REVIEW
Large Density Perturbations from Reheating to Standard Model particles due to the Dynamics of the Higgs Boson during Inflation
High Energy Physics - Phenomenology · Submitted 29 Sep 2020 · 80 references
Pith's verdict: Perturbative constraints are solid and citable; the resonant exclusion is a real claim but is undercut by the uncentered rms perturbations in Sec. IIE.
T0 · AI review
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Referee report
The paper
The paper claims
This paper argues that quantum fluctuations of the Standard Model Higgs during inflation make the inflaton decay rate patch-dependent, and that the resulting density perturbations exceed CMB observations for most reheating channels into…
The reading
What carries the argument
The central object is the Higgs field as a stochastic light spectator, whose equilibrium probability distribution $\tilde{f}_{\rm eq}(h) \propto \exp(-2\pi^2\lambda_I h^4/3H_I^4)$ sets a characteristic value $\tilde h = \sqrt{\langle h^2\rangle} \propto H_I$ in a typical Hubble patch. That value controls the fermion mass $m_f = y h/\sqrt{2}$ and the gauge-field mass $M = g|h|/2$, which enter the inflaton decay rate of Eq. (21) through the phase-space factor and the Heaviside blocking function. The perturbation of the decay rate, Eq. (25), feeds the modulated-reheating perturbation equations (Eqs. (12)-(14)) that evolve the gravitational potential and the Bardeen parameter $\zeta$ on superhorizon scales; for resonant decay, the per-patch gauge-field mode equation with a tachyonic Chern-Simons term provides the energy-density spread from which $\zeta$ is computed.
Extended reading notes
Core claim
The paper's central claim is that the stochastic Higgs VEV during inflation modulates the inflaton decay rate $\Gamma_\varphi(h)$ through a phase-space factor and a kinematic blocking term, generating curvature perturbations that grow on superhorizon scales until reheating completes. For perturbative decay into fermions with Yukawa coupling $y$, the characteristic perturbation is $\delta\Gamma = -6y^2\langle h^2\rangle/m_\varphi^2\,(1-2y^2\langle h^2\rangle/m_\varphi^2)^{-1}$ while $m_\varphi^2 > 4m_f^2$, and zero otherwise. Solving the modulated-reheating perturbation equations, the authors find temperature fluctuations exceeding $\Delta T/T|_{\rm CMB}\sim 10^{-5}$ by orders of magnitude for $y \gtrsim 0.1$ and $\Gamma_0/m_\varphi \gtrsim 10^{-4}$ at $\lambda_I = 10^{-3}$. The resulting bound on decays into top quarks is $T_{\rm reh} < 2.4 \times 10^{12}\,{\rm GeV}\,(m_\varphi/10^{13}\,{\rm GeV})^{1/2}$, and for tau leptons $T_{\rm reh} < 2.8 \times 10^{14}\,{\rm GeV}\,(m_\varphi/10^{13}\,{\rm GeV})^{1/2}$. For resonant preheating into abelian gauge bosons with mass $M = g|h|/2$ via a Chern-Simons coupling, the computed Bardeen parameter is significantly larger than observed for both $g=0.8$ and $g=0.1$ with $\lambda_I = 10^{-2}$, supporting the conclusion that preheating into Higgsed Standard Model gauge bosons cannot be the main source of reheating.
Load-bearing premise
The quantitative size of the computed fluctuations assumes the Higgs-induced decay-rate variation between Hubble patches is a small perturbation; if the variation is large, the curvature perturbation could be misestimated by an order-one factor.
Editorial extensions
If this is right
- For high-scale inflation with $m_\varphi \sim H_I$, inflaton decay into Standard Model fermions with $y \gtrsim 0.1$ and $\Gamma_0/m_\varphi \gtrsim 10^{-4}$ produces CMB temperature anisotropies larger than observed, so such a decay channel can only dominate reheating if the decay rate is strongly suppressed.
- Decays into top quarks require $\Gamma_0/m_\varphi \lesssim 3 \times 10^{-6}$, corresponding to $T_{\rm reh} < 2.4 \times 10^{12}\,{\rm GeV}\,(m_\varphi/10^{13}\,{\rm GeV})^{1/2}$, a bound that can create tension with thermal leptogenesis models requiring high reheat temperatures.
- Resonant preheating into Higgsed gauge bosons with gauge couplings $g$ in the range $0.1$-$0.8$ and $\lambda_I = 10^{-2}$ generates curvature perturbations larger than the CMB allows, so such preheating cannot be the main reheating mechanism under the paper's assumptions.
- The constraints relax as the inflationary scale is lowered: keeping $\Gamma_0/H_I$ and $H_I y/m_\varphi$ fixed reproduces the same perturbation amplitude, so lower-scale inflation allows larger Yukawa couplings.
- Reheating channels into photons or the lightest fermions ($e$, $\mu$) escape the constraints, since their couplings to the Higgs produce negligible modulation.
Reading between the lines
- Beyond the paper, the constraints imply that any inflationary model that reheats through a Standard Model–coupled sector must either suppress the Higgs stochastic fluctuations with new dynamics or reheat predominantly into massless or very weakly coupled states; this turns the Higgs-modulated reheating bound into a generic filter on inflationary model building.
- The linearized treatment likely underestimates the curvature perturbation where Higgs blocking is strong, so the true excluded region for perturbative decays may extend to somewhat larger ranges of $\Gamma_0/m_\varphi$ and $y$ than shown in the figures, making the paper's constraints conservative.
- A direct numerical test of the central mechanism would be a fully non-linear lattice simulation of tachyonic gauge preheating with a stochastic Higgs field and Standard-Model-like couplings, computing $\zeta$ without the linearized $\delta\Gamma$ expansion; such a simulation would either confirm or displace the preheating exclusion.
- If extended to the full electroweak sector with $W^\pm$ and $Z$ bosons, the resonant constraint is expected to persist but be diluted relative to the abelian proxy, with the final exclusion depending on the fraction of inflaton energy that goes into the massive rather than the massless gauge modes.
Original abstract
Cosmic Microwave Background (CMB) observations are used to constrain reheating to Standard Model (SM) particles after a period of inflation. As a light spectator field, the SM Higgs boson acquires large field values from its quantum fluctuations during inflation, gives masses to SM particles that vary from one Hubble patch to another, and thereby produces large density fluctuations. We consider both perturbative and resonant decay of the inflaton to SM particles. For the case of perturbative decay from coherent oscillations of the inflaton after high scale inflation, we find strong constraints on the reheat temperature for the inflaton decay into heavy SM particles. For the case of resonant particle production (preheating) to (Higgsed) SM gauge bosons, we find temperature fluctuations larger than observed in the CMB for a range of gauge coupling that includes those found in the SM and conclude that such preheating cannot be the main source of reheating the Universe after inflation.
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
Cosmic Microwave Background (CMB) observations are used to constrain reheating to Standard Model (SM) particles after a period of inflation. As a light spectator field, the SM Higgs boson acquires large field values from its quantum fluctuations during inflation, gives masses to SM particles that vary from one Hubble patch to another, and thereby produces large density fluctuations. We consider both perturbative and resonant decay of the inflaton to SM particles. For the case of perturbative decay from coherent oscillations of the inflaton after high scale inflation, we find strong constraints on the reheat temperature for the inflaton decay into heavy SM particles. For the case of resonant particle production (preheating) to (Higgsed) SM gauge bosons, we find temperature fluctuations larger than observed in the CMB for a range of gauge coupling that includes those found in the SM and conclude that such preheating cannot be the main source of reheating the Universe after inflation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Cosmic Microwave Background (CMB) observations are used to constrain reheating to Standard Model (SM) particles after a period of inflation. | background 0.98 | 0.13 | 0.03 | asserted 1.00 |
| s1 | As a light spectator field, the SM Higgs boson acquires large field values from its quantum fluctuations during inflation, gives masses to SM particles that vary from one Hubble patch to another, and thereby produces large density fluctuations. | contribution 0.34 | 0.20 | 0.22 | asserted 0.99 |
| s2 | We consider both perturbative and resonant decay of the inflaton to SM particles. | method 0.57 | 0.68 | 0.03 | asserted 0.81 |
| s3 | For the case of perturbative decay from coherent oscillations of the inflaton after high scale inflation, we find strong constraints on the reheat temperature for the inflaton decay into heavy SM particles. | result 1.00 | 0.95 | 0.11 | asserted 1.00 |
| s4 | For the case of resonant particle production (preheating) to (Higgsed) SM gauge bosons, we find temperature fluctuations larger than observed in the CMB for a range of gauge coupling that includes those found in the SM and conclude that such preheating cannot be the main source of reheating the Universe after inflation. | result 0.95 | 0.95 | 0.57 | asserted 1.00 |
What was examined, and what was not
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Figures
Showing 9 of the paper's 10 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2009.14218 by the authors.
References
How the literature uses it
10 arXiv papers cite this in 16 sentences
Papers citing it · 10 sentences without a confident label
Uses its method or tool 1 paper
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The gauge-invariant Bardeen parameter [ref] produced by Higgs effects in each patch, $ζ_H^i$, is obtained by solving [ref] [equation] where $Φ_H^i$ is the gravitational potential perturbation.
Primordial non-Gaussianity from the Effects of the Standard Model Higgs during Reheating after Inflation · Introduction · 0.84
Compares with it 1 paper
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We find that CMB bounds on NG set by the Planck measurements [ref] provide even more powerful constraints than those obtained in Ref. [ref] and, thus, exclude the possibility of perturbations from Higgs-modulated reheating providing the dominant contribution to the observed power spectrum of temperature anisotropies.
Primordial non-Gaussianity from the Effects of the Standard Model Higgs during Reheating after Inflation · Introduction · 0.80
Cites it as background 3 papers
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We refer the reader to Ref. [ref] for the general formalism of modulated reheating, and to Refs. [ref] for models with a specific focus on the Higgs field.
Higgs-like spectator field as the origin of structure · Introduction · 0.98
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Given the inferred limit on the scale of inflation, in recent years a considerable effort was also dedicated to the investigation of the Higgs boson as a concrete realization of spectator field [ref] .
Primordial black holes from spectator field bubbles · Introduction · 0.87
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Complementary to this, reheating as Cosmological Heavy Ion Collider [ref] , namely, reheating as a playground in which to study thermalization in quantum field theory, has seen a recent resurgence [ref] , as has reheating as a testing ground for Higgs physics [ref] .
Catastrophic Production of Slow Gravitinos · Introduction · 0.98
What it cites · 54 sentences without a confident label
Uses the method or tool of 1 paper
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We follow the method used in Ref. [ref] to assess the effects of such a perturbation.
A new mechanism for generating density perturbations from inflation · Perturbed equations · 1.00
Uses data or values from 6 papers
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Assuming no new physics couples to SM Higgs, RG evolution of $λ$ between the electroweak and the inflation scale will yield $λ_I ≃10^-2$ at the end of high scale inflation [ref] .
Higgs mass and vacuum stability in the Standard Model at NNLO · Results for the Case of Perturbative Inflaton Decay · 0.95
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where the factor $μ_0 = 0.185$ is obtained from a numerical fit to the exact solution for the time dependence of $n_k$ [ref] and the occupation number at wave number $k=0$ is
The Higgs Boson can delay Reheating after Inflation · Including the effects of backreaction on Perturbative Reheating · 0.99
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The mass scale $μ= O(10^-6) M_Pl$ is chosen to set the amplitude of curvature perturbations $ζ∼10^-5$, in line with the results of the Planck collaboration [ref] .
Planck 2018 results. X. Constraints on inflation · Lowering the scale of inflation · 0.81
Compares with 2 papers
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While Ref. [ref] has a similar parameterization of Higgs effects on reheating, the amplitudes of temperature fluctuations we calculate in this work are notably larger for equivalent choices of parameters and we are able to show that large temperature fluctuations are even possible in the case of perturbative reheating without the full effects of Higgs blocking.[We note our calculations are broadly consistent with those in Ref. [ref] , which dynamically track the growth of density perturbations on superhorizon scales from the end of inflation.
A new mechanism for generating density perturbations from inflation · Introduction · 0.97
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While Ref. [ref] has a similar parameterization of Higgs effects on reheating, the amplitudes of temperature fluctuations we calculate in this work are notably larger for equivalent choices of parameters and we are able to show that large temperature fluctuations are even possible in the case of perturbative reheating without the full effects of Higgs blocking.[We note our calculations are broadly consistent with those in Ref. [ref] , which dynamically track the growth of density perturbations on superhorizon scales from the end of inflation.
Novel mechanism for CMB modulation in the Standard Model · Introduction · 0.97
Cites as support 1 paper
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Although this approximation does not account for the back-reaction on gauge boson production, lattice simulations have shown that tachyonic resonance of this form can efficiently preheat the Universe [ref] .
Magnetogenesis from axion inflation · Resonant decay: patch-by-patch energy densities · 0.98
Cites as background 29 papers
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Typical mechanisms for reheating are perturbative decay of the inflaton [ref] and resonant particle production [ref] .
Probing Planckian physics: resonant production of particles during inflation and features in the primordial power spectrum · Introduction · 0.98
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Inhomogeneous reheating due to the stochastic behavior of a light spectator field is known as modulated reheating [ref] .
Dark Radiation from Modulated Reheating · Introduction · 0.98
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Inhomogeneous reheating due to the stochastic behavior of a light spectator field is known as modulated reheating [ref] .
Cosmological Perturbations From Inhomogeneous Reheating, Freeze-Out, and Mass Domination · Introduction · 0.98
Discussion
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