In the presence of a real singlet scalar field with ${\mathbb{Z}}_2$ symmetry in addition to the Higgs field in the Standard Model, we analytically investigate all possible one-step and two-step electroweak phase transitions (EWPT) in the high-temperature expansion limit. In particular, we examine the possibility of a first-order phase transition in an intermediate temperature interval of the universe for two-step scenarios. In all scenarios, we provide with necessary conditions on the parameters of the model to address a first- or second-order phase transition if ever possible in the high-temperature approximation. We show that among all possible EWPT channels in this model, only the two-step phase transition $(0,0)\to (0,w)\to (v,0)$ can be of first-order type, either in the first or second step. The conditions obtained for EWPT is confronted with the dark matter (DM) and collider constraints. It is shown that the second-order one-step $(0,0)\to (v,0)$ scenario can evade the DM constraints, but it is not accessible to future colliders. The two-step first-order EWPT scenario $(0,0)\to (0,w)\to (v,0)$, except for small DM masses, is excluded by direct detection experiments XENON1T/LUX, but it is accessible in future colliders ILC/TLEP.

在存在真实单线态标量场的情况下 ${\mathbb{Z}}_2$除了标准模型中的希格斯场之外，我们还分析了在高温膨胀极限下所有可能的一步和两步电弱相变 (EWPT) 的对称性。特别是，我们研究了两步情景下宇宙中间温度区间内一阶相变的可能性。在所有情况下，我们都为模型参数提供了必要条件，以尽可能在高温近似中解决一阶或二阶相变。我们表明，在该模型中所有可能的 EWPT 通道中，只有两步相变$(0,0)\to (0,瓦)\to (v,0)$可以是一阶类型，在第一步或第二步。EWPT 获得的条件面临着暗物质 (DM) 和对撞机约束。可见二阶一步$(0,0)\to (v,0)$场景可以逃避 DM 约束，但未来的对撞机无法访问它。两步一阶 EWPT 场景$(0,0)\to (0,瓦)\to (v,0)$，除了小的 DM 质量，被直接检测实验 XENON1T/LUX 排除，但它可以在未来的对撞机 ILC/TLEP 中访问。