REVIEW
On the reheating stage after inflation
High Energy Physics - Phenomenology · Submitted 18 Jul 2003 · 25 references
Pith's verdict: A correct, useful transplant of Linde's plasma-blocking observation to reheating; the coupling-independence claim is real but narrower than the conclusions suggest.
T0 · AI review
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Referee report
The paper
The paper claims
The paper argues that thermal masses of inflaton decay products can block the decay, holding the plasma at a plateau temperature set by the inflaton mass rather than by its decay coupling.
The reading
What carries the argument
The load-bearing mechanism is the in-medium decay width, Eq. (4) of the paper. The authors model the universe with inflaton energy density $rho_phi$ and radiation energy density $rho_R$, take the plasma mass of the decay products to be $m_p(T)simeq gT$, and write $Gamma_phi(T)=alpha_phi M_phi sqrt{1-4g^2T^2/M_phi^2}$. This factor is the phase-space suppression for a two-body decay into equal-mass thermal products; it vanishes at $T=M_phi/(2g)$ and makes the decay rate temperature-dependent. The Boltzmann equations for $rho_phi$ and $rho_R$ then produce three regimes depending on whether $T_{rm MAX}$ and the conventional $T_{rm RH}$ lie above or below $M_phi$. In case III the plateau ends when $rho_phi$ drops below $rho_R$ at $Tsim M_phi/g$, which is the paper's route to a coupling-independent reheat temperature.
Extended reading notes
Core claim
The central claim is that plasma masses can make reheating self-limiting. The vacuum width $Gamma_phi=alpha_phi M_phi$ is replaced by $Gamma_phi(T)=alpha_phi M_phi sqrt{1-4g^2T^2/M_phi^2}$. When $T$ reaches $M_phi/(2g)$ the width vanishes; if $T_{rm MAX}$ would be larger, the system enters a constant-temperature phase. In the authors' case III, where the conventionally computed $T_{rm RH}$ exceeds $M_phi$, the plateau lasts until the inflaton energy density falls below the radiation energy density, and the universe enters radiation domination at $T_{rm RH}simeq M_phi/g$ up to order-one factors, independent of $alpha_phi$. They support this with a two-component Boltzmann system for $rho_phi$ and $rho_R$ and numerical solutions showing the plateau.
Load-bearing premise
The load-bearing premise is that the only in-medium effect relevant to inflaton decay is a common thermal mass $m_p(T)simeq gT$ in a single two-body channel, so that inserting that mass into the vacuum width correctly captures when decay is blocked.
Editorial extensions
If this is right
- Thermal gravitino production during reheating is cut off at the plateau, so in case III the relevant bound is on $M_phi$ rather than on the conventionally defined $T_{rm RH}$.
- The number of e-folds after inflation changes because the radiation era starts at $Tsim M_phi$; the usual $Delta Npropto (1/3)ln T_{rm RH}$ is replaced by a dependence on $M_phi$, shifting CMB constraints on inflation models.
- Superheavy dark matter produced by annihilations at the end of reheating has an abundance set by $M_X/M_phi$ and the exponential $e^{-2M_X/M_phi}$, not by the usual reheat temperature.
- Leptogenesis from right-handed neutrino production at $Tsim M_phi$ gives a baryon asymmetry that depends on $M_N/M_phi$; the paper estimates that $M_N/M_phi$ cannot exceed about 15 for the observed asymmetry.
Reading between the lines
- If the plateau is real, any relic whose abundance is dominated by the highest temperatures reached after inflation sees a ceiling set by the parent particle's mass; this suggests looking for a common mass scale in reheating histories rather than only in couplings.
- A dedicated finite-temperature calculation with multiple decay channels and a nonzero inflaton width would test whether the plateau leaks; even a small leakage would change the coupling-independence claim.
- The mechanism is not specific to inflation: any early matter-dominated era from a decaying nonrelativistic species could have its final temperature fixed by the parent mass, which may be relevant to hidden-sector cosmologies.
- If future CMB analyses infer a reheating temperature near $M_phi/g$, that would be consistent with the plateau but would not by itself prove it, because the same temperature could arise from a tuned coupling in the standard picture.
Original abstract
We point out that inflaton decay products acquire plasma masses during the reheating phase following inflation. The plasma masses may render inflaton decay kinematicaly forbidden, causing the temperature to remain frozen for a period at a plateau value. We show that the final reheating temperature may be uniquely determined by the inflaton mass, and may not depend on its coupling. Our findings have important implications for the thermal production of dangerous relics during reheating (e.g., gravitinos), for extracting bounds on particle physics models of inflation from Cosmic Microwave Background anisotropy data, for the production of massive dark matter candidates during reheating, and for models of baryogenesis or leptogensis where massive particles are produced during reheating.
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.
The abstract, sentence by sentence
We point out that inflaton decay products acquire plasma masses during the reheating phase following inflation. The plasma masses may render inflaton decay kinematicaly forbidden, causing the temperature to remain frozen for a period at a plateau value. We show that the final reheating temperature may be uniquely determined by the inflaton mass, and may not depend on its coupling. Our findings have important implications for the thermal production of dangerous relics during reheating (e.g., gravitinos), for extracting bounds on particle physics models of inflation from Cosmic Microwave Background anisotropy data, for the production of massive dark matter candidates during reheating, and for models of baryogenesis or leptogensis where massive particles are produced during reheating.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We point out that inflaton decay products acquire plasma masses during the reheating phase following inflation. | contribution 0.49 | 0.39 | 0.07 | asserted 1.00 |
| s1 | The plasma masses may render inflaton decay kinematicaly forbidden, causing the temperature to remain frozen for a period at a plateau value. | result 0.90 | 0.33 | 0.16 | hedged possibility 1.00 |
| s2 | We show that the final reheating temperature may be uniquely determined by the inflaton mass, and may not depend on its coupling. | result 1.00 | 0.92 | 0.71 | hedged possibility 0.90 |
| s3 | Our findings have important implications for the thermal production of dangerous relics during reheating (e.g., gravitinos), for extracting bounds on particle physics models of inflation from Cosmic Microwave Background anisotropy data, for the production of massive dark matter candidates during reheating, and for models of baryogenesis or leptogensis where massive particles are produced during reheating. | interpretation 1.00 | 0.69 | 0.11 | asserted 0.87 |
What was examined, and what was not
- arXiv listing abstract v1
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References
How later papers used it
50 later papers cite it
1 later paper by other authors is listed below: 1 used its method or tool.
Uses its method or tool 1 paper
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Rewrote its Boltzmann equations in terms of dimensionless quantities following this paper.
The long-lived stau as a thermal relic (2009) · 1.00 · paraphrased: the licence does not allow quoting
How the literature uses it
49 arXiv papers cite this in 57 sentences
Papers citing it · 47 sentences without a confident label
Uses its method or tool 1 paper
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[For the actual integration we rewrite the Boltzmann equations ([ref]) and ([ref]) in terms of dimensionless quantities following [ref] . ]
The long-lived stau as a thermal relic · Reheating phase · 1.00
Cites it as support 2 papers
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Consequently, the time scale for thermalization is expected to be much shorter than the time scale of inflaton decay [ref] .
Resonant Reheating · Bosonic reheating · 0.99
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This is because, when the decay products acquire a thermal mass comparable to the inflaton mass, the available phase space will be reduced [ref] .
Running Kinetic Inflation · A case of $n=2$ and $m≥2$ · 0.96
Cites it as background 7 papers
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The spontaneous breaking of $U(1)_PQ$ with a vacuum expectation value proportional to $f_a$ occurs before inflation and it is never restored by either quantum or thermal fluctuations as long as [equation] Here the first term denotes the Gibbons-Hawking temperature [ref] during inflation with a Hubble rate $H_I$, $T_max$ the maximum temperature during inflationary reheating [ref] and $T_RH$ the temperature of the radiation bath after reheating.[$T_max$ is typically expected to be larger than $T_RH$, but exceptions to this common lore exist [ref] .] In this preinflationary scenario there is no threat from topological defects and the massless axion $a ≡θf_a$ develops long wavelength quantum fluctuations $δθ≃H_I /(2πf_a )$ during the quasi-de Sitter phase, that give rise to a scale invariant power spectrum with an amplitude proportional to $H_I/(2π^2)$.
Minimal solution to the axion isocurvature problem from a nonminimal coupling · Introduction · 0.90
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However, in such a regime it is very difficult to relate collider signatures to cosmological observables in any case, as strong feedback effects tend to introduce a dependence on a large set of unknown parameters, cf. Sec. [ref]. ] thermal corrections can impact observables in two ways: They can either modify the efficiency of reheating characterised by $$ [ref] , or they can impact the DM production rate $$ [ref] .
Thermal effects on Dark Matter production during cosmic reheating · Introduction · 0.82
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This region of parameter space, with $T ≳M_ϕ$, affords a rich variety of interesting and model-dependent phenomena, including nonperturbative particle production [ref] and thermal effects such as thermal blocking and Landau damping [ref] , and as such has been a focus of exploration in detailed studies of reheating.
Chilly Dark Sectors and Asymmetric Reheating · Discussion and Conclusions · 0.94
Discussion
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