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Anisotropic Solutions for \(\boldsymbol{R^{2}}\) Gravity Model with a Scalar Field

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Abstract

We study anisotropic solutions for the pure \(R^{2}\) gravity model with a scalar field in the Bianchi I metric. The evolution equations have a singularity at zero value of the Ricci scalar \(R\) for anisotropic solutions, whereas these equations are smooth for isotropic solutions. So, there is no anisotropic solution with the Ricci scalar smoothly changing its sign during evolution. We have found anisotropic solutions using the conformal transformation of the metric and the Einstein frame. The general solution in the Einstein frame has been found explicitly. The corresponding solution in the Jordan frame has been constructed in quadratures.

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Funding

The work of V.R.I. was supported by the ‘‘BASIS’’ Foundation, grant no. 22-2-2-6-1.

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Authors and Affiliations

  1. Physics Department, Lomonosov Moscow State University, Moscow, Russia

    V. R. Ivanov

  2. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia

    S. Yu. Vernov

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  1. V. R. Ivanov
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  2. S. Yu. Vernov
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Correspondence to V. R. Ivanov or S. Yu. Vernov.

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Ivanov, V.R., Vernov, S.Y. Anisotropic Solutions for \(\boldsymbol{R^{2}}\) Gravity Model with a Scalar Field. Phys. Atom. Nuclei 86, 1526–1532 (2023). https://doi.org/10.1134/S1063778824010204

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