Diffeomorphism invariance of the effective gravitational action
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918046410473472 |
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| author | Branchina, Carlo Branchina, Vincenzo Contino, Filippo Gandolfo, Riccardo Pernace, Arcangelo |
| author_facet | Branchina, Carlo Branchina, Vincenzo Contino, Filippo Gandolfo, Riccardo Pernace, Arcangelo |
| contents | We investigate on the diffeomorphism invariance of the effective gravitational action, focusing in particular on the path integral measure. In the literature, two different measures are mainly considered, the Fradkin-Vilkovisky and the Fujikawa one. With the help of detailed calculations, we show that, despite claims to the contrary, the Fradkin-Vilkovisky measure is diffeomorphism invariant, while the Fujikawa measure is not. In particular, we see that, contrary to naive expectations, the presence of $g^{00}$ factors in the Fradkin-Vilkovisky measure is necessary to ensure the invariance of the effective gravitational action. We also comment on results recently appeared in the literature, and show that formal calculations can easily miss delicate points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffeomorphism invariance of the effective gravitational action Branchina, Carlo Branchina, Vincenzo Contino, Filippo Gandolfo, Riccardo Pernace, Arcangelo High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We investigate on the diffeomorphism invariance of the effective gravitational action, focusing in particular on the path integral measure. In the literature, two different measures are mainly considered, the Fradkin-Vilkovisky and the Fujikawa one. With the help of detailed calculations, we show that, despite claims to the contrary, the Fradkin-Vilkovisky measure is diffeomorphism invariant, while the Fujikawa measure is not. In particular, we see that, contrary to naive expectations, the presence of $g^{00}$ factors in the Fradkin-Vilkovisky measure is necessary to ensure the invariance of the effective gravitational action. We also comment on results recently appeared in the literature, and show that formal calculations can easily miss delicate points. |
| title | Diffeomorphism invariance of the effective gravitational action |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.05100 |