In this paper, we find exact string cosmological solutions for FRW cosmology, by using the Hojman symmetry approach. The string cosmology under consideration includes a scalar field [Formula: see text] with the potential [Formula: see text], and a totally antisymmetric field strength [Formula: see text] which is specifically defined in terms of the scale factor [Formula: see text]. We show that for this string cosmology, Hojman conserved quantities exist using which new exact solutions for the scale factor and the scalar field are obtained for specific potentials [Formula: see text] with some free parameters. The presence of these parameters, together with those of arising from Hojman symmetry, is an important advantage using which one can construct the solutions [Formula: see text] and [Formula: see text] with variety of cosmological behaviors.

中文翻译：

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通过 Hojman 对称性的 FRW 弦宇宙学解

在本文中，我们通过使用 Hojman 对称方法找到了 FRW 宇宙学的精确弦宇宙学解。正在考虑的弦宇宙学包括一个标量场 [Formula: see text] 与势 [Formula: see text]，以及一个完全反对称的场强 [Formula: see text]，它是根据比例因子 [Formula:见正文]。我们表明，对于这种弦宇宙学，存在 Hojman 守恒量，使用这些量可以针对具有一些自由参数的特定势 [公式：参见文本] 获得比例因子和标量场的新精确解。这些参数的存在，连同由霍伊曼对称性产生的参数，是一个重要的优势，利用它可以构建具有各种宇宙学行为的解 [公式：见文本] 和 [公式：见文本]。