We study the f(R,T) cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case f(R,T) = f1(R) + f2(T) and the case f(R,T) = f1(R) + f2(R)f3(T). In each case, we state general theorems which determine completely the form of the unknown functions fi such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric. In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

中文翻译：

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f(R,T) 引力理论中的自相似宇宙学解

我们研究F(R,吨)自相似假设下的宇宙学模型。我们确定每个物理和几何量可能采用的确切形式，以便场方程 (FE) 通过物质准线方法允许精确的自相似 (SS) 解。我们研究两个模型：案例F(R,吨) = F1(R) + F2(吨)和案例F(R,吨) = F1(R) + F2(R)F3(吨). 在每种情况下，我们都陈述了完全确定未知函数形式的一般定理F一世这样 FE 承认 SS 解决方案。我们还将一些推论陈述为限制性案例。这些结果对于任何同质 SS 度量都是非常普遍和有效的.通过这种方式，我们能够生成新的宇宙学情景。例如，我们通过找到这些特定模型的精确解来研究两个案例。