Tweaking General Relativity to explain dark matter


The observation that the Standard Model of particle physics works really well in explaining most of what we see in our present experience, and yet is incapable as yet of explaining, much less predicting the experimental evidence of large scale deviations from gravitational predictions of the modern universe is hardly unremarked upon. The anomalous gravitational effects seen in galactic rotation curves and in the unexplained apparent change in gravity at great look-back distance is today explained by invoking Dark Matter and/or Dark Energy. Modern models that include dark matter and energy generally calculate that the normal matter that you and I are made of represents less than 10 percent, perhaps only 1 percent of the total gravitational matter in the Universe.

It’s pretty disconcerting that the model which does so well in explaining what we can “see” does so badly for the vast majority of everything else. Either we’ve just gotten lucky, or there’s something wrong with the model, or with the observations.

Lots of folks have played around with the Standard Model trying to make it more sophisticated. That’s primarily what String Theory is all about. But there are some who want to leave the Standard Model as is, and who would rather look again at the anomalous gravitational observations with the idea that perhaps we’d be better off messing around with gravity theory instead.

That might not be such a terrible thing. Einstein’s theory is already known to fail in certain high-energy regimes, and it has never yet been successfully made to interact with quantum theory.

What if we tried to tune the gravitational model by introducing some variable parameters which could then be tweaked to make gravitation predict what we observe without having to invent dark matter and dark energy?

Jose Cembranos is trying to do just that. An article on reports on what Cembranos is calling the R2 model of gravitation:

“The model that Cembranos developed also allows you to tune the parameters of the system in order to explain dark matter. ‘I wanted to focus on the dark matter issue,’ he says, ‘because dark matter seems a little more straightforward. All you need to do is introduce more stuff into the model. We can do this with R2 gravity.’

Cembranos points out that while R2 gravity is an interesting approach to the problem, it doesn’t hold all the answers. ‘Many people have used different modifications of gravity in order to explain dark matter and even dark energy,’ he says. ‘However, usually these explanations end up being worse than Einstein gravity. Einstein gravity clearly has problems, but nearly all the other explanations are worse.’

What makes the model studied by Cembranos more promising, he insists, is that using the R2 term isn’t worse than Einstein’s gravity theory. ‘It’s not any better, but it’s also not any worse. It’s more or less the same, but a little more complicated.’”

Read the full article here.

What I find so interesting about this attempt is that it is very similar to what Plank did back in the 19th century to find a solution to the UV disaster in the black-body radiation curve. Plank introduced a tunable parameter that he called “h” (now called the Plank constant), and worked out its magnitude by fitting the black-body radiation curve to the spectrum that would be created by a simple harmonic oscillator limited with an “h” sized granularity.

That worked well so well that we now have an entire regime of physics based on Plank’s work (as explained interestingly enough by Einstein in his work on the Photo-electric effect).

Perhaps here’s another go that will have the same sorts of payoff?

The Author

Episcopal bishop, dad, astronomer, erstwhile dancer...


  1. Stefano Caligari says

    It may be interesting, but the comparison with Planck’s work is a little exaggerated

  2. A little exaggerated? Heh. It’s a blog… what do you expect?
    But seriously – I’m really making the comparison in terms of whether or not trying to mathematically tune a model to arrive at sense of what needs to be modified from GR. This is clearly not being done from an new suggestion of first principles, it’s much more speculative. But I think so was Plank’s original work.

  3. Stefano Caligari says

    I see. From this point of view, I agree. Thank you for your blog!!

  4. I think there are people who want dark energy and dark matter to be mathematical constructs and not real things. So, we have what appears to be too much mass for the luminous amount of matter we see in galaxies. It’s as if there were unseen or “dark” matter there. Similarly with dark energy. There appears to be an anomalous increase in the rate of expansion, it behaves like energy, but “dark” energy that we can’t see in any other way.
    But, astronomers have “mapped” the dark matter in a galactic collision and it seems to be a distinct thing from the luminous matter. That tends to tell me that it’s not just a mathematical construct which can be eliminated with a few extra terms.

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