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A decade or so ago, when I was still a science undergrad, one of the open questions in astrophysics was to explain the uneven distribution of galaxies in the observable universe. That is, why did the universe look lumpy instead of evenly distributed.

Is this still an open question, and if so who is working on it?

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The "lumpy" distribution of galaxies in the universe is now well understood. In the current cosmological paradigm, the very early Universe was seeded with fluctuations in the distribution of matter and energy. Some regions of the universe happened to be slightly more dense than average, and some happened to be slightly under-dense.

Over time, these perturbations evolve. Gravity, for instance, will cause the initially over-dense regions to become more over-dense. When galaxy formation occurs, it usually happens in the dense regions where there is more material with which to form galaxies. Therefore, galaxies will tend to trace (to some degree) the underly fluctuations in the matter density.

In short, the lumpy distribution of galaxies results from (a) the initial density fluctuations set down in the early universe, and (b) the evolution of these fluctuations according to well known laws of physics. Cosmologists frequently model the lumpy distribution of galaxies using, for instance, numerical simulations or theoretical models; we find that these models agree extremely well with the observed distribution of galaxies in our Universe. In fact, measurement of the galaxy distribution is used as a powerful tool to test and constrain our cosmological models.

Of course, the above answer doesn't explain the process responsible for laying down the initial density perturbations. One theory that attempts to address this question is called Inflation.

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The issue is twofold: (a) whether the formation of cosmological structure is an open question and (b) if that is the case who is working on it? Structure formation always was and still is an important issue for cosmology since we need to understand that structure in order to say that we understand our Universe. As with all aspects of science, the nature of the study of structure formation has changed considerably over the past decades: today's problems are quite different from yesterday's. For one thing, we now realise that the baryonic component of the Universe is but a few percent of the total mass density. Over 97% of our Universe is made up of dark matter and dark energy. The game has changed.

(a) The issue of cosmological structure formation goes back to the work of Gamow in the 1940's, but we now have very strong, I would say almost incontrovertible, evidence that the formation of the structure on large scales was driven by gravity. We understand the formation of what is referred to as the "Cosmic web", the large scale filamentary structures surrounding great voids that dominate the observed structure. This is the environment for the formation of the galaxies that we see. We have models for the process of galaxy formation. These are based around numerical gravitatinal N-Body models dressed up with semi-analytic descriptions of the star formation process. The results can look rather good: http://www.illustris-project.org/ and we can choose parameters that bring such models into some kind of accord with what is observed.

The models tell us, for example, how we might study the dark matter component through observations of satellite galaxies of larger galaxies. Since we can observe the galaxy formation process out to redshifts of 2 or more (the most distant galaxy observed has a redshift in excess of 8) we can check the evolution seen in the models. If you are a cynic you might say we can "re-tune" the models.

(b) We are now measuring the 6-7 parameters that describe our universe by observing various aspects of that large scale structure. We can for example look at the clustering on scale > 100Mpc and detect an excess of clustering at what is called the Baryonic Acoustic Oscillation (BAO) scale, a feature that emerges from the primordial Universe. We can also look at the voids in the cosmic web to do the same thing in an entirely different way. All that can be calibrated by N-Body models and compared with the answers obtained from the cosmic microwave background. So we find groups with nice names like WiggleZ looking at the BAOs: http://wigglez.swin.edu.au/site/ who use redshift surveys containing millions of galaxies. It's quite amazing, even to one who works in this field.

What's the importance of all this? We find that the Universe can be described by just 6 parameters. We can measure these parameters with any of these methods with an accuracy of a few percent or better. What is convincing us that we have a good model is that these quite independent ways of measuring the 6 parameters all come up with the same answer to within the experimental accuracy. This is "Precision Cosmology". We can feel confident that the Universe is made up of ~70% of dark energy because we detect its influence in different ways and all those ways provide the same values. What is it? That's the 21st century question.

In short - the important questions are still open and hundreds, if not thousands, of astronomers are working on it.

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