There was a new paper last week on the arXiv by Sunny Vagnozzi about the Hubble constant controversy (see this blog *passim*). I was going to refrain from commenting but I see that one of the bloggers I follow has posted about it so I guess a brief item would not be out of order.

Here is the abstract of the Vagnozzi paper:

I posted this picture last week which is relevant to the discussion:

The point is that if you allow the equation of state parameter w to vary from the value of w=-1 that it has in the standard cosmology then you get a better fit. However, it is one of the features of Bayesian inference that if you introduce a new free parameter then you have to assign a prior probability over the space of values that parameter could hold. That prior penalty is carried through to the posterior probability. Unless the new model fits observational data significantly better than the old one, this prior penalty will lead to the new model being disfavoured. This is the Bayesian statement of Ockham’s Razor.

The Vagnozzi paper represents a statement of this in the context of the Hubble tension. If a new floating parameter w is introduced the data prefer a value less than -1 (as demonstrated in the figure) but on posterior probability grounds the resulting model is less probable than the standard cosmology for the reason stated above. Vagnozzi then argues that if a new *fixed* value of, say, *w = -1.3* is introduced then the resulting model is not penalized by having to spread the prior probability out over a range of values but puts all its prior eggs in one basket labelled *w = -1.3*.

This is of course true. The problem is that the value of *w = -1.3* does not derive from any *ab initio* principle of physics but by *a posteriori *of the inference described above. It’s no surprise that you can get a better answer if you know what outcome you want. I find that I am very good at forecasting the football results if I make my predictions after watching *Final Score*…

Indeed, many cosmologists think any value of *w < -1* should be ruled out *ab initio* because they don’t make physical sense anyway.

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