In this paper, we consider conservation equation in cosmology and propose four possible forms of space-times for universe resulting from dual symmetry between scale factor and energy density in the universe with constant equation of state. We start to describe these four possible types of space-times for universe and it’s possible consequences. Due to the uniformity of the metric signature in Euclidean space-time, for the first time, we introduce a new symmetry for Euclidean space-time and consider it as a transition unstable state between the visible 4D universe and the invisible world with an extra dimension. Finally, we schematically represent these four possible space-times in a unique scenario for the universe.

在本文中，我们考虑了宇宙学中的守恒方程，并提出了宇宙的四种可能的时空形式，这是由宇宙中尺度因子和能量密度之间的双重对称性产生的，具有常数状态方程。我们开始描述这四种可能的宇宙时空类型及其可能的后果。由于欧几里得时空度量特征的一致性，我们首次为欧几里得时空引入了一种新的对称性，并将其视为可见 4D 宇宙和具有额外维度的不可见世界之间的过渡不稳定状态. 最后，我们在宇宙的一个独特场景中示意性地表示了这四种可能的时空。