The various hypothetical design models for the universe, multiverse, and loop quantum gravity could have various general covariant principle results.
Scientific consensus suggests that 3 minutes after the Big Bang: protons and neutrons began to come together to form the nuclei of simple elements.
Lee Smolin's books about loop quantum gravity posit that this theory contains the evolutionary ideas of "reproduction" and "mutation" of universes, elementary particles, as well as being formally analogous to models of population biology.
Alternatively, there has been much talk about possible local and global violations of Lorentz invariance beyond those expected in straightforward general relativity.
It is expected that these questions will all remain open as long as the classical limits of various LQG models (see below for the sources of variation) cannot be calculated.
Smolin and Joao Magueijo then went on to study doubly special relativity, in which not only there is a constant velocity c but also a constant distance l. They showed that there are nonlinear representations of the Lorentz Lie algebra with these properties (the usual Lorentz group being obtained from a linear representation).
Giovanni Amelino-Camelia then proposed that the mystery of ultra-high-energy cosmic rays might be solved by assuming such violations of the special-relativity dispersion relation for photons.
Phenomenological (hence, not specific to LQG) constraints on anomalous dispersion relations can be obtained by considering a variety of astrophysical experimental data, of which high-energy cosmic rays are one part.
Published in 2024, the Large High Altitude Air Shower Observatory Collaborative examined the gamma ray output from GRB 221009A and was unable to detect any invariance based on the color (wavelength) of light, something Loop Quantum Gravity predicts should happen.