# The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials

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## Abstract

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## 1. Introduction

## 2. The Relations

## 3. The Reconstruction

## 4. Reheating

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The constraints on ${n}_{s}$ and ${r}_{0.002}$ from Planck data [5] and the theoretical predictions for the parameterization (26) in the high friction limit. The Planck constraints on ${n}_{s}$ and r are displayed in the left panel and the constraints on $\beta $ and $\gamma $ for $N=60$ are displayed in the right panel. The red and blue regions denote the $68\%$ and $95\%$ confidence level, respectively.

**Figure 2.**The reconstructed potentials are normalized with ${V}_{0}$ from Equation (30), and the inflaton field is normalized with $1/\sqrt{{F}_{0}+1}$. We choose the value of ${\varphi}_{0}$ that could make ${\varphi}_{e}=0$.

**Figure 3.**(

**Top**) The relations between ${N}_{re}$ and ${n}_{s}$; and (

**Bottom**) the relations between ${T}_{re}$ and ${n}_{s}$. The corresponding values of $\beta $ and $\gamma $ for each model are indicated in each panel. The $1\sigma $ Planck constraint ${n}_{s}=0.9649\pm 0.0042$ [5] is denoted by the gray band, and the $1\sigma $ Planck constraint on the e-folds N is also indicated. The black, red, blue and green lines correspond to the reheating models with ${w}_{re}=-1/3$, 0, 1/6 and 2/3, respectively; in each line, the arrow denotes the direction of N enlargement. The horizontal gray solid and dashed lines in the bottom panels denote the electroweak scale ${T}_{EW}\sim 100$ GeV and the big bang nucleosynthesis scale ${T}_{BBN}\sim 10$ MeV, respectively.

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**MDPI and ACS Style**

Fei, Q.; Yi, Z.; Yang, Y.
The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials. *Universe* **2020**, *6*, 213.
https://doi.org/10.3390/universe6110213

**AMA Style**

Fei Q, Yi Z, Yang Y.
The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials. *Universe*. 2020; 6(11):213.
https://doi.org/10.3390/universe6110213

**Chicago/Turabian Style**

Fei, Qin, Zhu Yi, and Yingjie Yang.
2020. "The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials" *Universe* 6, no. 11: 213.
https://doi.org/10.3390/universe6110213