Varying speed of light in the conformal cosmology

In modelling the cosmic expansion, the conformal cosmology (CC) has several advantages over the standard cosmological model based on the FLRW metric: it is Lorentz invariant, it leaves the Maxwell’s equations unchanged from their form in the Minkowski spacetime, it properly predicts the cosmological redshift and cosmic time dilation, and it fits the Type Ia supernova luminosity data without introducing dark energy into cosmological equations. However, the CC metric seems controversial because it predicts a varying speed of light with cosmic time. Here, we show that this controversy is apparent, because the measured physical speed of light is always coordinate-dependent being not referred to an inertial free-falling system but to a non-inertial system experiencing the gravity field. Hence, the CC universe is fully consistent with the general relativity theory and physically well justified. Since the universe is dynamic and evolves in time, the space curvature is time dependent and the speed of light should vary. Importantly, the photons redshifted due to the expansion conserve their energy in the CC universe. The frequency of photons decreases due to the redshift, but their speed increases with the scale factor a ( t ). Hence, both effects are compensated and the photon energy is conserved.