I know the the theory of the pulsating universe. But I am (we all are ) talking about light moving away from a massive body such as a heavy star or blackhole. This effect is called a gravitational redshift, also known as the Einstein effect.
Light coming from a region of weaker gravity shows a gravitional blueshift. I didnt say anything about light losing its speed
I did read one article concerning measurements with atomic clocks (pound-rebka experiment) but didnt read much further into it . So I cant give any comments on the last part