# Challenges in Supersymmetric Cosmology

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## Abstract

**:**

## 1. Introduction

## 2. Inflation from Supersymmetry Breaking

#### The Set Up

## 3. Microscopic Model

#### 3.1. The Generalised Fayet-Iliopoulos Model

#### 3.2. Integrating Out Heavy Fields

#### 3.3. Effective K ähler Potential and Superpotential

#### 3.4. Inflation from the Effective Low-Energy Theory

**Region I**: with $\Delta >0$, $c\u2a7e0$,**Region II**: with $\Delta >0$, $c\u2a7d0$,**Region III**: with $\Delta <0$, $c\u2a7d0$,**Region IV**: with $\Delta <0$, $c\u2a7e0$.

**Region I**and

**III**, while the scalarpotential with parameters in

**Region II**and

**IV**have only de Sitter minimum with a large cosmological constant. We can also show that

**Region I**does not satisfy the integrating out condition. Therefore, we conclude that

**Region III**is the only possible domain that allows for slow-roll inflation with a nearby minimum having a small and tuneable vacuum energy.

#### 3.5. The Effective Scalar Potential and Slow-Roll Parameters

## 4. Fayet-Iliopoulos (Fi) D-Terms in Supergravity

#### 4.1. Review

#### 4.2. The Scalar Potential in a Non R-Symmetry Frame

#### 4.3. Example for Slow-Roll D-Term Inflation

#### 4.4. A Small Field Inflation Model from Supergravity with Observable Tensor-to-Scalar Ratio

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Sample Availability: Samples of the compounds...... are available from the authors. |

**Figure 1.**(

**a**) Allowed parameter space (v, x) with 0 < v < 2.0 and 0 < x < 2.0. The colored regions in which A

_{2}> 0 can be divided into 4 parts, namely I, II, III and IV. (

**b**)

**Region I**and part of

**Region II**are in the excluded area where ${v}^{2}-\frac{1}{4}x(x-1-{v}^{2})<0$ where the integrating out condition is not satisfied.

**Figure 2.**The scalar potential in

**Region III**of Figure 1 is plotted as a function of the coordinate c in (

**a**) and ρ in (

**b**) with parameters (71) . The inflaton ρ as a function of c is shown in (

**c**). Finally (

**d**) shows the slow-roll parameters ϵ and η.

**Figure 3.**This plot presents the scalar potentials for $F=0$ and $F\ne 0$ cases. For $F=0$, we have a local maximum at ${\rho}_{\mathrm{max}}=0$ and the global minimum has zero cosmological constant. For $F\ne 0$, the origin $\rho =0$ is still the maximum but the global minimum now has a positive cosmological constant.

**Figure 4.**A plot of the predictions for the scalar potential with $F=0$, $b=3$, $A=0.176$, $B=0.091$, $\xi =-1.101$ and $q=8.68\times {10}^{-6}$ in the ${n}_{s}$ - r plane, versus Planck’15 results.

**Table 1.**The chiral multiplet ${\mathsf{\Phi}}_{+}$ and ${\mathsf{\Phi}}_{-}$ are charged under ${\mathrm{U}\left(1\right)}_{m}\times {\mathrm{U}\left(1\right)}^{\prime}$. Note that ${\mathrm{U}\left(1\right)}^{\prime}$ becomes the R-symmetry in the low-energy theory and does not play any role during the integrating out process.

${\mathbf{U}\left(1\right)}_{\mathit{m}}$ | ${\mathbf{U}\left(1\right)}^{\prime}$ | |
---|---|---|

${\mathsf{\Phi}}_{+}$ | $+{q}_{+}$ | q |

${\mathsf{\Phi}}_{-}$ | $-{q}_{-}$ | 0 |

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**MDPI and ACS Style**

Antoniadis, I.; Chatrabhuti, A.
Challenges in Supersymmetric Cosmology. *Symmetry* **2020**, *12*, 468.
https://doi.org/10.3390/sym12030468

**AMA Style**

Antoniadis I, Chatrabhuti A.
Challenges in Supersymmetric Cosmology. *Symmetry*. 2020; 12(3):468.
https://doi.org/10.3390/sym12030468

**Chicago/Turabian Style**

Antoniadis, Ignatios, and Auttakit Chatrabhuti.
2020. "Challenges in Supersymmetric Cosmology" *Symmetry* 12, no. 3: 468.
https://doi.org/10.3390/sym12030468