Recently, reinvestigating Rastall idea \({{\mathcal{T}}}_{ \mu ;\nu }^\nu = a_{,\mu }\) through relativistic thermodynamics proposed new non-conservation theory of gravity in which scalar parameter \(a_{,\mu }\) depends on 4-vector entropy \(S_\mu\), comoving temperature \(T_0\) and density of charge of whole the system (Fazlollahi in Eur Phys J C 83:923, 2023). Considering this model deeply shows unlike other modified theories of gravity it cannot explain current phase of the Universe in absence of the cosmological constant and or other dark energy models. Hence, in this paper, by implementing the Granda–Oliveros infrared cut-off the late time evolution of the Universe is studied. As shown, for non-interaction scenario model yields same results given by Granda–Oliveros holographic dark energy in standard Einstein field equations. As result, the non-conservation term gives no tangible effects in this scenario. However, in interaction scenario one finds tangible effects of non-conservation term in evolution of dark energy which supports observations with some small errors in structure formation during matter dominated-era.

最近，通过相对论热力学重新研究拉斯托尔思想\({{\mathcal{T}}}_{ \mu ;\nu }^\nu = a_{,\mu }\)提出了新的非守恒引力理论，其中标量参数\(a_{,\mu }\)取决于 4-向量熵\(S_\mu\)、同动温度\(T_0\)和整个系统的电荷密度（Eur Phys JC 83:923 中的 Fazlollahi， 2023）。深入考虑这个模型表明，与其他修正的引力理论不同，在没有宇宙学常数和/或其他暗能量模型的情况下，它无法解释宇宙的当前阶段。因此，在本文中，通过实施格兰达-奥利维罗斯红外截止来研究宇宙的晚期演化。如图所示，对于非相互作用场景模型，产生与标准爱因斯坦场方程中 Granda-Oliveros 全息暗能量相同的结果。因此，非守恒项在这种情况下没有产生任何实际效果。然而，在相互作用场景中，人们发现非守恒项对暗能量演化的明显影响，这支持了物质主导时代结构形成中存在一些小错误的观测结果。