Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Covariant Space-Time Line Elements in the Friedmann-Lemaitre-Robertson-Walker Geometry

Version 1 : Received: 28 October 2021 / Approved: 29 October 2021 / Online: 29 October 2021 (10:33:36 CEST)
Version 2 : Received: 6 December 2021 / Approved: 7 December 2021 / Online: 7 December 2021 (11:37:55 CET)

A peer-reviewed article of this Preprint also exists.

Journal reference: Axioms 2022, 11, 310
DOI: 10.3390/axioms11070310


Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.


Lorentz invariance violation; FRW metric; general relativity; quantum mechanics; uncertainty principle; quantum gravity


PHYSICAL SCIENCES, Astronomy & Astrophysics

Comments (1)

Comment 1
Received: 7 December 2021
Commenter: David Escors
Commenter's Conflict of Interests: Author
Comment: Equation 8 was replaced by its correct form, and the text was changed subsequently.
+ Respond to this comment

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 1
Metrics 0

Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.