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Most quantum gravity theories quantize space time on the order of Plancklength (lp). Some of these theories, such as loop quantum gravity (LQG),predict that this discreetness could be manifested through Lorentz invarianceviolations (LIV) over travelling particles at astronomical length distances.However, reports on LIV are controversial, and space discreetness could stillbe compatible with Lorentz invariance. Here, it is tested whether spacequantization on the order of Planck length could still be compatible withLorentz invariance through the application of a covariant geometric uncertaintyprinciple (GeUP) as a constraint over geodesics in FRW geometries. Space timeline elements compatible with the uncertainty principle are calculated for ahomogeneous, isotropic expanding Universe represented by the Friedmann LemaitreRobertson Walker solution to General Relativity (FLRW or FRW metric). A genericexpression for the quadratic proper space time line element is derived,proportional to Planck length squared, and dependent on two contributions. Thefirst is associated to the energy time uncertainty, and the second depends onthe Hubble function. The results are in agreement with space-time quantizationon the expected length orders, according to quantum gravity theories, andwithin experimental constraints on putative LIV.

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