# Degravitation and the Cascading DGP Model

## Abstract

**:**

## 1. Introduction

^{−3}eV, to the value inferred by observations, it is not expected to remain small when we consider higher energy descriptions where new particles enter in the effective Lagrangian. In other words, the smallness of the Cosmological Constant is not technically natural (in a Wilsonian sense) [3].

## 2. The 6D Cascading DGP Model

## 3. De Sitter Solutions

#### 3.1. Symmetry Properties and Gauge Choice

- The bulk can be foliated into 4D leaves, whose (pseudo-Riemannian) induced metric is spatially homogeneous and isotropic.
- The translations along the 3D spatial dimensions are a symmetry of the bulk metric.
- There exists a smooth hypersurface $\Sigma $ with respect to which the bulk is ${\mathbb{Z}}_{2}$-symmetric. The codimension-2 brane coincides with the intersection of $\Sigma $ and the codimension-1 brane.
- The ${\mathbb{Z}}_{2}$-symmetry and the foliation into spatially homogeneous and isotropic leaves are compatible.

#### 3.1.1. The Bulk

#### 3.1.2. The Branes

#### 3.2. Degrees of Freedom and Flat Bulk Configurations

## 4. The Role of the Bulk Equations

#### 4.1. Initial Value Analysis

#### 4.2. Diagonal Solutions

#### 4.3. De Sitter Solutions Again

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zel’dovich, Y.B. The Cosmological Constant and the Theory of Elementary Particles. Sov. Phys. Uspekhi
**1968**, 11, 381–393. [Google Scholar] [CrossRef] - Weinberg, S. The Cosmological Constant Problem. Rev. Mod. Phys.
**1989**, 61, 1–22. [Google Scholar] [CrossRef] - Burgess, C.P. The Cosmological Constant Problem: Why it’s hard to get Dark Energy from Micro-physics. In Proceedings of the 100th Les Houches Summer School: Post-Planck Cosmology, Les Houches, France, 8 July–2 August 2013; Deffayet, C., Peter, P., Wandelt, B., Zaldarriaga, M., Cugliandolo, L.F., Eds.; Oxford University Press: Oxford, UK, 2015; pp. 149–197, ISBN 9780198728856. [Google Scholar]
- Rubakov, V.A.; Shaposhnikov, M.E. Extra Space-Time Dimensions: Towards a Solution to the Cosmological Constant Problem. Phys. Lett. B
**1983**, 125, 139–143. [Google Scholar] [CrossRef] - Akama, K. Pregeometry. Lect. Notes Phys.
**1982**, 176, 267–271. [Google Scholar] - Rubakov, V.A.; Shaposhnikov, M.E. Do We Live Inside a Domain Wall? Phys. Lett. B
**1983**, 125, 136–138. [Google Scholar] [CrossRef] - Vinet, J.; Cline, J.M. Can codimension-two branes solve the cosmological constant problem? Phys. Rev. D
**2004**, 70, 083514. [Google Scholar] [CrossRef] - Garriga, J.; Porrati, M. Football shaped extra dimensions and the absence of self-tuning. J. High Energy Phys.
**2004**, 2004, 28. [Google Scholar] [CrossRef] - Dvali, G.R.; Gabadadze, G.; Porrati, M. 4-D gravity on a brane in 5-D Minkowski space. Phys. Lett. B
**2000**, 485, 208–214. [Google Scholar] [CrossRef] - Dvali, G.R.; Gabadadze, G.; Shifman, M. Diluting cosmological constant in infinite volume extra dimensions. Phys. Rev. D
**2003**, 67, 044020. [Google Scholar] [CrossRef] - Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G.; Gabadadze, G. Non-local modification of gravity and the cosmological constant problem. arXiv, 2002; arXiv:hep-th/0209227. [Google Scholar]
- De Rham, C.; Dvali, G.; Hofmann, S.; Khoury, J.; Pujolas, O.; Redi, M.; Tolley, A.J. Cascading gravity: Extending the Dvali-Gabadadze-Porrati model to higher dimension. Phys. Rev. Lett.
**2008**, 100, 251603. [Google Scholar] [CrossRef] [PubMed] - De Rham, C.; Khoury, J.; Tolley, A.J. Cascading Gravity is Ghost Free. Phys. Rev. D
**2010**, 81, 124027. [Google Scholar] [CrossRef] - Sbisà, F.; Koyama, K. The critical tension in the Cascading DGP model. J. Cosmol. Astropart. Phys.
**2014**, 9, 38. [Google Scholar] [CrossRef][Green Version] - Dubovsky, S.L.; Rubakov, V.A. Brane induced gravity in more than one extra dimensions: Violation of equivalence principle and ghost. Phys. Rev. D
**2003**, 67, 104014. [Google Scholar] [CrossRef] - Berkhahn, F.; Hofmann, S.; Niedermann, F. Brane Induced Gravity: From a No-Go to a No-Ghost Theorem. Phys. Rev. D
**2012**, 86, 124022. [Google Scholar] [CrossRef] - De Rham, C.; Hofmann, S.; Khoury, J.; Tolley, A.J. Cascading Gravity and Degravitation. J. Cosmol. Astropart. Phys.
**2008**, 802, 11. [Google Scholar] [CrossRef] - Sbisà, F.; Koyama, K. Perturbation of nested branes with induced gravity. J. Cosmol. Astropart. Phys.
**2014**, 6, 29. [Google Scholar] [CrossRef][Green Version] - Geroch, R.; Traschen, J.H. Strings and Other Distributional Sources in General Relativity. Phys. Rev. D
**1987**, 36, 1017. [Google Scholar] [CrossRef] - Sbisà, F. Thin limit of the 6D Cascading DGP model. J. Cosmol. Astropart. Phys.
**2018**, 5, 62. [Google Scholar] [CrossRef] - Israel, W. Singular Hypersurfaces and Thin Shells in General Relativity. Nuovo Cimento B
**1966**, 44, 4349. [Google Scholar] [CrossRef] - Minamitsuji, M. Self-accelerating solutions in cascading DGP braneworld. Phys. Lett. B
**2010**, 684, 92–95. [Google Scholar] [CrossRef]

1. | The codimension of a brane is defined as the difference between the dimension of the ambient spacetime and the dimension of the brane. |

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Sbisà, F.
Degravitation and the Cascading DGP Model. *Universe* **2018**, *4*, 136.
https://doi.org/10.3390/universe4120136

**AMA Style**

Sbisà F.
Degravitation and the Cascading DGP Model. *Universe*. 2018; 4(12):136.
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**Chicago/Turabian Style**

Sbisà, Fulvio.
2018. "Degravitation and the Cascading DGP Model" *Universe* 4, no. 12: 136.
https://doi.org/10.3390/universe4120136