Structure Formation Mythology

Do not be too proud of this technological terror you’ve constructed. The ability to simulate the formation of large scale structure is insignificant next to the power of the Force.

– Darth Vader, Lord of the Sith

The now standard cosmology, ΛCDM, has a well developed cosmogony that provides a satisfactory explanation of the formation of large scale structure in the universe. It provides a good fit to both the galaxy power spectrum at low redshift and that of the cosmic microwave background (CMB) at z=1080. This has led to a common misconception among cosmologists that this is only way it can be.

The problem is this: the early universe was essentially homogeneous, while the current universe is not. At the time of recombination, one patch of plasma had the same temperature and density as the next patch to 1 part in 100,000. Look around at the universe now, and you see something very different: galaxies strung along a vast web characterized chiefly by empty space and enormous voids. Trouble is, you can’t get here from there.

Gravity will form structure, making the over-dense patches grow ever denser, in a classic case of the rich getting richer. But gravity is extraordinarily weak. There simply is not enough time in the ~13 Gyr age of the universe for it to make the tiny density variation observed in the CMB into the rich amount of structure observed today.

We need something to goose the process. This is where non-baryonic cold dark matter (CDM) comes in. It outweighs the normal matter, and does not interact with the photons of the CMB. This latter part is critical, as the baryons are strongly coupled to the photons, which don’t let them clump up enough early on. The CDM can. So it starts to form structure early which the baryons subsequently trace. Since structure formed, CDM must exist.

This is a sound line of reasoning. It convinced many of us, including myself, that there had to be some form of non-baryonic mass made of some particle outside the standard model of particle physics. The other key fact was that the gravitating mass density was inferred to outweigh the amount of baryons indicated by Big Bang Nucleosynthesis (Ωm ≫ Ωb).

Does anyone spot the problem with this line of thinking?

It took me a long time to realize what it was. Both the structure formation argument and the apparent fact that Ωm ≫ Ωb implicitly assume that gravity is normal. All we need to know to approach either problem is what Newton and Einstein taught us. Once we make that assumption, we are absolutely locked into the line of reasoning that leads us to CDM.

I worry that CDM is a modern æther. Given our present understanding of physics, it has to exist. In the nineteenth century, so too did æther. Had to. Only problem was, it didn’t.

If, for a moment, we let go of our implicit assumption, then we may realize that what structure formation needs is an extra push (or pull, to make overdensities collapse faster). That extra push may come from CDM, or it may come from an increase in the strength of the effective force law. Rather than being absolute proof of the existence of CDM, the rapid formation of structure might also be another indication that we need to tweak for force law.

I have previously outlined how structure might form in a modified force law like MOND. Early efforts do not provide as good a fit to the power spectrum as ΛCDM. But they provide a much better approximation than did the predecessor of ΛCDM, SCDM.

Indeed, there have been some striking predictive successes. As we probe to ever higher redshift, we see time and again more structure than had been anticipated by ΛCDM. Galaxies form early in MOND, so this is quite natural. So too does the cosmic web, which I predict to be more developed in MOND at redshifts of 3 and even 5. By low redshift, MOND does a much better job of emptying out the voids than does ΛCDM. Ultimately, I expect we may get a test from 21 cm reverberation mapping in the dark ages, where I predict we may find evidence of strong baryonic oscillations. (These predictions were made, and published in refereed journals, in the previous millennium.)

I would not claim that MOND provides a satisfactory description of large scale structure. The subject requires a lot more work.  Structure formation in MOND is highly non-linear. It is a tougher problem than standard perturbation theory. Yet we have lavished tens of thousands of person-years of effort on ΛCDM, and virtually no effort on the harder problem in the case of MOND. Having failed to make an effort does not suffice as evidence.

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