# Nothing into Something and Vice Versa: A Cosmological Scenario

## Abstract

**:**

## 1. Introduction

## 2. Grigori Vereshkov’ s Equations for Stochastic Gravitational Waves of Finite Amplitude

## 3. Solution for (13)–(16) Is the de Sitter Regime

## 4. Invariance of de Sitter Regime with Respect to Wick Rotation

## 5. What Kind of SGWs are Capable to Provide the Invariance of the de Sitter Regime with Respect to Lorentzian and Euclidean Spacetime?

## 6. Cosmological Scenario

## 7. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | The material constituting the content of the Appendix A of work [8] was prepared by the late Grigory Vereshkov. It was to be included in our joint paper [9]. We did not include it in the final version of [9], since [9] was entirely devoted to quantum effects. After Grigory passed away, I decided to publish his work, including it as Appendix A to my paper [8] with a reference to its author. |

2 | |

3 | In this paper, averaging is conducted over a three-space (see, e.g., [11]). |

4 | Note that in Section 1.2 of work [8] the incorrect normalization was used. In the right hand sides (RHS) of Formulas (16)–(20), (23) and (25) of [8], the Hubble constant H must be changed for 1. This correction does not change the main result of this section, which proves that the back reaction of SGWs of small amplitude can produce a de Sitter expansion in Euclidean spacetime only. |

5 |

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**MDPI and ACS Style**

Marochnik, L.
Nothing into Something and Vice Versa: A Cosmological Scenario. *Universe* **2023**, *9*, 445.
https://doi.org/10.3390/universe9100445

**AMA Style**

Marochnik L.
Nothing into Something and Vice Versa: A Cosmological Scenario. *Universe*. 2023; 9(10):445.
https://doi.org/10.3390/universe9100445

**Chicago/Turabian Style**

Marochnik, Leonid.
2023. "Nothing into Something and Vice Versa: A Cosmological Scenario" *Universe* 9, no. 10: 445.
https://doi.org/10.3390/universe9100445