Reheating after Inflation

Alexei Starobinsky; Andrei Linde; Lev Kofman

REVIEW

Reheating after Inflation

Lev Kofman, Andrei Linde, Alexei Starobinsky

High Energy Physics - Theory · Submitted 30 May 1994 · 7 references

Pith's verdict: The pre-heating paper: the Mathieu mechanism is right and checkable, but the resonance shutdown and the numbers that follow from it are asserted here and deferred to an unpublished companion.

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arXiv IDhep-th/9405187 (version 2)

Pith IDTJO7PEA3, Pith's permanent record of this paper and its review

CitationAlexei Starobinsky, Andrei Linde, Lev Kofman. "Reheating after Inflation." arXiv:hep-th/9405187 (1994). https://pith.science/paper/TJO7PEA3

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Editor's note

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This is the paper that put pre-heating on the map, and the core of it holds up. The mode equation for the chi fluctuations in an oscillating phi background reduces cleanly to the Mathieu equation (Eqs. 2-3), the identification of q = g^2 Phi^2 / 4 m_phi^2 > 1 as the broad-resonance regime is correct, and the instability parameters quoted along A = 2q are standard results that check out arithmetically. The qualitative conclusion follows directly: for q > 1 the occupation numbers grow as exp(2 mu_k m_phi t) with mu_k of order 0.1, so the condensate dumps a large fraction of its energy in a few oscillations. That is the real contribution, and it is derived, not asserted. Two smaller things also deserve credit: the footnote 6 retraction of the Gamma phi-dot friction prescription is an honest correction to a bad habit in the literature, and the point that Pauli blocking kills explosive fermion production is right and worth stating. The lambda phi^4 section and the symmetry-breaking section are sketched but the reasoning is sound as far as it goes. Where I would push back is the back-reaction. The shutdown criterion Phi^2 ~ , the final amplitude Phi^2 ~ g^-1 m_phi M_p, the typical energy E ~ sqrt(g m_phi M_p), and the termination time are all quoted in Sec. 3 and all rest on modeling back-reaction as a single homogeneous one-loop mass shift. It is not shown here that this captures the shutdown rather than rescattering and the self-consistent shift of the band structure as Phi is depleted. Those numbers are load-bearing for the equation-of-state claim, the suppression of a long matter-dominated stage, and the inflaton-as-dark-matter remark, and they are deferred to reference [5], listed as in preparation. That is a real gap, though a gap the authors openly flag rather than an internal inconsistency. The same applies to the negative claim in the abstract about the friction term. One more, minor: the citation to Traschen and Brandenberger [4] is thin. It is listed as prior work on reheating without saying what resonant production that paper already contained, which leaves the boundary of the new contribution partly implicit. This is for anyone working on reheating, preheating, or post-inflationary cosmology; it is the starting point for that literature and still worth reading in the original. It deserves a serious referee, and the referee's main job is to press on the back-reaction treatment.

Referee report

Significance

If correct, this is a foundational result: it identifies parametric resonance as the first stage of reheating and shows that the standard perturbative treatment of Dolgov–Linde and Abbott–Farhi–Wise describes only the late stages. The Mathieu reduction in Eqs. (2)–(3) is elementary and checkable, and the quoted instability parameters are standard: ln 3/(2π) ≈ 0.175 along A = 2q and ln(1+√2)/π ≈ 0.28 as the maximum. The internal energy bookkeeping is self-consistent: with q^{1/4}m_φ = √(g m_φ M_p) and ⟨χ²⟩ ∼ g^{-1}m_φ M_p, one gets E²⟨χ²⟩ ∼ m_φ²M_p², so the produced bosons do carry essentially the whole post-inflationary energy density, supporting the p ≈ ε/3 conclusion. The paper also makes falsifiable statements — the absence of a Γφ̇ term, the constraint that complete reheating requires a single-φ decay channel, and the possibility that a strongly coupled scalar can still be cold dark matter — which is a genuine strength.

Major objections (3)

[Sec. 3 and footnote 6] The quantitative results that make the scenario predictive are asserted and deferred to Ref. [5], listed as 'in preparation': the termination time t ∼ m_φ^{-1} ln(m_φ/g⁵M_p), the final amplitude Φ² ∼ g^{-1}m_φM_p, and the typical energy E ∼ √(g m_φ M_p). The same applies to the negative claim in footnote 6 and in the circulated abstract, that particle production does not generate a Γφ̇ term and that inflation cannot be supported by such a term. Because [5] is unpublished, these load-bearing statements cannot be checked from the letter as it stands. I would ask the authors to add a short derivation sketch — even a few lines showing how the q^{1/4}m_φ band position and the Φ² ∼ ⟨χ²⟩ condition combine into the quoted scalings — or, at minimum, to state explicitly which approximations enter and that the details rest on [5]. The band position and energy bookkeeping themselves check out, so the request concerns the termination estimate, not the resonance mechanism.
[Sec. 3, back-reaction and shutdown criterion] The shutdown of the explosive stage rests on two steps that are asserted rather than argued: modeling back-reaction as a homogeneous one-loop mass m_{φ,eff}² = m_φ² + g²⟨χ²⟩_ren, and the criterion Φ² ∼ ⟨χ²⟩ for when resonance ceases. At the end of the explosive stage the occupied modes have n_k ∼ g^{-2} ≫ 1, so rescattering processes such as χχ → χχ and χχ → φφ are not obviously negligible, and the instability parameter A depends on Φ, which is itself being depleted, so the band structure shifts self-consistently during the shutdown. It is not shown here that a homogeneous tadpole captures the termination point rather than these effects. Since the downstream claims — the immediate p ≈ ε/3, the suppression of a prolonged matter-dominated stage, and the subsequent narrow-resonance history with Φ ∝ t^{-3/4} — all depend on where the shutdown occurs, the authors should either justify the criterion or flag it explicitly as an approximation whose validity is argued in [5].
[Sec. 4, Eq. (4) and the λφ⁴ case] The reduction of the Lamé equation to the approximate Mathieu form (4) via φ(t) ∼ Φ sin(c√λ∫Φ dt) with c ≈ 0.85 is introduced without an error estimate, and the resulting parameters A ≈ 2.08 and q ≈ 1.04 sit in the second instability band where μ_k ≈ 0.07 is small and correspondingly sensitive to the approximation. The strong conclusion that decay 'stops altogether' when Φ ∼ m_φ/√λ, and the slow Φ ∝ t^{-7/12} law, inherit that sensitivity. A brief statement of the regime of validity of Eq. (4), or a comparison with the exact Lamé result, would make this section considerably more convincing. Separately, the quoted growth exp(√λΦt/5) does not quite follow from the preceding expression: with c ≈ 0.85, μ_k ≈ 0.07 and η = 2t/a one obtains 4cμ_k ≈ 0.24 rather than 0.20, so the numerical coefficient should be rechecked.

Minor objections (6)

[Sec. 3, paragraph following Eq. (3)] The statement that the main contribution to χ production comes from excitations with k/a ≫ m_φ sits uneasily with the instability-chart argument, which is drawn along the line A = 2q corresponding to k = 0. The resolution is that the relevant modes satisfy A − 2q ∼ √q, i.e. k/a ∼ q^{1/4}m_φ, which is indeed ≫ m_φ for q ≫ 1; this should be said where the claim is first made, since as written the two statements appear to conflict.
[Secs. 3 and 4] The symbol q is used with two different meanings: q = g²Φ²/(4m_φ²) in Sec. 3 and q = Φ²/(4⟨φ²⟩) in the back-reaction regime of Sec. 4. A distinct symbol for the second would help the reader follow the transition from broad to narrow resonance.
[Fig. 1 and caption] The instability chart is the central quantitative object of the paper, but the caption is a single sentence. It would benefit from labelling the instability bands by their index n, marking the line A = 2q and the k = 0 locus, and indicating what the curves inside the white bands represent.
[Eq. (1) and Sec. 2] The decay rate Γ(φ → χχ) = g⁴σ²/(8πm_φ) applies only in the broken phase and vanishes for σ = 0; the text implies this but does not state it at the equation. Making it explicit would sharpen the later argument that complete reheating requires a linear-in-φ vertex.
[Abstract and metadata] The abstract printed with the letter omits the statements about the absence of a Γφ̇ friction term and about the scalar field as a cold dark matter candidate that appear in the circulated version of the abstract. The two should be reconciled before publication.
[References] Reference [2] gives 'E. Fahri', which should read 'E. Farhi'; Ref. [4] gives 'Sov. Nucl. Phys.', which should read 'Sov. J. Nucl. Phys.'; and 'Lame' in Sec. 4 should be 'Lamé'. Reference [5], listed as 'in preparation', should be updated at proof if it has appeared by then.

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The paper

The paper claims

The oscillating inflaton field decays explosively at the start of reheating through broad parametric resonance, not through ordinary perturbative particle decay, and this pre-heating stage sets the initial conditions for everything that follows.

The reading

After inflation ends, the energy of the Universe sits in a single scalar field, the inflaton, oscillating around the minimum of its potential. The standard picture was that individual inflaton particles slowly decay into other particles, and the Universe gradually thermalizes. This paper argues that the standard picture misses the first and fastest stage. While the inflaton oscillates, its coupling to other bosons makes their effective mass swing up and down periodically. That periodic swing is described by the Mathieu equation, which has bands of unstable solutions. Inside those bands, quantum fluctuations of the coupled field grow exponentially rather than linearly. When the oscillation amplitude is large enough, the relevant band is broad and the growth rate per oscillation is of order one, so the inflaton dumps a large fraction of its energy into bosons within a few dozen oscillations. The authors call this pre-heating. It ends when the created particles back-react, adding to the inflaton's effective mass and shrinking the resonance. After that, a narrow resonance and ordinary perturbative decays take over. Fermions cannot be produced this way because the Pauli exclusion principle blocks exponential occupation growth. The authors also argue that complete reheating requires a single inflaton particle to be able to decay into other particles, which happens if there is a linear coupling from spontaneous symmetry breaking or a fermion Yukawa coupling. Without such a term, a residual inflaton condensate survives and can behave as cold dark matter.

Extended reading notes

Core claim

The claim is that the first stage of reheating is a broad parametric resonance, not perturbative decay: 'typically at the first stage of reheating the classical inflaton field phi rapidly decays into phi-particles or into other bosons due to a broad parametric resonance' (Abstract). The supporting mechanism is Eq. (2)-(3): the mode equation for chi fluctuations reduces to the Mathieu equation with q = g^2 Phi^2 / (4 m_phi^2), and for q > 1 the instability parameter mu_k is O(0.1), so occupation numbers grow as exp(2 mu_k m_phi t) and the condensate loses a large fraction of its energy within a few oscillations. If correct, the standard perturbative reheating calculation does not describe the beginning of reheating in a broad class of models.

Load-bearing premise

The termination of the explosive stage rests on modeling back-reaction as a one-loop effective mass, m_phi,eff^2 = m_phi^2 + g^2 <chi^2>_ren, and on the criterion Phi^2 ~ <chi^2> for when the resonance shuts off (Sec. 3). The quantitative consequences, the time t ~ m_phi^-1 ln(m_phi / g^5 M_p), the final amplitude Phi^2 ~ g^-1 m_phi M_p, and the typical energy E ~ sqrt(g m_phi M_p), are quoted as results to be shown in the companion paper [5], listed as 'in preparation'. If that single-mode back-reaction treatment misestimates when the resonance terminates, the predicted energy fraction, equation of state, and subsequent narrow-resonance history all shift.

Original abstract

The theory of reheating of the Universe after inflation is developed. The transition from inflation to the hot Universe turns out to be strongly model-dependent and typically consists of several stages. Immediately after inflation the field $\phi$ begins rapidly rolling towards the minimum of its effective potential. Contrary to some earlier expectations, particle production during this stage does not lead to the appearance of an extra friction term $\Gamma\dot\phi$ in the equation of motion of the field $\phi$. Reheating becomes efficient only at the next stage, when the field $\phi$ rapidly oscillates near the minimum of its effective potential. We have found that typically in the beginning of this stage the classical inflaton field $\phi$ very rapidly (explosively) decays into $\phi$-particles or into other bosons due to broad parametric resonance. This stage cannot be described by the standard elementary approach to reheating based on perturbation theory. The bosons produced at this stage, as well as some part of the classical field $\phi$ which survives the stage of explosive reheating, should further decay into other particles, which eventually become thermalized. The last stages of decay can be described in terms of perturbation theory. Complete reheating is possible only in those theories where a single massive $\phi$-particle can decay into other particles. This imposes strong constraints on the structure of inflationary models. On the other hand, this means that a scalar field can be a cold dark matter candidate even if it is strongly coupled to other fields.

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, 8,767 input tokens, $0.0004 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.83 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The theory of reheating of the Universe after inflation is developed. The transition from inflation to the hot Universe turns out to be strongly model-dependent and typically consists of several stages. Immediately after inflation the field $\phi$ begins rapidly rolling towards the minimum of its effective potential. Contrary to some earlier expectations, particle production during this stage does not lead to the appearance of an extra friction term $\Gamma\dot\phi$ in the equation of motion of the field $\phi$. Reheating becomes efficient only at the next stage, when the field $\phi$ rapidly oscillates near the minimum of its effective potential. We have found that typically in the beginning of this stage the classical inflaton field $\phi$ very rapidly (explosively) decays into $\phi$-particles or into other bosons due to broad parametric resonance. This stage cannot be described by the standard elementary approach to reheating based on perturbation theory. The bosons produced at this stage, as well as some part of the classical field $\phi$ which survives the stage of explosive reheating, should further decay into other particles, which eventually become thermalized. The last stages of decay can be described in terms of perturbation theory. Complete reheating is possible only in those theories where a single massive $\phi$-particle can decay into other particles. This imposes strong constraints on the structure of inflationary models. On the other hand, this means that a scalar field can be a cold dark matter candidate even if it is strongly coupled to other fields.

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	The theory of reheating of the Universe after inflation is developed.	contribution 0.96	0.78	0.07	asserted 0.98
s1	The transition from inflation to the hot Universe turns out to be strongly model-dependent and typically consists of several stages.	result 0.88	0.32	0.15	asserted 0.84
s2	Immediately after inflation the field $\phi$ begins rapidly rolling towards the minimum of its effective potential.	background 0.55	0.23	0.04	asserted 1.00
s3	Contrary to some earlier expectations, particle production during this stage does not lead to the appearance of an extra friction term $\Gamma\dot\phi$ in the equation of motion of the field $\phi$.	result 1.00	0.50	0.10	asserted 1.00
s4	Reheating becomes efficient only at the next stage, when the field $\phi$ rapidly oscillates near the minimum of its effective potential.	result 0.96	0.32	0.23	asserted 0.97
s5	We have found that typically in the beginning of this stage the classical inflaton field $\phi$ very rapidly (explosively) decays into $\phi$-particles or into other bosons due to broad parametric resonance.	result 0.99	0.94	0.17	asserted 1.00
s6	This stage cannot be described by the standard elementary approach to reheating based on perturbation theory.	result 0.59	0.36	0.07	asserted 1.00
s7	The bosons produced at this stage, as well as some part of the classical field $\phi$ which survives the stage of explosive reheating, should further decay into other particles, which eventually become thermalized.	result 0.80	0.45	0.07	asserted 0.78
s8	The last stages of decay can be described in terms of perturbation theory.	method 0.48	0.43	0.05	asserted 0.95
s9	Complete reheating is possible only in those theories where a single massive $\phi$-particle can decay into other particles.	result 0.83	0.69	0.28	asserted 0.75
s10	This imposes strong constraints on the structure of inflationary models.	interpretation 0.99	0.41	0.14	asserted 0.99
s11	On the other hand, this means that a scalar field can be a cold dark matter candidate even if it is strongly coupled to other fields.	interpretation 0.97	0.49	0.12	hedged possibility 0.61

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.88.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

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

levels run

P abstract

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 sketch of the stability/instability chart of the canonical Mathieu equation (3). 6

Figures reproduced from arXiv:hep-th/9405187 by the authors.

References

Works cited (7)

[5]

L.A. Kofman, A.D. Linde and A.A. Starobinsky, in prepara tion

View on Pith
[4]

A.D. Dolgov and D.P. Kirilova, Sov. Nucl. Phys., 51, 273 (1990); J. Traschen and R. Bran- denberger, Phys. Rev. D 42, 2491 (1990)

View on Pith 1990
[1]

A.D. Linde, Particle Physics and Inﬂationary Cosmology (Harwood, Chur, Switzerland, 1990)

View on Pith 1990
[2]

A.D. Dolgov and A.D. Linde, Phys. Lett. 116B, 329 (1982); L.F. Abbott, E. Fahri and M. Wise, Phys. Lett. 117B, 29 (1982)

View on Pith 1982
[3]

A.A. Starobinsky, in: Quantum Gravity, Proc. of the Second Seminar “Quantum Theor y of Gravity” (Moscow, 13-15 Oct. 1981) , eds. M.A. Markov and P.C. West (Plenum, New York, 1984), p. 103

View on Pith 1981
[6]

Some authors discussed a possibility to add additional t erms of the type of Γ ˙φ to the equation of motion in order to describe energy transfer due to particl e creation. There was a hope that such terms may lead to a longer stage of inﬂation. We have foun d that this prescription does not correctly describe particle creation at the stage prece ding a st...

View on Pith
[7]

It is interesting that the rapid decay of the ﬁeld φ can occur even if the ﬁeld χ has a bare mass mχ(0) much greater than the frequency of oscillations mφ. This rather unexpected regime is possible if the amplitude of oscillations is suﬃciently lar ge, gΦ ≫m2χ/mφ. Figure Caption: Fig. 1. The sketch of the stability/instability chart of the canoni cal Math...

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A transiently dominant rotating axion sources an induced gravitational wave background whose amplitude and large-scale anisotropy trace the axion's isocurvature fluctuations, with detection prospects for BBO and DECIGO.
Preheated inflation
hep-ph 2025-07 conditional novelty 6.0 of 10

Slow-roll inflation can sustain a subdominant non-thermal radiation bath through narrow parametric resonance, producing observable oscillatory features in the curvature power spectrum and secondary gravitational waves.
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.
Post-inflationary enhancement of adiabatic perturbations in modular cosmology
astro-ph.CO 2025-07 conditional novelty 6.0 of 10

In modular inflation models, entropic perturbations frozen during inflation are converted into curvature perturbations after inflation, producing an enhanced power spectrum while preserving the spectral index ns.
Acoustically driven dark matter freeze-out
hep-ph 2025-06 accept novelty 6.0 of 10

Thermal dark matter freeze-out under small-scale acoustic density perturbations requires about a 10 percent larger annihilation cross section to match the observed relic abundance.
Freezing-in Cannibals with Low-reheating Temperature
hep-ph 2025-06 conditional novelty 6.0 of 10

Non-instantaneous (low-temperature) reheating combined with 3-to-2 cannibal self-interactions reshapes the freeze-in dark matter parameter space and opens new light-DM regions for future colliders.
Particle decay as asymptotic narrow parametric resonance
hep-ph 2025-05 conditional novelty 6.0 of 10

A Boltzmann equation with Gaussian momentum spread reproduces the asymptotic growth rate and number density of narrow parametric resonance to within about 20 percent.
Ephemeral Oscillons in Scalar-Tensor Theories: The Higgs-like case
hep-ph 2025-01 conditional novelty 6.0 of 10

In a Higgs-like Einstein-Cartan inflation model, oscillons formed after inflation are short-lived and their decay drives radiation domination within about four e-folds.
Reconstructing Primordial Curvature Perturbations via Scalar-Induced Gravitational Waves with LISA
astro-ph.CO 2025-01 conditional novelty 6.0 of 10

LISA can reconstruct the primordial curvature power spectrum from scalar-induced gravitational waves, with percent-level precision near the peak and Bayesian tests separating SIGWs from other sources.
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.
More on scattering processes of dressed particles with a time-dependent mass
hep-th 2024-11 conditional novelty 6.0 of 10

An exact calculation shows that a scalar with a localized, time-dependent mass can decay into lighter particles through a kinematically forbidden channel, producing exponentially more daughters than parents.
Precision Inflationary Predictions: Impact of Accurate End-of-Inflation Dynamics
astro-ph.CO 2024-07 unverdicted novelty 6.0 of 10

Improved end-of-inflation dynamics shift the Starobinsky model's predicted spectral index n_s by up to 1.2×10^{-3} within the allowed reheating range.
The Cosmic Axion Background
hep-ph 2021-01 conditional novelty 6.0 of 10

Relativistic axions from the early universe, or from decaying dark matter, could be detected by repurposing existing axion dark matter experiments, with decaying dark matter already within projected reach of ADMX data.
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.
On Quantum Simulation Of Cosmic Inflation
quant-ph 2020-09 conditional novelty 6.0 of 10

A polynomial-time quantum simulation algorithm for scalar inflationary cosmology is proposed, with lattice regularization, HKLL-type encoding, adiabatic vacuum preparation, and Trotter time evolution.
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...
Potential of radio telescopes as high-frequency gravitational wave detectors
astro-ph.CO 2020-06 accept novelty 6.0 of 10

Graviton-photon conversion in cosmic magnetic fields during the dark ages distorts the CMB, letting EDGES and ARCADE 2 data bound MHz-GHz gravitational wave backgrounds.
Axion Fragmentation
hep-ph 2019-11 conditional novelty 6.0 of 10

A rolling axion that traverses many cosine wiggles resonantly amplifies its own quantum fluctuations, and the resulting back-reaction can stop the zero mode, with a closed-form stopping condition and field excursion.
Constraining axion inflation with gravitational waves across 29 decades in frequency
astro-ph.CO 2019-09 conditional novelty 6.0 of 10

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

Kinetic equilibration of particles produced by broad resonance preheating after inflation is almost instantaneous on the Hubble time, with an e-fold duration of about 4.4 for benchmark parameters.
A Cosmological Higgs Collider
hep-th 2019-07 conditional novelty 6.0 of 10

Higgs-modulated reheating can generate primordial density perturbations and imprint Standard Model particle masses in the squeezed bispectrum, provided the inflaton decays into Higgs-portal scalars.
Primordial black holes from the preheating instability
astro-ph.CO 2019-07 conditional novelty 6.0 of 10

The preheating instability in single-field inflation generically produces primordial black holes that can dominate the early universe and reheat it by Hawking evaporation.
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.
Pixelated Dark Energy
hep-th 2019-01 conditional novelty 6.0 of 10

The pixel model of dark energy predicts w_a = -1.5 Omega_m,0 (1+w_0) and a cutoff l_max ~ N on the CMB angular power spectrum, both consequences of a cosmological constant scaling as 1/N in the pixel number.
Parametric Resonance Production of Ultralight Vector Dark Matter
hep-ph 2018-10 conditional novelty 6.0 of 10

Parametric resonance from an oscillating dark Higgs can produce vector dark matter with mass as low as 10^-18 eV, extending the cosmologically viable range well below the keV freeze-in floor.
Gravitational reheating through conformally coupled superheavy scalar particles
gr-qc 2018-09 conditional novelty 6.0 of 10

Conformally coupled superheavy scalars are produced abundantly at the inflation-to-kination transition only if the transition time is shorter than the inverse mass, yielding reheating temperatures around 10^4 to 10^8 GeV.
A New Semiclassical Picture of Vacuum Decay
hep-th 2018-06 conditional novelty 6.0 of 10

Classical evolution of sampled vacuum fluctuations reproduces bubble nucleation and the instanton decay rate in a 1+1D scalar field theory, suggesting vacuum decay need not involve tunneling.

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586 later papers cite it

Evidence: substantial. 572 of the citing papers share no author with it, and 26 of those carry a confident label from Pith's citation classifier.

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3 later papers by other authors are listed below: 1 used its method or tool, 1 used its data or values and 1 compared its own results with it. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 2 of 15 papers with this label · 1 by the same authors

Varied an action from this paper to obtain the equation of motion of the curvaton field.

The running curvaton (2019) · 0.98 · paraphrased: the licence does not allow quoting

By the same authors

Calculated the vacuum expectation value of the field with the analytic machinery of particle creation with the coupling from this paper.

Cosmological Fluctuations from Infra-Red Cascading During Inflation (2009) (same authors) · 0.96 · paraphrased: the licence does not allow quoting

Uses its data or values 1 paper

Used this paper's number density of particles at the moment production terminates, when the produced modes back-react on the producing homogeneous modes.

Kinetic Equilibration after Preheating (2019) · 0.84 · paraphrased: the licence does not allow quoting

Compares with it 1 of 8 papers with this label

Compared the efficiency of particle production between its own mechanism and the usual reheating mechanism of this paper at linear order in perturbation theory.

Pre-heating in the framework of massive gravity (2015) · 1.00 · paraphrased: the licence does not allow quoting

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Contests it 1 paper

This led Kofman, Linde, and Starobinsky [ref] to propose that the residual field could act as dark matter, but in fact detailed calculations [ref] show the relic abundance is far too high under standard assumptions.

Triple unification of inflation, dark matter, and dark energy using a single field · Cosmological evolution · contest 0.75

Uses its method or tool 13 papers

Following Refs. [ref] , the Higgs decay to one such field $A ∈{ Z, W^±}$ can be modeled using a set of $3$ scalar fields $χ_i$, one for each helicity, and a corresponding scalar-Higgs interaction $ℒ_int = - g_A^2 χ⃗^2 h^2 / 8$ which is familiar from studies of inflationary preheating [ref] .

The Secret Higgstory of the Highest Temperature during Reheating · Condensate decay · 0.88
In this case, $n_χ$ after a number of inflaton oscillations is calculated as [ref] [equation] We have used the steepest descent method.[Even with $k$ fixed, the growth factor at each inflaton zero crossing is not the same.

Moduli Oscillation Induced by Reheating · Evaluation of $⟨χ^2⟩$ during preheating · 0.95
In order to take into account the back-reaction effects of $h$ quantum fluctuations, we use the Hartree approximation [ref] , and write the equation of motion for $ϕ$ as [equation] where the vacuum expectation value for $h^2$ is given by [equation] Using the angular frequency ([ref]), numerical calculations show that [equation] When instant preheating occurs we have $ϕ≃0$, and the equation of motion ([ref]) becomes [equation] One can use the approximation that the back-reaction effects are negligible if the effective inflationary scale $m_ϕ, eff = m^2 + m^2/2 ⟨h ⟩^2$ does not change significantly and the term in ([ref]) arising from the quantum fluctuations of $h$ is significantly smaller than the first term.

Non-Oscillatory No-Scale Inflation · Preheating · 1.00

Compares with it 8 papers

At the linear order in perturbation theory, we also compared the efficiency of the particle production between our mechanism and the usual reheating mechanism [ref] .

Pre-heating in the framework of massive gravity · Conclusion · 1.00
For both massless and massive particles, the associated particle number grows exponentially in time and a large number of particles can be produced by this mechanism, just as in the case of preheating after inflation [ref] .

Resonant particle production in branonium · Conclusions · 0.80
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

Cites it as support 3 papers

In cases like the ones described in [ref] (see also [ref] ), $w_re$ may therefore be rightfully treated as a constant throughout the entire reheating era.

Reheating predictions in single field inflation · Introduction · 0.97
In general, the preheating process can be reasonably efficient even for $m_ϕ∼m_h$ [ref] .

WIMP Dark Matter Inflation with Observable Gravity Waves · Introduction · 0.96
This suggests that the initial plasma is far from full thermal equilibrium initially [ref] .

Cosmic phase transitions: their applications and experimental signatures · Perturbative decay and thermalization phase: · 0.98

Cites it as background 323 papers

The standard cold model of inflation [ref] , in term of second-order phase transition, is described by two main parts, first part is the accelerated expansion of the universe which is presented by inflaton field, rolling slowly, and the second part is the reheating epoch as a connection between inflaton dominated era and radiation dominated era which is explained by oscillation of the inflaton around the minimum of the potential transferring its energy to mainly light standard particles [ref] .

Reheating After Swampland Conjecture · Introduction · 0.97
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
This inflationary period is supposed to be driven by one (inflaton field) or more scalar fields which at the end of inflation decay to relativistic particles which thermalise by reaching a common temperature, quoted as the reheating temperature [For more details on reheating see [ref] ].[After inflation, the inflaton or/and the other scalar fields oscillates at the bottom of his/their potential, a fact which sources a parametric instability in the equation of motion of the metric perturbations, that are enhanced on small scales.

Studying Aspects of the Early Universe with Primordial Black Holes · The Thermal History of the Universe · 0.96

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] [5]

L.A. Kofman, A.D. Linde and A.A. Starobinsky, in prepara tion

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[2] [4]

A.D. Dolgov and D.P. Kirilova, Sov. Nucl. Phys., 51, 273 (1990); J. Traschen and R. Bran- denberger, Phys. Rev. D 42, 2491 (1990)

View on Pith 1990

[3] [1]

A.D. Linde, Particle Physics and Inﬂationary Cosmology (Harwood, Chur, Switzerland, 1990)

View on Pith 1990

[4] [2]

A.D. Dolgov and A.D. Linde, Phys. Lett. 116B, 329 (1982); L.F. Abbott, E. Fahri and M. Wise, Phys. Lett. 117B, 29 (1982)

View on Pith 1982

[5] [3]

A.A. Starobinsky, in: Quantum Gravity, Proc. of the Second Seminar “Quantum Theor y of Gravity” (Moscow, 13-15 Oct. 1981) , eds. M.A. Markov and P.C. West (Plenum, New York, 1984), p. 103

View on Pith 1981

[6] [6]

Some authors discussed a possibility to add additional t erms of the type of Γ ˙φ to the equation of motion in order to describe energy transfer due to particl e creation. There was a hope that such terms may lead to a longer stage of inﬂation. We have foun d that this prescription does not correctly describe particle creation at the stage prece ding a st...

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[7] [7]

It is interesting that the rapid decay of the ﬁeld φ can occur even if the ﬁeld χ has a bare mass mχ(0) much greater than the frequency of oscillations mφ. This rather unexpected regime is possible if the amplitude of oscillations is suﬃciently lar ge, gΦ ≫m2χ/mφ. Figure Caption: Fig. 1. The sketch of the stability/instability chart of the canoni cal Math...

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