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Many people discussing the rotation curves of the stars in galaxies explain that the rotation curves are influenced by a cosmological acceleration of about $1.2 \cdot 10^{-10}\,\rm m/s^2$, and that this value is due to the cosmological constant (Smolin, Milgrom, McGough).

The cosmological constant corresponds to a vacuum temperature of about $10^{-31}\,\rm K$. In other words, one relates the acceleration of stars on the outer edge of galaxies to this tiny temperature.

On the other hand, the cosmic background radiation has a temperature of $2.7\,\rm K$, and is much more powerful and intense that the vacuum temperature, but has no effect on the stars. How does this fit together?

Edit: I am very skeptical of MOND (modified Newtonian gravity), as the question shows. But there is no doubt that the experimental baryonic Tully-Fisher relation holds. This measurement result, and many others, are most easily explained with a cosmological acceleration of 0.12 nm/s^2, mentioned above. It corresponds to a vacuum temperature of 10^-31 K. Or to the cosmological constant.

The baryonic Tully-Fisher relation has no other explanation.

More drastically: how do fans of MOND explain the flat rotation curves of outer stars in galaxies as an effect of the cosmological constant, or of vacuum temperature? How can such tiny effects change the orbits of stars?

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The acceleration needed in Milgrom's theory (MOND) 'Modified Newtonian Dynamics' is similar to $$cH$$ where $H$ is the Hubble constant in SI units, about $2\times 10^{-18} s^{-1}$.

So some people have wondered if there's a connection. There may not be a connection to temperature, it's not thought that a vacuum temperature or the cosmic background radiation causes the acceleration. The cause of the extra constant acceleration isn't specified in Milgrom's theory, but MOND matches the data for velocities in the rotation curves well.

Because of the good match to data and the value of $cH$, people have wondered if there's a connection to the Hubble constant and the expansion of the universe. However there is, as yet, no definite theory for the cause of the acceleration. Here Stacy McGaugh says

I am not convinced MOND itself is completely correct. But it obviously contains an important element of truth that has to be part of the final story.

John Hunter
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