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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.19451 |
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| _version_ | 1866909565756375040 |
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| author | Liu, Yang |
| author_facet | Liu, Yang |
| contents | In our previous paper [1,2], we proposed a probabilistic argument to explain the reason why the cosmological constant is very small in $4D$. We can ask a question: if the behavior of tunneling exponent $B$ can be generalized to $D$-dimension. Moreover, in higher dimensional theory motivated by string theory the Gauss-Bonnet term plays an important role. Therefore, in this paper, we generalize our result in [1,2] to arbitrary $D$ dimensions including the Gauss-Bonnet term. As a result, we have two main results. We find that the Euclidean action of the bounce, $B$, describing the decay of a de Sitter vacuum, is proportional to $k^{-(D-2)}_{+}$, which has a pole as $k^2_{+} \rightarrow 0$ where $k^2_{+}$ is the curvature of the parent vacuum. This result is similar to the result in $4D$. The other result is that we find a new decay channel, describing up-tunneling from anti-de Sitter into de Sitter. The meaning of this new decay channel in the string landscape should be explored in the future. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19451 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vacuum transitions with the Gauss-Bonnet term in $D$ dimensions Liu, Yang High Energy Physics - Theory In our previous paper [1,2], we proposed a probabilistic argument to explain the reason why the cosmological constant is very small in $4D$. We can ask a question: if the behavior of tunneling exponent $B$ can be generalized to $D$-dimension. Moreover, in higher dimensional theory motivated by string theory the Gauss-Bonnet term plays an important role. Therefore, in this paper, we generalize our result in [1,2] to arbitrary $D$ dimensions including the Gauss-Bonnet term. As a result, we have two main results. We find that the Euclidean action of the bounce, $B$, describing the decay of a de Sitter vacuum, is proportional to $k^{-(D-2)}_{+}$, which has a pole as $k^2_{+} \rightarrow 0$ where $k^2_{+}$ is the curvature of the parent vacuum. This result is similar to the result in $4D$. The other result is that we find a new decay channel, describing up-tunneling from anti-de Sitter into de Sitter. The meaning of this new decay channel in the string landscape should be explored in the future. |
| title | Vacuum transitions with the Gauss-Bonnet term in $D$ dimensions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.19451 |