For 100 years we believed in CC.
We need to conduct experiments to confirm the speed of light remains constant at Cosmic and Universe scales.
As per my understanding, it will not. One good test of this is that forever we will keep hearing the Voyager 1 and Voyager 2 beeps, no matter what the delays are.
Anything in the Universe has a DOB and DOD. Light needs to follow that rule.
So CMB is not the first known radiation but the last relic of radiation which has lost all momentum and energy.
Gravity is not a constant, as I have already shown in my paper on evidence of gravity in the He-2-4 model that accurately calculated its mass in two parity ways.
If we were constantly accelerating and expanding, all galaxies will fly away and red-shifted. But some galaxies are coming towards us. Like retrograde motions of planets, the galaxies also have the same. In Elliptical paths, sometimes there is an expansion and sometimes there is a contraction.