# Probing the Vacuum Decay Hypothesis with Growth Function Data

## Abstract

**:**

## 1. Introduction

## 2. The Method

#### 2.1. Approach I

#### 2.2. Approach II

## 3. Observational Constraints

#### 3.1. Dark Energy Equivalence

#### 3.2. Growth Function

#### 3.3. Constraints

## 4. Final Remarks

## Acknowledgments

## Conflicts of Interest

## References

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1. | Although it is possible, coupling with baryons implies a variation of baryonic particles masses, which are tightly constrained by Big Bang nucleosynthesis. Furthermore, solar system experiments [17,18], bounds on the variation of fundamental constants [19,20] and even background tests [21] constrained a possible coupling with baryons to be very small and despicable in front of dark matter coupling. |

2. | The vacuum energy is assumed homogeneous since, in the scales considered in this paper (subhorizon), the matter perturbations dominates over the vacuum energy density perturbations, which can be neglected [33]. |

**Figure 1.**The ${\mathrm{\Omega}}_{1,0}-{\mathrm{\Omega}}_{2,0}$ (

**top**) and ${\mathrm{\Omega}}_{1,0}-{\mathrm{\Omega}}_{3,0}$ (

**bottom**) parametric spaces from Approaches I and II. The contours are drawn for $\Delta {\chi}^{2}=2.30$ and 6.17.

**Figure 2.**Deceleration parameter for the $\mathrm{\Lambda}$CDM model (solid line) and for the best fit points of Approaches I (dotted line) and II (dashed line). The $q=0$ line marks the transition from the decelerated to accelerated phase, and the $q=0.5$ line marks the matter-dominated era.

z | f | ${\mathit{\sigma}}_{\mathit{f}}$ | Ref. |
---|---|---|---|

0.15 | 0.49 | 0.14 | [36] |

0.15 | 0.51 | 0.11 | [37,38] |

0.22 | 0.60 | 0.10 | [39] |

0.32 | 0.654 | 0.18 | [40] |

0.34 | 0.64 | 0.09 | [41] |

0.35 | 0.70 | 0.18 | [42] |

0.41 | 0.70 | 007 | [39] |

0.42 | 0.73 | 0.09 | [43] |

0.55 | 0.75 | 0.18 | [44] |

0.59 | 0.75 | 0.09 | [43] |

0.60 | 0.73 | 0.07 | [39] |

0.77 | 0.91 | 0.36 | [36] |

0.78 | 0.70 | 0.08 | [39] |

1.4 | 0.90 | 0.24 | [45] |

2.125 | 0.78 | 0.24 | [46] |

2.72 | 0.78 | 0.24 | [46] |

3.0 | 0.99 | 0.24 | [47] |

**Table 2.**The best fit values for ${\mathrm{\Omega}}_{1,0}$, ${\mathrm{\Omega}}_{2,0}$ and ${\mathrm{\Omega}}_{3,0}$. The upper and lower limits stand for $2\sigma $ errors.

${\mathbf{\Omega}}_{1,0}$ | ${\mathbf{\Omega}}_{2,0}$ | ${\mathbf{\Omega}}_{3,0}$ | ${\mathit{\chi}}_{\mathit{min}}^{2}$ | |
---|---|---|---|---|

Approach I | $-{0.072}_{-0.198}^{+0.198}$ | ${0.004}_{-0.064}^{+0.088}$ | ${0.10}_{-0.27}^{+0.31}$ | 1.941 |

Approach II | ${0.33}_{-0.41}^{+0.29}$ | ${0.11}_{-0.14}^{+0.36}$ | ${0.36}_{-0.46}^{+0.33}$ | 1.285 |

$\mathrm{\Lambda}$CDM model | 0 | 0 | 0 | 2.857 |

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**MDPI and ACS Style**

Barboza, E.M., Jr.
Probing the Vacuum Decay Hypothesis with Growth Function Data. *Universe* **2018**, *4*, 39.
https://doi.org/10.3390/universe4020039

**AMA Style**

Barboza EM Jr.
Probing the Vacuum Decay Hypothesis with Growth Function Data. *Universe*. 2018; 4(2):39.
https://doi.org/10.3390/universe4020039

**Chicago/Turabian Style**

Barboza, Edésio M., Jr.
2018. "Probing the Vacuum Decay Hypothesis with Growth Function Data" *Universe* 4, no. 2: 39.
https://doi.org/10.3390/universe4020039