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Post-inflationary phases stiffer than radiation and Palatini formulation
General Relativity and Quantum Cosmology · Submitted 15 May 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In the Palatini formulation the addition such a term does not affect the scalar modes during the inflationary phase and throughout the course of the subsequent stiff epoch but it suppresses the tensor power spectrum and the tensor-to-scalar ratio.
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The abstract, sentence by sentence
If the inflaton and the quintessence fields are identified, the background geometry evolves through a stiff epoch undershooting the expansion rate of a radiation-dominated plasma. For some classes of inflationary potentials this scenario is at odds with the current observational evidence since the corresponding tensor-to-scalar ratio is too large. Quintessential inflation is analyzed when the gravitational action is supplemented by a contribution quadratic in the Einstein-Hilbert term. In the Palatini formulation the addition such a term does not affect the scalar modes during the inflationary phase and throughout the course of the subsequent stiff epoch but it suppresses the tensor power spectrum and the tensor-to-scalar ratio. While in the Palatini formulation the power-law potentials leading to a quintessential inflationary dynamics are again viable, the high-frequency spike of the relic graviton spectrum is squeezed and the whole signal is suppressed at least when the higher-order contributions appearing in the action are explicitly decoupled from the inflaton.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | If the inflaton and the quintessence fields are identified, the background geometry evolves through a stiff epoch undershooting the expansion rate of a radiation-dominated plasma. | result 0.59 | 0.29 | 0.10 | asserted 0.79 |
| s1 | For some classes of inflationary potentials this scenario is at odds with the current observational evidence since the corresponding tensor-to-scalar ratio is too large. | background 0.44 | 0.17 | 0.05 | asserted 0.70 |
| s2 | Quintessential inflation is analyzed when the gravitational action is supplemented by a contribution quadratic in the Einstein-Hilbert term. | contribution 0.74 | 0.58 | 0.07 | asserted 0.93 |
| s3 | In the Palatini formulation the addition such a term does not affect the scalar modes during the inflationary phase and throughout the course of the subsequent stiff epoch but it suppresses the tensor power spectrum and the tensor-to-scalar ratio. | result 0.98 | 0.74 | 0.61 | asserted 1.00 |
| s4 | While in the Palatini formulation the power-law potentials leading to a quintessential inflationary dynamics are again viable, the high-frequency spike of the relic graviton spectrum is squeezed and the whole signal is suppressed at least when the higher-order contributions appearing in the action are explicitly decoupled from the inflaton. | result 0.98 | 0.74 | 0.44 | asserted 0.65 |
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The paper
Original abstract
If the inflaton and the quintessence fields are identified, the background geometry evolves through a stiff epoch undershooting the expansion rate of a radiation-dominated plasma. For some classes of inflationary potentials this scenario is at odds with the current observational evidence since the corresponding tensor-to-scalar ratio is too large. Quintessential inflation is analyzed when the gravitational action is supplemented by a contribution quadratic in the Einstein-Hilbert term. In the Palatini formulation the addition such a term does not affect the scalar modes during the inflationary phase and throughout the course of the subsequent stiff epoch but it suppresses the tensor power spectrum and the tensor-to-scalar ratio. While in the Palatini formulation the power-law potentials leading to a quintessential inflationary dynamics are again viable, the high-frequency spike of the relic graviton spectrum is squeezed and the whole signal is suppressed at least when the higher-order contributions appearing in the action are explicitly decoupled from the inflaton.
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References
How the literature uses it
19 arXiv papers cite this in 21 sentences
Papers citing it · 12 sentences without a confident label
Cites it as background 8 papers
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Regarding inflation, the difference in the predictions between the two variational principles has been recently studied in [ref] .
Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories · Introduction · 0.88
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This has been first pointed out in [ref] and has attracted the interest of many authors since, [ref] , with still continuing activity, [ref] .
Reheating in $R^2$ Palatini inflationary models · Introduction · 0.85
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This ceases to be the case though in more elaborate theories when for example higher-curvature terms are taken into account and/or matter couples non-minimally with gravity [ref] .
Palatini-Higgs inflation with non-minimal derivative coupling · Introduction · 0.80
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