# Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time

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## Abstract

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## 1. Introduction

- The first one concerns the representation of the quantum-wave equation, which should be cast in a manifestly-covariant form. A prerequisite for this to happen is, of course, that the quantum canonical variables (i.e., both the Lagrangian coordinates and the conjugate canonical momentum operators) should be expressed in $4-$tensor form.
- The second one is that QG-theory should be such to permit a second-quantization theory for the gravitational field in the sense indicated above. More precisely, QG-theory should be capable of prescribing also the non-linear quantum modifications of the background space–time. Thus, besides prescribing the universe quantum state function $\psi $, QG-theory should predict also the related quantum-modified form of EFE which determines the background metric field tensor. As a consequence, the same equation—just as the original EFE - should be realized by means of a tensor (and therefore frame-independent) PDE, so that it must preserve its form with respect to the group of coordinate transformations (1) between two arbitrary GR-frames.

## 2. Quantum-Modified Einstein Field Equations

## 3. Momentum Quantum-Modified Einstein Field Equations

## 4. Case of Quantum Non-Unitarity

## 5. Physical Properties and Applications: DeSitter Solution and Graviton Mass

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Cremaschini, C.; Tessarotto, M.
Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time. *Symmetry* **2020**, *12*, 531.
https://doi.org/10.3390/sym12040531

**AMA Style**

Cremaschini C, Tessarotto M.
Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time. *Symmetry*. 2020; 12(4):531.
https://doi.org/10.3390/sym12040531

**Chicago/Turabian Style**

Cremaschini, Claudio, and Massimo Tessarotto.
2020. "Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time" *Symmetry* 12, no. 4: 531.
https://doi.org/10.3390/sym12040531