Universe Reheating after Inflation

Brown University); J.Traschen (University of Massachusetts); R.Brandenberger (Brown University); Y.Shtanov (Bogolyubov Institute

REVIEW

Universe Reheating after Inflation

Y.Shtanov (Bogolyubov Institute, Brown University), J.Traschen (University of Massachusetts), R.Brandenberger (Brown University)

High Energy Physics - Phenomenology · Submitted 6 Jul 1994 · 14 references

Pith's verdict: A founding preheating paper: the parametric-resonance enhancement over Born estimates is real and well-scoped, but the backreaction closure that fixes the quoted numbers is an ansatz, not a derivation.

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arXiv IDhep-ph/9407247 (version 2)

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CitationBrown University), J.Traschen (University of Massachusetts), R.Brandenberger (Brown University), Y.Shtanov (Bogolyubov Institute. "Universe Reheating after Inflation." arXiv:hep-ph/9407247 (1994). https://pith.science/paper/BT5AAXTC

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Editor's note

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This is one of the papers that made preheating standard, and it earns that place. Traschen and Brandenberger (their Ref. 10) established parametric resonance in new inflation; this paper carries the analysis into chaotic inflation with λφ⁴ and ½m²φ², adds a backreaction treatment for the quartic case, and derives freeze-out boundaries for the quadratic case. The Bogoliubov machinery is set out properly in Appendices A and B — the first instability band, the growth rate μ₊, the adiabatic generalization to Eq. (B32) — so a reader can check the mode equation rather than take the result on faith. The scoping is honest: everything is claimed only where Eq. (44) holds, and the paper says plainly that perturbation theory breaks down at the onset of oscillations for the coupling ranges (128) and (133). It also discloses that the first version had errors corrected after comments from Kofman, Linde and Starobinsky. That is the right way to handle it. One correction to the record: the classifier reports no stated limitations, which is wrong. The Introduction explicitly flags rescattering and decay of the produced χ particles as an open question deferred to future work, and the Section 5 footnote says thermalization is assumed instantaneous. Both are acknowledged, not hidden. The sharper unaddressed item is the backreaction closure in Section 5. Eqs. (67)–(70) posit that the inflaton loses energy only through χ production at rate Γ, convert that into a resonance sweep rate dΔω_k/dt = ¼Γω_res, and invert the resulting energy budget in Eq. (76). Three things are assumed rather than checked: that ω = c√λφ₀ survives backreaction, that one dominant band saturates the sum in (74), and that the O(1) coefficient inside the log, 32π²/c⁴λ, is right. The qualitative enhancement ~1/λ is robust to all three; the quoted 10¹² GeV is not, since the log is the whole difference between the resonance and Born rates. Minor but real: the abstract claims both the lowest and highest freeze-out bounds, while the body attributes the highest (Eqs. 136–137) to Ref. 13. Who should read it: anyone working on reheating, preheating, or post-inflationary cosmology, and anyone who wants the perturbative-regime calculation done carefully. Send it to referees — the central claim holds as scoped, and the backreaction closure is exactly the kind of thing a good referee should press on.

Referee report

Significance

This is a substantial and timely contribution. It is one of the papers that established parametric resonance as the dominant reheating channel and corrected the Born-approximation estimates that had been standard since Dolgov–Linde, Abbott–Farhi–Wise, and Albrecht–Steinhardt–Turner–Wilczek. The derivation is checkable: the mode equation (50), the resonance condition (54), and the growth rate (60) are given, and Appendices A and B make the Bogoliubov machinery explicit rather than asserted. The results are in principle falsifiable through the λ, h, σ dependence of T_rh and through the freeze-out boundaries. The principal physical caveat — rescattering and decay of the produced χ particles — is acknowledged in the Introduction (the paragraph beginning 'The opinion of the authors of Ref. 11…') and deferred to future work; the quantitative claims are contingent on it, and the authors say so.

Major objections (4)

[§5, Eqs. (67)–(70)] The enhancement factor is not read off the mode equation directly; it follows from the backreaction closure in this section. Eq. (67) posits that the inflaton loses energy only through χ production at rate Γ, Eq. (68) then forces φ̇₀/φ₀ = −(H + ¼Γ), and Eq. (69) converts this into the resonance sweep rate dΔω_k/dt = ¼Γω_res; Eq. (70) is the resulting energy budget and Eq. (76) its inversion. This assumes (i) that the frequency–amplitude relation ω = c√λφ₀ (Eq. 31) survives backreaction, i.e. that the 2hφ⟨χ²⟩ force term in the inflaton equation is negligible compared with the Γ term, and (ii) that a single dominant band saturates the sum in Eq. (74). Neither assumption is checked against a direct solution of the coupled inflaton-plus-χ mode equations. Because the entire difference between the resonance rate and the Born rate is the logarithm in Eqs. (79)/(81), a factor-of-few error in the log argument propagates directly into Γ_χ^(res) and hence into T_rh (Eq. 101). Please justify (i) and (ii), or state explicitly that the quoted T_rh is an order-of-magnitude estimate.
[§3, Eq. (44)] The perturbativity condition is printed as f², h, σφ₀ ≪ (ωφ₀)². With f and h dimensionless, σ of mass dimension one, and φ₀ of mass dimension one, the right-hand side has mass dimension four, so the inequality is not dimensionally consistent as written. The natural comparison for the hφ²χ² interaction is hφ₀² ≪ ω², which differs from the printed form by powers of φ₀. This matters because the perturbativity ranges (128) and (133) in §6 are derived from Eq. (44); if the condition is misstated, those ranges and the associated freeze-out bounds need rederivation. Please state the intended dimensionless combination and recheck (128) and (133) against it.
[§5, Eqs. (72)–(76) and (83)–(84)] The O(1) coefficient inside the logarithm, 32π²/c⁴λ (and 512π²/c⁴λ), is not derived from first principles; it comes from the phase-space volume and the Gaussian integral in Eq. (72), and the prefactors in Eqs. (62) and (64) are likewise not tracked. The qualitative statement (enhancement ~1/λ) is robust to such errors, but the numerical value T_rh ~ 10¹² GeV (Eq. 102) is not. Please either derive the coefficient or present the result with an explicit uncertainty band, and state the expected accuracy of the phase-space estimate in Eq. (62).
[§6, Eqs. (126)–(137)] The freeze-out boundaries are obtained by substituting extreme values of H into the condition Γ > 4H: the lowest bound (127)/(132) uses the inflaton-only H from Eq. (12), while the highest (136)/(137) uses H ~ m at the end of inflation. The authors themselves note that the latter lies 'just on the boundary of the applicability of perturbation theory.' The bracketing logic is reasonable, but the paper should state clearly that (136)–(137) lie outside the perturbative regime in which the rest of the analysis is conducted, so that the bracket is not a controlled error bar. Please make this consequence explicit where the bounds are quoted.

Minor objections (6)

[Throughout] The inflaton field is written both as φ and as ϕ, sometimes within the same paragraph (e.g. the abstract versus §2). Please unify the notation.
[§2, after Eq. (26)] The text refers to 'q = 4 (quadric potential)'; this should read 'quartic potential.' Similar typographical slips occur elsewhere: 'oscllations' (§4), 'Wee see' (§5), 'not ony' (§7), 'coinsides' and 'procede' (§6), 'detailes' (Appendix B), and 'deser ves' (Introduction).
[§1 and §3] The authors state that Sections 2 and 3 closely follow Ref. 12 (Shtanov, Ukr. Fiz. Zh. 38, 1425, 1993, in Russian). Please state explicitly which results are new relative to that reference, so the reader can locate the novel contribution.
[§7] The comparison with Ref. 13 (Kofman–Linde–Starobinsky) is qualitative and conducted in the notation of the present paper. A short table mapping the two sets of estimates (narrow versus broad resonance, the h ≃ 2λ/5 and h ≃ 0.22λ correspondences) would make the comparison much easier to follow.
[Abstract, sentence [abstract:s5]] The abstract states that the reheating temperature 'is [λ log(1/λ)]⁻¹ times larger' than the Born estimate. Since the quoted T_rh carries order-unity prefactors (Eqs. 101, 115), please phrase this as an estimate or scaling rather than an exact ratio.
[§4, Eq. (62)] The factor 1/2π² and the 1/2 in Eq. (62) are not explained. Please state the convention used for the phase-space volume so the reader can reproduce the coefficient.

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The paper

The paper claims

Parametric resonance, not ordinary perturbative decay, controls how the universe reheats after inflation, and the correction can raise the reheating temperature by many orders of magnitude.

The reading

The paper asks how the cold, empty universe produced by inflation gets filled with particles. The standard answer computed the rate at which an oscillating inflaton field decays into fermions and scalars using first-order Born approximation. The authors show that for the scalar channel this misses the dominant physics: the oscillating inflaton acts as a periodic drive on the mode equation for the produced field $k$, and, exactly as in a parametrically driven oscillator, modes whose frequency sits near half-integer multiples of the inflaton frequency, $omega_k approx (n/2),omega$, grow exponentially rather than linearly in time. In the quartic case $V(varphi)=lambda varphi^4$ this makes reheating efficient even for tiny couplings, and the resulting temperature exceeds the Born estimate by a factor of order $[lambda log(1/lambda)]^{-1}$. In the quadratic case $V(varphi)=tfrac12 m^2varphi^2$ the resonance is narrow and shuts off as the universe expands, so the paper instead derives freeze-out boundaries below which particle creation becomes inefficient and the residual inflaton oscillations can survive as cold dark matter.

What carries the argument

The load-bearing device is the reduction of the produced-field mode equation to a Hill/Matthiue-type oscillator, $ddot{Y}_k + (omega_k^2(t) + g(omega t))Y_k = 0$, with $g$ a periodic drive containing harmonics at $omega$ (from the linear coupling $sigma varphi$) and $2omega$ (from the quadratic coupling $h varphi^2$). Bogoliubov averaging in the small drive amplitude gives the first instability band, its width $|g_n|$, and the exponential rate $mu_+$; the occupation number follows from $N_k simeq sinh^2(int mu_+ dt)$ with the integral taken over the time a mode spends inside the band. The second device is the bookkeeping that turns this into a cosmological rate: in the quartic case, energy conservation ties the inflaton's amplitude loss to the drift speed $|dDeltaomega_k/dt|$ through the band, so the resonance rate and the back-reaction on the inflaton must be solved simultaneously. That closure is what converts a statement about instability bands into a number for $T_{rh}$.

Extended reading notes

Core claim

The central claim is that within the regime where perturbation theory in the inflaton couplings is legitimate, parametric resonance dominates scalar particle production and first-order Born estimates systematically underestimate it. The authors reduce the mode equation for the produced scalar $chi$ to a periodically driven oscillator, identify the instability bands $omega_k^2 - (nomega/2)^2 < |g_n|$, and compute the growth exponent $mu_+ = (1/nomega)sqrt{|g_n|^2 - Delta_n^2}$, so that the mean occupation number of a mode swept through a band is $N_k simeq sinh^2(int mu_+ dt)$. For $V=lambda varphi^4$ the resonance frequency redshifts at the same rate as the mode frequencies, so the authors close the system with a back-reaction equation: energy lost by the inflaton fixes the rate at which modes drift through the band, which in turn fixes $N_k$, giving an implicit equation for the effective production rate $Gamma_chi^{(res)}$ (their Eq. 74). The resulting enhancement over Born approximation is a factor $sim 32pi^2 c^{-2}lambda^{-1}log^{-1}(512pi^2 c^{-4}lambda^{-1})$ for the linear coupling and $sim pi^2 c^{-2}lambda^{-1}log^{-1}(32pi^2 c^{-4}lambda^{-1})$ for the quadratic coupling, which for $lambda sim 10^{-12}$ is enormous. The reheating temperature follows as $T_{rh} sim lambda^{1/4}phi_0$ with $phi_0$ at the onset of efficient reheating, giving $T_{rh} sim 10^{-1}M_P lambda^{1/4}(h/lambda)^2 log^{-1}(1/lambda)$, roughly $10^{12}$ GeV for the illustrative couplings. For the quadratic potential the frequency is constant, the drift rate is set by Hubble expansion rather than back-reaction, and the same machinery instead yields the amplitude at which production switches off: $(phi_0/m)^3 gtrsim 65(m/h^2 M_P)log(m/h^2 M_P)$ for quadratic coupling and $(phi_0/m) gtrsim (m^3/sigma^2 M_P)log(m^3/sigma^2 M_P)$ for linear coupling, with the minimum possible freeze-out energy density of order $m^4$.

Load-bearing premise

The calculation assumes that nothing removes particles from a resonantly amplified mode before the mode leaves the resonance band; the authors state in the Introduction, in the paragraph beginning 'The opinion of the authors of Ref. 11 is that parametric resonance effects of scalar particle production are likely to be suppressed by the processes of scattering and decay,' that rescattering and decay of the produced $chi$ particles are not treated here and are left to future work, so the enhancement factors and reheating temperatures hold only if those processes are slower than the resonance.

Editorial extensions

If this is right

For $V=lambda varphi^4$, reheating is efficient for arbitrarily small inflaton couplings, so the quartic chaotic model does not suffer the reheating problem that Born-approximation estimates suggested; the temperature scales as $lambda^{1/4}(h/lambda)^2 log^{-1}(1/lambda)$ rather than as a much smaller Born rate.
The reheating temperature inferred from any model with a quartic inflaton potential should be revised upward by the factor $[lambda log(1/lambda)]^{-1}$ relative to first-order calculations, which for $lambda sim 10^{-12}$ is a difference of many orders of magnitude.
For $V=tfrac12 m^2varphi^2$, there is a definite amplitude below which particle production stops competing with Hubble redshift; the inflaton then decouples and its residual oscillations can supply cold dark matter, with the freeze-out energy density bracketed between about $m^4$ and the highest possible boundary set by the Hubble scale at the end of inflation.
Fermions are unaffected: the resonance mechanism has no fermionic analogue, so the Born result $Gamma_psi = O(1) f^2 omega/(4pi)$ and the reheating condition $phi_0 lesssim 10^{-2}f^2 M_P$ stand as previously computed.
Which channel dominates reheating depends on whether $phi_0$ is above or below $sigma/h$, giving a sharp crossover in the predicted reheating temperature as a function of the two scalar couplings.

Reading between the lines

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

If resonance really drives reheating in the quartic model, the produced particles arrive in narrow, highly occupied bands rather than in a thermal spectrum, which would leave a non-thermal transient and possibly a distinctive gravitational-wave or fluctuation signature; the paper does not compute one.
The freeze-out boundaries for the quadratic potential give a concrete handle on inflaton dark matter: the relic abundance depends on where between the lowest and highest boundary the inflaton actually freezes out, which is exactly the range the paper leaves undetermined.
The narrow-resonance treatment here and the broad-resonance treatment of the cited concurrent work should connect continuously as the coupling grows; a calculation that interpolates between them would test whether the enhancement factors quoted here are the small-coupling limit of a single curve.
Because the whole result rests on occupation numbers growing before anything depletes them, a coupled lattice simulation of the inflaton and the produced field would be the natural arbiter, and would also indicate how far into the reheating epoch the analytic rate survives.

Original abstract

We study the problem of scalar particle production after inflation by a rapidly oscillating inflaton field. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first order Born approximation often underestimate the particle production. In the case of the quartic inflaton potential $V(\varphi) = \lambda \varphi^4$, the particle production process is very efficient even for small values of coupling constants. The reheating temperature of the universe in this case is $\left[\lambda\, \log\, (1/\lambda) \right]^{- 1}$ times larger than the corresponding estimates based on first order Born approximation. In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the other scalar field and on the magnitudes of the coupling constants. If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde and Starobinsky (see e.g. Ref. 13), the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe. In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.

The compiled record

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.63 · human participants 0.01 · controlled comparison 0.20 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.96 · 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.

We study the problem of scalar particle production after inflation by a rapidly oscillating inflaton field. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first order Born approximation often underestimate the particle production. In the case of the quartic inflaton potential $V(\varphi) = \lambda \varphi^4$, the particle production process is very efficient even for small values of coupling constants. The reheating temperature of the universe in this case is $\left[\lambda\, \log\, (1/\lambda) \right]^{- 1}$ times larger than the corresponding estimates based on first order Born approximation. In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the other scalar field and on the magnitudes of the coupling constants. If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde and Starobinsky (see e.g. Ref. 13), the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe. In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.

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 study the problem of scalar particle production after inflation by a rapidly oscillating inflaton field.	contribution 0.86	0.85	0.03	asserted 0.52
s1	We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials.	method 0.99	0.72	0.02	asserted 0.94
s2	Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field.	contribution 0.42	0.19	0.03	asserted 0.69
s3	We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first order Born approximation often underestimate the particle production.	result 1.00	0.95	0.43	asserted 1.00
s4	In the case of the quartic inflaton potential $V(\varphi) = \lambda \varphi^4$, the particle production process is very efficient even for small values of coupling constants.	result 1.00	0.86	0.19	asserted 1.00
s5	The reheating temperature of the universe in this case is $\left[\lambda\, \log\, (1/\lambda) \right]^{- 1}$ times larger than the corresponding estimates based on first order Born approximation.	result 1.00	0.87	0.23	asserted 1.00
s6	In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the other scalar field and on the magnitudes of the coupling constants.	result 0.96	0.57	0.09	asserted 1.00
s7	If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde and Starobinsky (see e.g. Ref. 13), the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe.	interpretation 0.50	0.12	0.08	hedged possibility 0.98
s8	In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.	result 0.97	0.94	0.10	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.97.

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

References

Works cited (14)

[1]

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

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[2]

A.Starobinsky, Phys. Lett. 91B, 99 (1980)

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[3]

A.Dolgov and A.Linde, Phys. Lett. 116B, 329 (1982)

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[4]

L.Abbott, E.Farhi and M.Wise, Phys. Lett. 117B, 29 (1982)

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[5]

A.Albrecht, P.Steinhardt, M.Turner and F.Wilczek, Phys. Rev. Lett. 48, 1437 (1982)

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[6]

D.Nanopoulos, K.Olive and M.Srednicki, Phys. Lett. 127B, 30 (1983)

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[7]

M.Morikawa and M.Sasaki, Progr. Theor. Phys. 72, 782 (1984)

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[8]

A.Hosoya and M.Sakagami, Phys. Rev. D29, 2228 (1984)

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[9]

E.Kolb and M.Turner, The Early Universe (Addison-Wesley Publishing Company, Redwood City, California, 1990)

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[10]

J.Traschen and R.Brandenberger, Phys. Rev. D42, 2491 (1990)

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[11]

A.Dolgov and D.Kirilova, Sov. Nucl. Phys. 51, 273 (1990)

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[12]

Y.Shtanov, Ukr. Fiz. Zh. 38, 1425 (1993) (in Russian)

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[13]

L.Kofman, A.Linde and A.Starobinsky, UH-IfA-94/35, SU -ITP-94-13, YITP/U- 94-15, and HEP-TH-9405187, Submitted to: Phys. Rev. Lett. (1994)

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[14]

N.Bogoliubov and Y.Mitropolsky Asymptotic Methods in the Theory of Non- Linear Oscillations (translated from Russian, Hindustan Publishing Corpn., Delhi, 1961). 51

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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.
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 ...
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.
Preheating Axions in String Cosmology
hep-th 2024-11 conditional novelty 6.0 of 10

Preheating of closed-string axions in fibre inflation can overproduce dark matter, yielding new upper bounds on the axion mass and constraints on model parameters.
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.
Gravitational Wave and CMB Probes of Axion Kination
hep-ph 2021-08 conditional novelty 6.0 of 10

An era of axion-driven kination preceded by matter domination imprints a triangular peak on primordial gravitational waves, detectable by DECIGO and BBO if inflation was near its current energy scale.
Gravitational Waves and Dark Photon Dark Matter from Axion Rotations
hep-ph 2021-04 conditional novelty 6.0 of 10

A rotating axion drives tachyonic dark photon production, correlating a stochastic gravitational wave background with the warmness and mass of dark photon dark matter.
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...
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...
Reheating and Post-inflationary Production of Dark Matter
hep-ph 2020-04 accept novelty 6.0 of 10

For inflaton potentials steeper than quadratic (k > 2), dark matter production during reheating becomes sensitive to the peak temperature at a lower scattering power n than in the standard quadratic case.
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.
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.
Gravitational production of super-Hubble-mass particles: an analytic approach
hep-ph 2018-12 accept novelty 6.0 of 10

A double expansion in H/omega_star and H/m_chi yields closed-form Bogoliubov coefficients and relic abundances for gravitationally produced super-Hubble-mass particles, reproducing prior numerical estimates.
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.
Gravitational waves from gauge preheating
astro-ph.CO 2018-05 conditional novelty 6.0 of 10

Gauge-field preheating after inflation produces a stochastic gravitational-wave background reaching Omega h^2 of order 5e-7, helically polarized for axion couplings, together with a gravitational topological charge of...
Dark Matter Axion Clump Resonance of Photons
hep-ph 2018-05 conditional novelty 6.0 of 10

Parametric resonance of photons from spherically symmetric QCD axion clumps is absent for conventional couplings, but appears for larger couplings or for clumps with sufficient angular momentum.
On preheating in alpha-attractor models of inflation
astro-ph.CO 2018-01 conditional novelty 6.0 of 10

In alpha-attractor T-models with alpha below about 10^-3, the spectator field's geometrical tachyonic instability dominates post-inflationary preheating, driving the equation of state to radiation-like within roughly ...
On Thermal Gravitational Contribution to Particle Production and Dark Matter
hep-ph 2017-08 conditional novelty 6.0 of 10

Gravitational annihilation of thermal particles and inflatons can produce dark matter with mass from a TeV to 10^16 GeV at the observed abundance, with weak dependence on the dark matter spin.
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...
Standard Model-Axion-Seesaw-Higgs Portal Inflation. Five problems of particle physics and cosmology solved in one stroke
hep-ph 2016-10 conditional novelty 6.0 of 10

A single new physics scale near 10^11 GeV, tied to a Peccei-Quinn symmetry, is claimed to solve five open problems of particle physics and cosmology simultaneously.
Violent Preheating in Inflation with Nonminimal Coupling
hep-ph 2016-09 conditional novelty 6.0 of 10

The inflaton's zero-crossing spike in nonminimally coupled inflation drives violent preheating, producing high-momentum particles that can drain the inflaton's energy within one oscillation for xi^2 lambda >~ 300.
Unifying inflation with the axion, dark matter, baryogenesis and the seesaw mechanism
hep-ph 2016-08 conditional novelty 6.0 of 10

Adding one new particle sector at about 10^11 GeV to the Standard Model is claimed to simultaneously drive inflation, supply axion dark matter, generate the baryon asymmetry, solve strong CP, and give neutrinos mass.
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 ...
Chilly Dark Sectors and Asymmetric Reheating
hep-ph 2016-04 accept novelty 6.0 of 10

Inflaton exchange between the Standard Model and a dark sector can wash out the temperature asymmetry that asymmetric reheating is supposed to create, and the paper maps the parameter regions where the asymmetry survives.
Fate of Electroweak Vacuum during Preheating
hep-ph 2016-02 accept novelty 6.0 of 10

The electroweak vacuum survives preheating only if the Higgs-inflaton quartic coupling stays below roughly 10^-4 and the Higgs-curvature coupling below roughly 10, bounds the authors confirm with classical lattice simulation.
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 ...
Dynamics of oscillating scalar field in thermal environment
hep-ph 2012-08 conditional novelty 6.0 of 10

A coherently oscillating scalar coupled to a thermal bath has its evolution and final abundance reshaped by thermal mass and thermal-log potentials, dissipation, preheating, and oscillon formation, with the dominant e...
Cosmological Inflation and the Quantum Measurement Problem
hep-th 2012-07 conditional novelty 6.0 of 10

CSL applied to inflation yields a two-branch power spectrum (n_S = 1 and n_S = 4), forcing the collapse parameter to be fine-tuned below 10^{-28} and leaving the collapse inefficient.
Oscillons After Inflation
astro-ph.CO 2011-06 conditional novelty 6.0 of 10

Inflationary potentials with a quadratic minimum and a shallower-than-quadratic plateau trigger self-resonance after inflation, producing oscillons that dominate the universe's energy density for several Hubble times.
The Matter Bounce Curvaton Scenario
hep-th 2011-01 conditional novelty 6.0 of 10

Isocurvature fluctuations of a light spectator field in a matter bounce convert to scale-invariant curvature fluctuations during the bounce, suppressing the tensor-to-scalar ratio and generating local non-Gaussianity.
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.
Flat-top oscillons in an expanding universe
astro-ph.CO 2010-02 conditional novelty 6.0 of 10

A large-coupling expansion yields analytic flat-topped oscillon profiles and indicates that, in 3+1 dimensions, these flat tops are linearly stable against long-wavelength perturbations while small-amplitude oscillons...
Primordial Curvature Fluctuation and Its Non-Gaussianity in Models with Modulated Reheating
astro-ph 2008-07 accept novelty 6.0 of 10

Non-linearity in how the inflaton decay rate depends on a modulus field can produce large primordial non-Gaussianity, and a derived consistency relation plus the sign of g_NL distinguishes modulated reheating from the...
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.
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.
Inflaton Oscillations and Post-Inflationary Reheating
hep-ph 2020-12 conditional novelty 5.5 of 10

For inflaton potentials V proportional to phi^k with k > 2, the plasma temperature during reheating falls as a different power of the scale factor depending on the spin of the decay products, which shifts predicted da...
The art of simulating the early Universe. Part III: Scalar-Gauge-Fluid Dynamics
astro-ph.CO 2026-07 accept novelty 5.0 of 10

Detailed continuum-to-lattice schemes are given for perfect/imperfect fluids alone or coupled to scalars/gauges in FLRW, enabling self-consistent CosmoLattice simulations of early-Universe plasma dynamics and GWs.

See all 112 Pith citations

How later papers used it

330 later papers cite it

Evidence: substantial. 303 of the citing papers share no author with it, and 15 of those carry a confident label from Pith's citation classifier.

Pith read 30 of the 431 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 2 used its method or tool.

Uses its method or tool 2 of 10 papers with this label

In this section we will follow the theory developed in [ref] .

Gravitational reheating formulas and bounds in oscillating backgrounds (2024) · Analytic results: Born approximation · 0.95
Applied the generalization of Floquet theory to slowly varying coefficients developed in this paper.

Quantum Field Theory Of Cosmological Perturbations Induced By Ultralight Dark Matter (2026) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

303 arXiv papers cite this in 397 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 · 196 sentences without a confident label

Uses its method or tool 9 papers

Then, for this frequency, the creation rate of $χ$-particles, satisfying $m_χ<ω(t)$, is [ref] [equation] and the leading frequency $ω$ is approximately [equation] where we have used that $Φ_END∼φ_END$, because at the end of reheating, $ρ_END=V(Φ_END)=3/2V(φ_END)$.

Gravitational reheating formulas and bounds in oscillating backgrounds · Analytic results: Born approximation · 0.85
These conditions allow us to apply the generalization of Floquet theory to slowly varying coefficients developed in [ref] , whose validity precisely requires adiabatic evolution of the characteristic frequencies.

Quantum Field Theory Of Cosmological Perturbations Induced By Ultralight Dark Matter · Pure squeezed state · 0.93
Once the equation of motion is identified with the Mathieu equation, we can use the same technique to solve this equation (e.g. the Bogoliubov coefficient technique) and derive the production rate in the narrow width limit, as found in literature [ref] .

Quantum decay of scalar and vector boson stars and oscillons into gravitons · Quantum decay into gravitons · 0.96

Compares with it 5 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
Interestingly, the above formula has the same power dependence on Hubble parameter as particle creation from vacuum fluctuations during inflation [ref] and oscillation [ref] .

On Thermal Gravitational Contribution to Particle Production and Dark Matter · Effects of Inflation Dynamics · 0.98
This marks a crucial difference with the well-studied case of parametric resonance due to a scalar field which oscillates coherently at the minimum of its potential [ref] .

Axion Fragmentation · Axion fragmentation in a nutshell · 0.85

Cites it as support 1 paper

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 170 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
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
In particular we examine the viability of $(g-2)_μ$ satisfying parameter space in providing a consistent cosmological scenario from the onset of primordial inflation to the end of matter-radiation equality with the intermediate reheating phase [ref] .

Cosmic inflation and $(g-2)_\mu$ in minimal gauged $L_\mu-L_\tau$ model · Introduction · 0.86

Discussion

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