The cosmic microwave background radiation (CMB) is not considered as evidence for variable light speed because it can be explained by other well-established phenomena within the framework of the Big Bang theory and the standard model of cosmology. Here's why:
Origin of the CMB: The CMB is believed to be the afterglow of the Big Bang, which occurred approximately 13.8 billion years ago. As the universe expanded and cooled down, the hot plasma that filled the early universe transitioned into a transparent gas. Photons present at that time were released and have been traveling through space ever since. The CMB is the remnant radiation from this early stage.
Homogeneity and isotropy: The CMB is highly isotropic and homogeneous, meaning it appears the same in all directions and from all regions of the sky. This uniformity is difficult to explain if light speed were variable, as it would introduce anisotropies and variations in the CMB that are not observed.
Time of emission: The CMB radiation we detect today was emitted when the universe was only about 380,000 years old. At that time, the universe was highly ionized and not transparent to light. However, as the universe expanded and cooled, electrons and protons combined to form neutral hydrogen atoms, making the universe transparent to photons. The time of emission of the CMB is well understood and consistent with the current understanding of the universe's evolution.
Other observational evidence: The CMB is just one piece of evidence supporting the Big Bang theory and the expanding universe. There are numerous other observations, such as the redshift of distant galaxies, the abundance of light elements, and the large-scale structure of the universe, that are consistent with an expanding universe and do not require a variable speed of light.
Variable light speed is an idea that has been explored in certain alternative theories of cosmology, but it has not gained wide acceptance due to the lack of compelling evidence and the successful explanations provided by the standard cosmological model. The observed properties of the CMB, combined with other lines of evidence, support the idea that the speed of light is a constant and not subject to significant variations over cosmological scales.