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Thermal curvature perturbations in thermal inflation
High Energy Physics - Phenomenology · Submitted 27 Jan 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations.
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The abstract, sentence by sentence
We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature $T_c$, below which thermal effects stop holding the field at the false potential minimum. This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for $T>T_c$. The larger thermal field variance also reduces the duration of a period of fast-roll inflation below $T_c$, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. | contribution 0.99 | 0.96 | 0.08 | asserted 0.98 |
| s1 | We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature $T_c$, below which thermal effects stop holding the field at the false potential minimum. | result 1.00 | 0.93 | 0.13 | hedged possibility 0.94 |
| s2 | This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. | result 0.67 | 0.87 | 0.31 | asserted 1.00 |
| s3 | In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for $T>T_c$. | result 0.68 | 0.94 | 0.31 | asserted 0.87 |
| s4 | The larger thermal field variance also reduces the duration of a period of fast-roll inflation below $T_c$, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales. | result 0.67 | 0.84 | 0.10 | asserted 0.53 |
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The paper
Original abstract
We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature $T_c$, below which thermal effects stop holding the field at the false potential minimum. This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for $T>T_c$. The larger thermal field variance also reduces the duration of a period of fast-roll inflation below $T_c$, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales.
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References
How the literature uses it
3 arXiv papers cite this in 4 sentences
Papers citing it · 1 sentence without a confident label
Contests it 1 paper
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In [ref] , the authors incorrectly considered flaton fluctuations, instead of thermal fluctuations, to calculate the curvature perturbations and so arrived at incorrect results.
The curvature perturbation generated by thermal fluctuations during thermal inflation · Discussion · contest 0.95
Cites it as background 1 paper
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Before returning to our dissipative dark sector scenario, we briefly note that it has recently been proposed that large fluctuations during thermal inflation might themselves result in PBHs [ref] .
Dissipative Dark Cosmology: From Early Matter Dominance to Delayed Compact Objects · Pre-BBN phase transition · 0.91
What it cites · 47 sentences without a confident label
Uses the method or tool of 3 papers
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The flaton field satisfies the Langevin-like equation [ref] :
Warm Inflation and its Microphysical Basis · Evolution of the temperature during thermal inflation · 0.88
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The time integration can then be performed using [ref]
Fate of oscillating scalar fields in the thermal bath and their cosmological implications · Derivation of the Langevin-like equation · 0.95
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Thus, the correlators can be simply written as [ref] :
A generalized Isserlis theorem for location mixtures of Gaussian random vectors · Curvature Perturbations · 0.83
Compares with 1 paper
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Surprisingly, we find that for thermal flaton fluctuations the amplitude of the curvature power spectrum is suppressed with respect to the purely quantum case analyzed in [ref] , at least for scales exiting the horizon before the temperature decreases below the critical value.
Primordial Black Holes from Thermal Inflation · Introduction · 0.92
Cites as support 1 paper
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However, the correlation function of the noise terms is exponentially suppressed for length scales smaller than the correlation length $ξ∼(πT)^-1$, that is for physical momentum scales larger than $p∼πT$ [ref] .
Effects of thermal fluctuations on thermal inflation · Curvature Perturbations · 0.96
Cites as background 27 papers
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We assume that the scalar field $ϕ$ corresponds to a renormalizable flat direction, or flaton field, common in several SUSY/supergravity scenarios [ref] , such that its potential is only lifted by soft terms (such as a mass term from SUSY breaking), and non-renormalizable terms.
Some aspects of thermal inflation: the finite temperature potential and topological defects · Thermal inflation · 0.94
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We assume that the scalar field $ϕ$ corresponds to a renormalizable flat direction, or flaton field, common in several SUSY/supergravity scenarios [ref] , such that its potential is only lifted by soft terms (such as a mass term from SUSY breaking), and non-renormalizable terms.
Gauge Hierarchy, Planck Scale Corrections And The Origin of GUT Scale In Supersymmetric $(SU(3))^3$ · Thermal inflation · 0.94
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We assume that the scalar field $ϕ$ corresponds to a renormalizable flat direction, or flaton field, common in several SUSY/supergravity scenarios [ref] , such that its potential is only lifted by soft terms (such as a mass term from SUSY breaking), and non-renormalizable terms.
Cosmology with a TeV mass GUT Higgs · Thermal inflation · 0.94
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