In this paper, we estimate the cross-correlation power spectra between the Planck 2018 cosmic microwave background (CMB) temperature anisotropy map and the unresolved $\gamma$-ray background (UGRB) from the 9-years Fermi-Large Area Telescope (LAT) data. In this analysis, we use up to nine energy bins over a wide energy range of [0.631, 1000] GeV from the Fermi-LAT UGRB data. Firstly, we find that the Fermi data with the energy ranges [1.202, 2.290] GeV and [17.38, 36.31] GeV show the positive evidence for the Integrated Sachs-Wolfe (ISW) effect at $1.8\sigma$ confidence level, and the significance would be increased to $2.7\sigma$ when using these two energy bins together. Secondly, we apply the single power-law model to normalize the amplitude and use all the nine Fermi energy bins to measure the significance of the ISW effect, we obtained ${\mathrm{A}}_{\mathrm{amp}}=0.95\pm 0.53$ (68% C.L.). For the robustness test, we implement a null hypothesis by randomizing the Fermi mock maps of nine energy bins and obtain the non-detection of ISW effect, which confirms that the ISW signal comes from the Fermi-LAT diffuse $\gamma$-ray data and is consistent with the standard $\Lambda$CDM model prediction essentially. We use a cross-correlation coefficient to show the relation between different energy bins. Furthermore, we vary the cut ranges $\left|b\right|$ of galactic plane on the mask of Fermi map and carefully check the consequent influence on the ISW signal detection.

在本文中，我们估计了Planck 2018宇宙微波背景（CMB）温度各向异性图与未解析图之间的互相关功率谱$\gamma$9年费米-大面积望远镜（LAT）数据得出的X射线背景（UGRB）。在此分析中，根据费米-LAT UGRB数据，我们在[ 0.631，1000 ] GeV的宽能量范围内使用了多达9个能量仓。首先，我们发现能量范围为[1.202，2.290] GeV和[17.38，36.31] GeV的费米数据显示了萨克斯-沃尔夫综合（ISW）效应的积极证据。$\mathrm{1个}。8\sigma$ 置信水平，其重要性将提高到 $2。7\sigma$当同时使用这两个能量箱时。其次，我们使用单幂定律模型对幅度进行归一化，并使用所有9个费米能量箱来测量ISW效应的显着性，${\mathrm{一种}}_{\mathrm{安培}}=0。95\pm 0。53$（68％CL）。对于鲁棒性测试，我们通过随机化九个能量箱的费米模拟图来实现零假设，并获得未检测到ISW效应的结果，这证实了ISW信号来自费米-LAT扩散$\gamma$射线数据并符合标准 $\Lambda$CDM模型预测本质上。我们使用互相关系数来显示不同能量仓之间的关系。此外，我们改变切割范围$\left|b\right|$在费米地图的蒙版上检查银河平面，并仔细检查其对ISW信号检测的影响。