bubble collisions in a nearly conformal TeV-scale phase transition, removing the need for hybrid inflation, though the baryon yield is argued rather than computed.
Inflaton Fragmentation and Oscillon Formation in Three Dimensions
astro-ph.CO 2010-09 conditional novelty 6.0 of 10

Full 3D simulations confirm that parametric resonance fragments the inflaton condensate into flat-topped oscillons that can dominate the post-inflationary energy budget for longer than a Hubble time.
Jordan Frame Supergravity and Inflation in NMSSM
hep-th 2010-04 accept novelty 6.0 of 10

A complete Jordan-frame N=1 supergravity action is derived and used to show that the Einhorn-Jones NMSSM Higgs inflation model has a strong tachyonic instability in the singlet direction, preventing inflation.
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...
Preheating in the Standard Model with the Higgs-Inflaton coupled to gravity
hep-ph 2008-12 conditional novelty 6.0 of 10

In Higgs-driven inflation, preheating proceeds through a mixed regime where non-perturbative gauge boson production at each zero crossing is offset by perturbative decays, delaying parametric resonance until roughly a...
Gravity Waves from Tachyonic Preheating after Hybrid Inflation
astro-ph 2008-12 conditional novelty 6.0 of 10

Gravitational waves from tachyonic preheating after hybrid inflation follow simple power laws in the model parameters, and reaching Advanced LIGO frequencies requires extremely small coupling constants.
Reheating in supersymmetric high scale inflation
hep-ph 2006-03 conditional novelty 6.0 of 10

MSSM flat direction VEVs kinematically block preheating in supersymmetric inflation, so the inflaton decays perturbatively at H around 10^-3 to 10^-1 TeV.
Preheating with Trilinear Interactions: Tachyonic Resonance
hep-ph 2006-02 accept novelty 6.0 of 10

A trilinear inflaton coupling produces particle bursts through periodic tachyonic instability, and a WKB transfer-matrix formula predicts the resulting occupation numbers and the accelerated approach to radiation domination.
Equation of state and Beginning of Thermalization After Preheating
hep-ph 2005-07 conditional novelty 6.0 of 10

In a chaotic inflation model with a φ²χ² coupling, the equation of state reaches near-radiation domination within roughly 10^-35 s of the end of inflation, far earlier than full thermal equilibrium.
Turbulent Thermalization
hep-ph 2004-03 conditional novelty 6.0 of 10

Inflation reheating proceeds through parametric resonance, driven turbulence, and free turbulence, and the middle stage, not parametric resonance, moves most of the inflaton energy into particles.
Beauty is Attractive: Moduli Trapping at Enhanced Symmetry Points
hep-th 2004-03 conditional novelty 6.0 of 10

Quantum particle production creates a linear confining force that traps rolling moduli at points of enhanced symmetry, and the same effect can drive a short burst of cosmic acceleration.
Self-resonance preheating in deformed attractor models: oscillon formation and evolution
astro-ph.CO 2026-02 unverdicted novelty 5.0 of 10

Deformed alpha-attractor T-models with a Gaussian feature near the minimum yield more smaller shorter-lived oscillons during self-resonance preheating, suppressing energy in oscillons and altering the high-frequency g...
Hybrid $\alpha$-attractors, primordial black holes and gravitational wave backgrounds
astro-ph.CO 2022-11 conditional novelty 5.0 of 10

A tiny linear term in the hybrid alpha-attractor potential lets the model keep CMB-compatible tilt while producing a tunable small-scale power peak that seeds primordial black holes and a testable stochastic gravitati...
NANOGrav Signal from the End of Inflation and the LIGO Mass and Heavier Primordial Black Holes
astro-ph.CO 2022-02 conditional novelty 5.0 of 10

A low-scale double-field inflation model with a first-order phase transition can be tuned to match the NANOGrav gravitational-wave spectrum, and the same transition would produce LIGO-mass and heavier primordial black holes.
CosmoLattice
astro-ph.CO 2021-02 accept novelty 5.0 of 10

The paper documents CosmoLattice v1.1, a public lattice code that evolves interacting scalar, U(1) and SU(2) gauge fields on an expanding grid with symplectic integrators that preserve the Gauss constraint to machine ...
Metric preheating and radiative decay in single-field inflation
astro-ph.CO 2020-02 conditional novelty 5.0 of 10

Perturbative decay of the inflaton into a perfect fluid does not disrupt the metric preheating instability until the fluid dominates the energy budget.
ALP inflation and Big Bang on Earth
hep-ph 2019-03 accept novelty 5.0 of 10

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

A lattice discretization that keeps gauge and shift symmetry exact on the grid is used to map preheating after axion inflation, finding a threshold coupling near 1/Lambda = 9.5/m_pl that separates failed from near-com...
Gravitational wave forest from string axiverse
astro-ph.CO 2018-07 conditional novelty 5.0 of 10

Lattice simulations show that string axions sitting on plateau potentials undergo resonant instabilities and emit gravitational waves peaked at frequencies set by their masses, producing a multi-band gravitational-wav...
CMB constraints on the inflaton couplings and reheating temperature in $\alpha$-attractor inflation
astro-ph.CO 2017-08 conditional novelty 5.0 of 10

For α-attractor E-models with perturbative reheating, the inflaton coupling to scalars or fermions is fixed by the spectral index n_s, with explicit relations given for gφχ², hφχ³ and Yukawa couplings.
Dynamics of Relaxed Inflation
hep-ph 2017-06 conditional novelty 5.0 of 10

Promoting the relaxion to the inflaton and coupling it to a dark photon gives a Schwinger-effect reheating mechanism and, in the authors' estimate, allows a cutoff close to the Planck scale, though the model does not ...
Gauss-Bonnet Chern-Simons gravitational wave leptogenesis
hep-th 2017-02 conditional novelty 5.0 of 10

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

One axion-like particle with mass of order 0.01 eV and photon coupling of order 10^-11 GeV^-1 can simultaneously drive inflation, reheat the universe, and account for dark matter.
Parametric Resonance in the Early Universe - A Fitting Analysis
astro-ph.CO 2016-09 conditional novelty 5.0 of 10

Lattice simulations of parametric resonance across preheating and spectator scenarios yield power-law fits for the backreaction time, the true decay time, and the late-time energy fractions, replacing the misleading l...
Postinflationary vacuum instability and Higgs-inflaton couplings
hep-ph 2016-08 conditional novelty 5.0 of 10

Resonant Higgs production during preheating destabilizes the electroweak vacuum for quartic Higgs-inflaton couplings above about 3e-8 and trilinear couplings above about 1e8 GeV, leaving a narrow viable window.
Living beyond the edge: Higgs inflation and vacuum metastability
hep-ph 2014-12 conditional novelty 5.0 of 10

Noncritical Higgs inflation survives a metastable electroweak vacuum if threshold jumps at M_P/xi make the Higgs self-coupling positive at inflationary scales and reheating exceeds about 7 times 10^13 GeV.
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.
Particle Production During Inflation: Observational Constraints and Signatures
astro-ph.CO 2009-09 conditional novelty 5.0 of 10

Cosmological data allow localized bump-like features in the primordial power spectrum as large as 10% of the scale-invariant fluctuations, bounding the inflaton-iso-inflaton coupling to roughly g^2 < 0.01 on CMB scales.
Baryon Asymmetry, Inflation and Squeezed States
gr-qc 2006-03 reject novelty 5.0 of 10

A non-perturbative calculation of baryon asymmetry from parametric resonance in preheating, flawed by an unjustified redefinition of energy and by a result independent of the CP-violating phase.
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...
On the gravitational production of superheavy dark matter
hep-ph 2001-04 conditional novelty 5.0 of 10

Gravitational production of superheavy dark matter yields Omega_X h^2 approximately (M_X/10^11 GeV)^2 (T_RH/10^9 GeV) for M_X < H_I, independent of the inflation model.
The ALP miracle revisited
hep-ph 2017-10 conditional novelty 4.0 of 10

A single axion-like particle with mass 0.01 to 1 eV and photon coupling of order 10^-11 GeV^-1 can plausibly drive inflation and account for dark matter, a window testable by next-generation axion experiments.
Reheating predictions in single field inflation
astro-ph.CO 2015-02 conditional novelty 4.0 of 10

Assuming a constant reheating equation of state, the expansion history fixes the reheating duration and temperature as functions of n_s, and requiring a consistent solution with 0 <= w_re <= 1/3 brackets the allowed (...

See all 71 Pith citations

How the literature uses it

129 arXiv papers cite this in 200 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential.

Tachyonic Preheating and Spontaneous Symmetry Breaking · 0.99

Papers citing it · 120 sentences without a confident label

Uses its method or tool 1 paper

As the physics is similar to the tachyonic resonance scenario of reheating [ref] , we use the technologies developed

Gauss-Bonnet Chern-Simons gravitational wave leptogenesis · Introduction · 0.93

Uses its data or values 1 paper

Preheating in these two cases has been studied in detail in [ref] , [ref] , and we will rely on their results for our estimations.

Theory and Numerics of Gravitational Waves from Preheating after Inflation · Expectations for Preheating after Hybrid Inflation · 0.86

Compares with it 6 papers

This is contrast to many resonant scenarios [ref] in which the universe is radiation-dominated or in some intermediate state [ref] following resonance.

Inflaton Fragmentation and Oscillon Formation in Three Dimensions · Qualitative Results · 0.98
The present analysis differs in various aspects from previous studies in the context of hybrid inflation, for which lattice simulations are also available [ref] .

Hubble-induced phase transitions on the lattice with applications to Ricci reheating · Introduction · 0.91
Tachyonic effects are therefore expected be negligible since, unlike the case in [ref] , the homogeneous mode has a VEV which is hierarchically larger than $m_ϕ$ (we remind that $ϕ_0 ≥10^14$ GeV) and oscillates at a frequency $ω∼m_ϕ$.

New developments on embedding inflation in gauge theory and particle physics · Reheating and Thermalization · 0.90

Cites it as support 3 papers

As demonstrated in [ref] , these instabilities rapidly convert most of the initial potential energy density $ρ_EDE$ into various forms of energy, including the mass of dark photons, the energy of produced particles, and the energy associated with field gradients.

Early Dark Energy and Dark Photon Dark Matter from Waterfall Symmetry Breaking · $H_0$ tension and/or dark photon DM · 0.99
This crucial observation implies that any description in terms of a homogeneous spectator field rolling down a potential is inaccurate to start with [ref] .

Quintessential inflation: A tale of emergent and broken symmetries · Spectator field dynamics · 0.98
Being a strong out of equilibrium process (and also turbulent, according to theoretical and numerical studies [ref] ), the reheating period is therefore a suitable scenario for primordial magnetogenesis.

Primordial magnetogenesis · Magnetogenesis during reheating · 0.96

Cites it as background 58 papers

At the end of hybrid inflation, the inflaton decays via a spinodal instability of the inhomogeneous modes accompanying the symmetry breaking, in the process of tachyonic preheating [ref] .

Theory and Numerics of Gravitational Waves from Preheating after Inflation · Expectations for Preheating after Hybrid Inflation · 0.87
Reheating in hybrid inflation was first studied in [ref] , and then in greater depth in [ref] where, in particular, the tachyonic instability channel was investigated [See also [ref] for an application of tachyonic decay to the cosmological moduli problem.].

A Study of Structure Formation and Reheating in the D3/D7 Brane Inflation Model · Reheating in the D3/D7 Brane Inflation Model · 0.96
Given the shape of the potential ([ref]), very different (p)reheating mechanisms could in principle take place, from a tachyonic production in the region between the end of inflation and the inflection point [ref] , an instant preheating mechanism [ref] and a parametric resonance effect around the minimum of the potential [ref] .

Preheating in the Standard Model with the Higgs-Inflaton coupled to gravity · Reheating in the Standard Model of particle physics · 0.80

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] [12]

G. Felder, J. Garc ´ ıa-Bellido, P. B. Greene, L. Kofman, A.D. Linde, and I. Tkachev, in preparation

View on Pith

[2] [1]

D.A. Kirzhnits, JETP Lett. 15, 529 (1972); D.A. Kirzh- 6 nits and A.D. Linde, Phys. Lett. 42B, 471 (1972); Sov. Phys. JETP 40, 628 (1974); S. Weinberg, Phys. Rev. D9, 3320 (1974); L. Dolan and R. Jackiw, Phys. Rev. D9, 3357 (1974)

View on Pith 1972

[3] [2]

D. A. Kirzhnits and A. D. Linde, Ann. Phys. 101, 195 (1976)

View on Pith 1976

[4] [3]

A. A. Anselm and M. G. Ryskin, Phys. Lett. B266, (1991) 482; J. D. Bjorken, K. L. Kowalski and C. C. Tay- lor, SLAC Report No. SLAC-PUB-6109; K. Rajagopal and F. Wilczek, Nucl. Phys. B399, 395 (1993) and B404, 577 (1993); D. Boyanovsky, H. J. de Vega and R. Holman, Phys. Rev. D51, (1995) 734

View on Pith 1991

[5] [4]

A. Linde, Phys. Lett. B259, 38 (1991); Phys. Rev. D49, 748 (1994)

View on Pith 1991

[6] [5]

J. Garc ´ ıa-Bellido and A. Linde, Phys. Rev. D57 6065 (1998)

View on Pith 1998

[7] [6]

L. A. Kofman, A. D. Linde and A. A. Starobinsky, Phys. Rev. Lett. 73, 3195 (1994); Phys. Rev. D 56, 3258 (1997)

View on Pith 1994

[8] [7]

B. R. Greene, T. Prokopec and T. G. Roos, Phys. Rev. D56, 6484 (1997) [hep-ph/9705357]

View on Pith Pith review arXiv 1997

[9] [8]

G. Felder, L. Kofman and A. Linde, Phys. Rev. D59, 123523 (1999) [hep-ph/9812289]

View on Pith Pith review arXiv 1999

[10] [9]

D. Boyanovsky, M. D’Attanasio, H. J. de Vega, R. Holman, and D.S. Lee, Phys. Rev. D52, 6805 (1995); D. Boyanovsky, H. J. de Vega, and R. Holman, hep- ph/9903534

View on Pith 1995

[11] [10]

S. Khlebnikov and I. I. Tkachev, Phys. Rev. Lett. 77, 219 (1996); Phys. Rev. Lett. 79, 1607 (1997); Phys. Rev. D56, 653 (1997)

View on Pith 1996

[12] [11]

G. Felder and I. Tkachev, “LATTICEEASY: A program for lattice simulations of scalar ﬁelds in an expanding universe,” hep-ph/0011159

View on Pith Pith review arXiv

[13] [13]

E.J. Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart, and D. Wands, Phys. Rev. D49 (1994) 6410

View on Pith 1994

[14] [14]

M. Bastelo-Gil, S. King, and J. Sanderson, Phys. Rev. D60, 103517 (1999)

View on Pith 1999

[15] [15]

J. Bardeen, J.R. Bond, N. Kaiser and A. Szalay, Astro- phys. J. 304, 15 (1986)

View on Pith 1986

[16] [16]

A. D. Linde, Nucl. Phys. B216, 421 (1983); A.D.Linde, Particle Physics and Inﬂationary Cosmology (Harwood, Chur, Switzerland,1990)

View on Pith 1983

[17] [17]

A. Linde, Nucl. Phys. B372, 421 (1992) [hep- th/9110037]

View on Pith 1992

[18] [18]

P. Binetruy and G. Dvali, Phys. Lett. B388, 241 (1996); E. Halyo, Phys. Lett. B387, 43 (1996) [hep-ph/9606423]

View on Pith Pith review arXiv 1996

[19] [19]

G. Felder and L. Kofman, “The development of equilib- rium after preheating,” hep-ph/0011160

View on Pith Pith review arXiv

[20] [20]

R. Kallosh, L. Kofman, A. Linde and A. Van Proyen, Phys. Rev. D61, 103503 (2000) [hep-th/9907124]; Class. Quant. Grav. 17, 4269 (2000) [hep-th/0006179]

View on Pith Pith review arXiv 2000

[21] [21]

G. F. Giudice, I. Tkachev and A. Riotto, JHEP 9908, 009 (1999) [hep-ph/9907510]; JHEP 9911, 036 (1999) [hep-ph/9911302]

View on Pith Pith review arXiv 1999

[22] [22]

J. Garc ´ ıa-Bellido, D. Grigoriev, A. Kusenko and M. Sha - poshnikov, Phys. Rev. D60, 123504 (1999). 7 This figure "1.gif" is available in "gif" format from: http://arxiv.org/ps/hep-ph/0012142v1 This figure "2.gif" is available in "gif" format from: http://arxiv.org/ps/hep-ph/0012142v1 This figure "3.gif" is available in "gif" format from: http://arxiv.o...

View on Pith Pith review arXiv 1999