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The reheating constraints to natural inflation in Horndeski gravity
Cosmology and Nongalactic Astrophysics · Submitted 14 Dec 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We place the observational constraints on a natural inflation model and show that the model is now consistent with the observational data for some plausible range of the model parameter $\Delta$, mainly due to the suppressed tensor-to-scalar ratio.
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For the subclass of Horndeski theory of gravity, we investigate the effects of reheating on the predictions of natural inflation. In the presence of derivative self-interaction of a scalar field and its kinetic coupling to the Einstein tensor, the gravitational friction to inflaton dynamics is enhanced. As a result, the tensor-to-scalar ratio $r$ is suppressed. We place the observational constraints on a natural inflation model and show that the model is now consistent with the observational data for some plausible range of the model parameter $\Delta$, mainly due to the suppressed tensor-to-scalar ratio. To be consistent with the data at the $1\sigma$ ($68\%$ confidence) level, a slightly longer $N_k\gtrsim60$ duration of inflation than usually assumed is preferred. Since the duration of inflation, for any specific inflaton potential, is related to reheating parameters, including the duration $N_{re}$, temperature $T_{re}$, and equation-of-state $\omega_{re}$ parameter during reheating, we imposed the effects of reheating to the inflationary predictions to put further constraints. The results show that the duration of inflation $N_k$ is affected by considerations of reheating, mainly by the $\omega_{re}$ and $T_{re}$ parameters. If reheating occurs instantaneously for which $N_{re}=0$ and $\omega_{re}=1/3$, the duration of inflation is estimated to be $N_k\simeq57$, where the exact value is less sensitive to the model parameter $\Delta$ compatible with the CMB data. The duration of inflation is longer (or shorter) than $N_k\simeq57$ for the equation of state larger (or smaller) than 1/3 hence $N_{re}\neq0$. The maximum temperature at the end of reheating is $T_{re}^\text{max}\simeq3\times 10^{15}$ GeV, which corresponds to the instantaneous reheating. The low reheating temperature, as low as a few MeV, is also possible when $\omega_{re}$ is closer to $1/3$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | For the subclass of Horndeski theory of gravity, we investigate the effects of reheating on the predictions of natural inflation. | contribution 1.00 | 0.92 | 0.04 | asserted 0.79 |
| s1 | In the presence of derivative self-interaction of a scalar field and its kinetic coupling to the Einstein tensor, the gravitational friction to inflaton dynamics is enhanced. | result 0.66 | 0.38 | 0.05 | asserted 1.00 |
| s2 | As a result, the tensor-to-scalar ratio $r$ is suppressed. | result 0.98 | 0.69 | 0.15 | asserted 1.00 |
| s3 | We place the observational constraints on a natural inflation model and show that the model is now consistent with the observational data for some plausible range of the model parameter $\Delta$, mainly due to the suppressed tensor-to-scalar ratio. | result 0.89 | 0.94 | 0.64 | asserted 0.68 |
| s4 | To be consistent with the data at the $1\sigma$ ($68\%$ confidence) level, a slightly longer $N_k\gtrsim60$ duration of inflation than usually assumed is preferred. | result 0.96 | 0.85 | 0.13 | asserted 0.66 |
| s5 | Since the duration of inflation, for any specific inflaton potential, is related to reheating parameters, including the duration $N_{re}$, temperature $T_{re}$, and equation-of-state $\omega_{re}$ parameter during reheating, we imposed the effects of reheating to the inflationary predictions to put further constraints. | method 0.77 | 0.91 | 0.06 | asserted 0.98 |
| s6 | The results show that the duration of inflation $N_k$ is affected by considerations of reheating, mainly by the $\omega_{re}$ and $T_{re}$ parameters. | result 0.99 | 0.92 | 0.11 | asserted 1.00 |
| s7 | If reheating occurs instantaneously for which $N_{re}=0$ and $\omega_{re}=1/3$, the duration of inflation is estimated to be $N_k\simeq57$, where the exact value is less sensitive to the model parameter $\Delta$ compatible with the CMB data. | result 1.00 | 0.89 | 0.09 | asserted 0.95 |
| s8 | The duration of inflation is longer (or shorter) than $N_k\simeq57$ for the equation of state larger (or smaller) than 1/3 hence $N_{re}\neq0$. | result 0.98 | 0.83 | 0.06 | asserted 1.00 |
| s9 | The maximum temperature at the end of reheating is $T_{re}^\text{max}\simeq3\times 10^{15}$ GeV, which corresponds to the instantaneous reheating. | result 1.00 | 0.89 | 0.05 | asserted 1.00 |
| s10 | The low reheating temperature, as low as a few MeV, is also possible when $\omega_{re}$ is closer to $1/3$. | result 1.00 | 0.88 | 0.05 | hedged possibility 0.78 |
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Original abstract
For the subclass of Horndeski theory of gravity, we investigate the effects of reheating on the predictions of natural inflation. In the presence of derivative self-interaction of a scalar field and its kinetic coupling to the Einstein tensor, the gravitational friction to inflaton dynamics is enhanced. As a result, the tensor-to-scalar ratio $r$ is suppressed. We place the observational constraints on a natural inflation model and show that the model is now consistent with the observational data for some plausible range of the model parameter $\Delta$, mainly due to the suppressed tensor-to-scalar ratio. To be consistent with the data at the $1\sigma$ ($68\%$ confidence) level, a slightly longer $N_k\gtrsim60$ duration of inflation than usually assumed is preferred. Since the duration of inflation, for any specific inflaton potential, is related to reheating parameters, including the duration $N_{re}$, temperature $T_{re}$, and equation-of-state $\omega_{re}$ parameter during reheating, we imposed the effects of reheating to the inflationary predictions to put further constraints. The results show that the duration of inflation $N_k$ is affected by considerations of reheating, mainly by the $\omega_{re}$ and $T_{re}$ parameters. If reheating occurs instantaneously for which $N_{re}=0$ and $\omega_{re}=1/3$, the duration of inflation is estimated to be $N_k\simeq57$, where the exact value is less sensitive to the model parameter $\Delta$ compatible with the CMB data. The duration of inflation is longer (or shorter) than $N_k\simeq57$ for the equation of state larger (or smaller) than 1/3 hence $N_{re}\neq0$. The maximum temperature at the end of reheating is $T_{re}^\text{max}\simeq3\times 10^{15}$ GeV, which corresponds to the instantaneous reheating. The low reheating temperature, as low as a few MeV, is also possible when $\omega_{re}$ is closer to $1/3$.
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