论文标题
De Sitter不变的宇宙学方法
De Sitter-invariant approach to cosmology
论文作者
论文摘要
普朗克量表的时空短距离结构受普朗克长度的控制，通常被解释为三维欧几里得长度。因此，它并不是洛伦兹不变的，并且与爱因斯坦的特殊相对论冲突，因此无法描述普朗克量表运动学。解决这个问题的解决方案是双重的。首先，必须将普朗克长度重新释放为洛伦兹不变的四维伪长。其次，要遵守非变化的宇宙学术语〜$λ$，必须用De Sitter-de Sitter-Invariant特殊相对论代替标准的Poincaré不变特殊相对论。由于Planck伪长没有与DE Sitvaris-Invariant的特殊相对论相冲突，因此在存在〜$λ$的情况下，它提供了对Planck量表运动学的一致描述。在上述替代品下，一般相对论变化了de Sitter不变的一般相对论，其中〜$λ$是本构成的。在本文中，得出了随后的弗里德曼方程，并探讨和讨论了对宇宙学的某些影响。
The spacetime short-distance structure at the Planck scale is governed by the Planck length, usually interpreted as a three-dimensional Euclidian length. As such, it is not Lorentz invariant and clashes with Einstein's special relativity, which is thus unable to describe the Planck scale kinematics. The solution to this problem is twofold. First, one has to re-interpret the Planck length as a Lorentz invariant four-dimensional pseudo-length. Second, to comply with a non-vanishing cosmological term~$Λ$, one has to replace the standard Poincaré-invariant special relativity with the de Sitter-invariant special relativity. Since the Planck pseudo-length does not clash with the de Sitter-invariant special relativity, it provides a consistent description of the Planck scale kinematics in the presence of~$Λ$. Under the above replacement, general relativity changes to the de Sitter-invariant general relativity, in which~$Λ$ is constitutive. In this paper, the ensuing Friedmann equations are derived, and some implications for cosmology are explored and discussed.
