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Preheating with Non-Standard Kinetic Term
High Energy Physics - Theory · Submitted 6 Aug 2008
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This equation is in general more unstable than the Mathieu equation, such that narrow resonance preheating may be efficient in theories with a non-canonical kinetic term.
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The abstract, sentence by sentence
We consider reheating after inflation in theories with a non-standard kinetic term. We show that the equation that exhibits parametric resonance is the Hill-Whittaker equation, which is a particular case of the more general Hill equation. This equation is in general more unstable than the Mathieu equation, such that narrow resonance preheating may be efficient in theories with a non-canonical kinetic term.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider reheating after inflation in theories with a non-standard kinetic term. | background 0.59 | 0.41 | 0.04 | asserted 0.53 |
| s1 | We show that the equation that exhibits parametric resonance is the Hill-Whittaker equation, which is a particular case of the more general Hill equation. | result 0.85 | 0.82 | 0.15 | asserted 1.00 |
| s2 | This equation is in general more unstable than the Mathieu equation, such that narrow resonance preheating may be efficient in theories with a non-canonical kinetic term. | interpretation 0.68 | 0.73 | 0.78 | hedged possibility 0.84 |
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The paper
Original abstract
We consider reheating after inflation in theories with a non-standard kinetic term. We show that the equation that exhibits parametric resonance is the Hill-Whittaker equation, which is a particular case of the more general Hill equation. This equation is in general more unstable than the Mathieu equation, such that narrow resonance preheating may be efficient in theories with a non-canonical kinetic term.
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References
How the literature uses it
23 arXiv papers cite this in 29 sentences
Papers citing it · 14 sentences without a confident label
Uses its method or tool 3 papers
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Hill's equation with three terms may be transformed in a type of equation which was already studied in [ref] by performing the following change of variables [ref] [equation] so that in terms of the new field, ([ref]) is rewritten as [equation] This has the generic form of [equation] with [equation] We observe that $q̅$ can be either positive or negative, depending on the relative strength of $θ_2$ and $θ_4$.
Enhanced (p)reheating in DBI Inflation · Fluctuations around the background solutions · 0.94
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According to the Floquet theorem, the solution can be written as a series of the form [equation] Plugging this Ansatz into the above equation, we obtain a recursive relation [equation] where [equation] For given values of $A$, $q$ and $p$ we can find the Floquet characteristic exponent $μ$ by solving for the roots of the determinant [equation] It is possible to prove (see, e.g., refs [ref] ) that this determinant can be written in a compact form as [equation] From this equation we can easily find [equation] The advantage of this representation of solutions is that it can be evaluated numerically very efficiently.
Postinflationary vacuum instability and Higgs-inflaton couplings · Computation of the Floquet Exponent · 0.86
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[ref] For a single degree of freedom, a simple algorithm for calculating Floquet exponents numerically may be found, for example, in Refs. Frolov:2010sz,Karouby:2011xs,Hertzberg:2014iza, and in the appendix to Ref. Amin:2011hu.
Nonperturbative Dynamics Of Reheating After Inflation: A Review · Preheating and parametric resonance · 0.89
Compares with it 1 paper
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This is a very different situation from the one studied in [ref] , where the masses and couplings were not functions of $ψ$.
Reheating and preheating in the simplest extension of Starobinsky inflation · The view from the Einstein frame · 1.00
Cites it as background 11 papers
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The extension to models with non-standard kinetic terms is in its early stages, though non-standard matter fields have been studied recently [ref] .
Enhanced (p)reheating in DBI Inflation · Introduction · 0.84
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For more details on the Whittaker-Hill equation and the Floquet theory, see, e.g., Refs. [ref] and references therein.
Electroweak Vacuum Metastability and Low-scale Inflation · Higgs dynamics during preheating · 0.80
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A particular type of scalar-tensor type modification to the reheaton's kinetic term was considered in [ref] .
Frustration of resonant preheating by exotic kinetic terms · Introduction · 0.88
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