The speed of light through space is constant at about 300,000 meters per second. However, space itself is expanding at a faster rate, thus carrying the light waves along with it. The physics fits the Standard Model and is well established.
The question is whether the expansion is constant, decelerating, or accelerating. This will determine the ultimate fate of the universe. Constant = heat death (all stars cool off and die, the universe goes dark). Decelerating = the Big Crunch (everything eventually re-compresses and you get another Big Bang). Accelerating = the Big Rip (everything flies apart faster and faster, with the acceleration itself speeding up so fast you can actually look up and see the stars fly apart a few days before the Earth does and then your atoms in your body a few seconds later).
Evidence is currently leaning towards the Big Rip, which makes me happy because the it fits the Bible nicely. The Big Rip is a spectacular and beautiful way for God to end His story.
If you are familiar with Douglas Adams’ book ‘The Restaurant at the End of the Universe’, it shows the Big Rip happening.