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Why what?
The Friedmann equation already assumes that space-time is variable. It is useful in that context. We were questioning the assumption. How do we know that space-time is really variable. Observations that seem to show that it is can be explained by assuming it is the material things that vary.
Why would a photon in the field you describe experience redshift?
It seems I remember that the amplitude of the CMBR radiation was first predicted to be on the order of 50 K and only became 3.5 K after it was measured. I also remember that Sir Arthur Eddington and a group of his collaborators predicted that the temperature of space should be about 4 K due to the warming of space debris by starlight.From UCLA