We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-æther theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann–Lemaître–Robertson–Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.

A preprint version of the article is available at ArXiv.

中文翻译：

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爱因斯坦-厄特-魏尔理论中的可积性和宇宙学解

我们考虑由Weyl可积几何中定义的改进的Einstein-æther理论给出的Lorentz违反标量场宇宙学模型。对于空间平坦的Friedmann-Lemaître-Robertson-Walker背景空间的情况，研究了精确解和解析解的存在。我们证明了该理论承认特殊利益的宇宙学解。此外，我们证明了宇宙场方程将刘易斯不变性作为第二守恒定律，这表明了场方程的可积性。

该文章的预印本可在ArXiv上获得。