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arXiv 2203.04824gr-qchep-th
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德西特不变宇宙学方法

De Sitter-invariant approach to cosmology

A. V. Araujo, D. F. López, J. G. Pereira, J. R. Salazar

AI总结:

本文提出德西特不变狭义相对论以解决普朗克长度与洛伦兹不变性的冲突,并推导出德西特不变广义相对论下的弗里德曼方程,探讨其对宇宙学的影响。

摘要:

普朗克尺度下的时空短距离结构由普朗克长度决定,该长度通常被解释为三维欧几里得长度。因此,它不满足洛伦兹不变性,与爱因斯坦狭义相对论相冲突,后者因而无法描述普朗克尺度的运动学。解决此问题的方法有两方面。首先,必须将普朗克长度重新解释为洛伦兹不变的四维伪长度。其次,为了与不为零的宇宙学常数Λ相符,必须将标准的庞加莱不变狭义相对论替换为德西特不变狭义相对论。由于普朗克伪长度与德西特不变狭义相对论不冲突,它在存在Λ的情况下提供了对普朗克尺度运动学的一致描述。在上述替换下,广义相对论转变为德西特不变的广义相对论,其中Λ是构成性的。本文推导了由此产生的弗里德曼方程,并探讨和讨论了对宇宙学的一些影响。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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