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Squared Quartic Hilltop Inflation
General Relativity and Quantum Cosmology · Submitted 30 Aug 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is shown that the correction terms are physically important during inflation and generally need to be accounted for when considering Hilltop models as a candidate for inflation.
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The abstract, sentence by sentence
A correction to the Quartic Hilltop inflationary model is proposed to account for stabilising terms in the potential. We derive analytical predictions for the spectral index $n_s$ and tensor-scalar ratio $r$ which lie within the Planck 2018 survey bounds. The reheating predictions of the corrected model are investigated and by considering the reheating temperature we further constrain the $(n_s,r)$ parameter space. It is shown that the correction terms are physically important during inflation and generally need to be accounted for when considering Hilltop models as a candidate for inflation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A correction to the Quartic Hilltop inflationary model is proposed to account for stabilising terms in the potential. | contribution 0.99 | 0.87 | 0.16 | asserted 0.95 |
| s1 | We derive analytical predictions for the spectral index $n_s$ and tensor-scalar ratio $r$ which lie within the Planck 2018 survey bounds. | result 0.99 | 0.95 | 0.22 | asserted 1.00 |
| s2 | The reheating predictions of the corrected model are investigated and by considering the reheating temperature we further constrain the $(n_s,r)$ parameter space. | contribution 0.81 | 0.92 | 0.10 | asserted 0.99 |
| s3 | It is shown that the correction terms are physically important during inflation and generally need to be accounted for when considering Hilltop models as a candidate for inflation. | interpretation 0.91 | 0.85 | 0.77 | asserted 0.98 |
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The paper
Original abstract
A correction to the Quartic Hilltop inflationary model is proposed to account for stabilising terms in the potential. We derive analytical predictions for the spectral index $n_s$ and tensor-scalar ratio $r$ which lie within the Planck 2018 survey bounds. The reheating predictions of the corrected model are investigated and by considering the reheating temperature we further constrain the $(n_s,r)$ parameter space. It is shown that the correction terms are physically important during inflation and generally need to be accounted for when considering Hilltop models as a candidate for inflation.
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How the literature uses it
4 arXiv papers cite this in 21 sentences
Papers citing it · 10 sentences without a confident label
Builds on it 1 paper
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[ref] is to convert it into a sombrero-hat potential (e.g. [ref] ) [equation] In this article, for the sake of curiosity and research, we give up the attempt of stabilization and relax the overall power that is currently 2 and consider it as a new parameter $n$, obtaining the following potential [equation] where $m$, $n$, $V_0$, $ϕ_0>0$ are free parameters and only positive values for $ϕ$ are considered as well.
Generalized Hilltop Inflation · Generalized hilltop inflation · 0.85
Compares with it 1 paper
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The model with $n = 2$ has also been already studied in the past (e.g. [ref] and refs. therein) and compatibility with the constraints required $m > 2$.
Generalized Hilltop Inflation · Conclusions · 0.84
Cites it as support 1 paper
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The fact that this issue does not arise for hilltop-squared theories has been a motivation to consider these models, see e.g. [ref] .
Scaling Characteristics of Hilltop and Hilltop-Squared Inflation · Introduction · 0.98
Cites it as background 3 papers
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This class of models has been investigated in a wide variety of contexts including inflation and dark energy (see e.g. [ref] ), and is described by a potential of the following form, [equation] where $V_0$ is the energy scale at the height of the potential, $μ$ is a mass scale, and $n$ is an integer.
Minimizing the tensor-to-scalar ratio in single-field inflation models · Observables are sensitive to corrections · 1.00
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In this Subsection, we remind the reader of the main features of hilltop inflation (e.g. [ref] and refs. therein).
Generalized Hilltop Inflation · Hilltop inflation · 1.00
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While hilltop models in general, and the $V_p,n$ above in particular, have traditionally been considered in the context of singlefield inflation (see e.g. [ref] ), this class of potentials is also of interest in the framework of multifield inflation models that describe saddle point inflation.
Scaling Characteristics of Hilltop and Hilltop-Squared Inflation · Introduction · 0.87
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