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Nonlinear multidimensional gravity and the Australian dipole

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Abstract

The existing observational data on possible variations of fundamental physical constants (FPC) confirm more or less confidently only a variability of the fine structure constant \(\alpha \) in space and time. A model construction method is described, where variations of \(\alpha \) and other FPCs (including the gravitational constant \(G\)) follow from the dynamics of extra space-time dimensions in the framework of curvature-nonlinear multidimensional theories of gravity. An advantage of this method is a unified approach to variations of different FPCs. A particular model explaining the observable variations of \(\alpha \) in space and time has been constructed. It comprises a FRW cosmology with accelerated expansion, perturbed due to slightly inhomogeneous initial data.

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Notes

  1. Our sign conventions are: the metric signature \((+{}-{}-{}-)\); the curvature tensor \(R^{\sigma }{}_{\mu \rho \nu } = \partial _\nu \Gamma ^{\sigma }_{\mu \rho }-\ldots ,\ R_{\mu \nu }= R^{\sigma }{}_{\mu \sigma \nu }\), so that the Ricci scalar \(R > 0\) for de Sitter space-time and the matter-dominated cosmological epoch. We use the natural units with the speed of light \(c\) and Planck’s constant \(\hbar \) equal to unity.

  2. We assume for certainty \(\phi > 0\), or, which is the same according to (12), \(K = +1\), but everything can be easily reformulated for \(\phi < 0\). A possible term linear in \(R\) in \(F(R)\) is dropped because its inclusion would make the calculations more bulky without adding any physically significant features.

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Acknowledgments

The authors wish to thank A. Panov for his interest in our work. The work of S. R. and I. S. was supported in part by the Ministry of Education and Science of the Russian Federation, project 14.A18.21.0789.

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Authors and Affiliations

  1. Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya St., 119361 , Moscow, Russia

    K. A. Bronnikov & V. N. Melnikov

  2. Institute of Gravitation and Cosmology, PFUR, 6 Miklukho-Maklaya St., 117198 , Moscow, Russia

    K. A. Bronnikov & V. N. Melnikov

  3. National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, 115409 , Moscow, Russia

    S. G. Rubin & I. V. Svadkovsky

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  1. K. A. Bronnikov
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  2. V. N. Melnikov
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  4. I. V. Svadkovsky
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Correspondence to S. G. Rubin.

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Bronnikov, K.A., Melnikov, V.N., Rubin, S.G. et al. Nonlinear multidimensional gravity and the Australian dipole. Gen Relativ Gravit 45, 2509–2528 (2013). https://doi.org/10.1007/s10714-013-1601-2

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