Redshift in varying speed of light cosmology

In standard cosmology, redshift is related to scale factor by z = a(-1) - 1. Varying speed of light cosmologies have also applied this relationship, in which c does not explicitly appear, with the assumption that PLANCK CONSTANT OVER TWO PI proportional to c. Measured redshift is not a comparison of an observed spectrum with the spectrum as it was emitted at a distant location, but a comparison with a reference spectrum generated more locally. This distinction suggests decomposition into two parts: (a) change during the flight of a photon and (b) difference in physics at the time of emission and at the time of observation of a photon associated with an electron transition between specific bound states of an atom. Based on atomic units consistent with data and a relativistic atomic model, redshift is given by z = beta(theta)theta a(-1) - 1, where theta = c/c(0), with c(0) the present value of c, and beta is a function of the atomic parameters describing the transition. The modified form appears to have a modest effect (a difference in scale factor <2 per cent) for redshifts that are not much greater than 10. However, the modification can have a major effect for an early universe with c significantly larger than the present. The simplified form z = theta a(-1) - 1, which results from a non-relativistic model, provides an approximation for redshift that is not transition-specific.

Automated summary

In standard cosmology, redshift is determined by the relationship between the scale factor and the speed of light. This relationship is also applied in varying speed of light cosmologies, assuming that the PLANCK CONSTANT OVER TWO PI is proportional to c. Measured redshift is compared not with the original emitted spectrum, but with a reference spectrum generated locally. Redshift can be decomposed into the change during the flight of a photon and the difference in physics at the time of emission and observation.