But the mapping the cosmic microwave background, and combining it to a ΛCDM model says that the expansion rate is only 67 km/s / Mpc.
This called the Hubble tension. In our previous blog post we suggested a simple solution to the Hubble tension: slow down the expansion rate of the universe by a factor about 1/2X, when the universe is 150 million ... 500 million years old.
We do not know why the expansion of the universe started to speed up some 5 billion years ago. We cannot take for granted that the universe has obeyed the ΛCDM formula during the previous 8.7 billion years, either.
Let us investigate how people derive the figure 67 km/s / Mpc.
What we know of the cosmic microwave background
Literature seems to be certain that the "last scattering" temperature of the CMB was 3,000 K, at a precision +-0.5%. Since the temperature today is 2.73 K, we know that the redshift since the last scattering is
z = 3,000 K / 2.73 K
= 1,100.
*** WORK IN PROGRESS ***
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