Saturday, August 04, 2007

Like grains of sand (cross the wounded galaxies)

Cross the wounded galaxies we intersect,
poison of dead sun in your brain slowly fading

(William S. Burroughs, "The soft machine")

I should have been in Japan this week and in China two weeks from now. Well, I didn't make it to either. Guess what - I am tired! Too tired to take another couple of bouncing trips to the other end of Asia and back, with one swing by the US in between. So I backed off. I'll be hiding in Paris for a couple of days and then hop westward across the Atlantic.

Archimedes derived in his famous text Ψαμμίτης a crude estimate of the size of the universe in a heliocentric system, based on the fact that one does not see any parallax when observing the stars. This puts a lower bound on the size of the universe, which he presented in terms of the number of grains of sand that would be needed to fill it. This work, which Archimedes presented as a disprove of the heliocentric system, in fact contains two major advances in scientific thought: a precise notation that can be used to talk about large numbers (not unlike the use we make today of orders of magnitudes, that is, powers of ten) and the possibility, if only at the hypothetical level, of a large universe, whose size is many orders of magnitude beyond the human scale.

Talking about the size of the universe in terms of grains of sand remained ingrained (excuse me) in our collective imagination since the time of Archimedes and we now talk about "more stars in the sky than grains of sand" or "Galaxies like grains of sand" (as in the title of the famous Aldiss 1960 science fiction novel).

I take this as an excuse to introduce here briefly the slow tour I am beginning to take into the world of cosmology and astrophysics. This is certainly one of the most fascinating subjects of physics nowadays: the wealth of recent observational data have effectively pushed the boundaries of cosmology far beyond what was considered possible until the recent past. The interplay between cosmology and particle physics will play as much of a dominant role in shaping our knowledge of high energy physics in the near future as will the LHC at CERN. I am not a cosmologist by training, but having done a little work on mathematical models of particle physics, it is only natural to attempt to walk the path from there to cosmology. To me research projects have the primary purpose to give me a good excuse to learn some stuff I would be otherwise too lazy to read through in sufficient detail. So I like it when the actual research takes some time to wind up, so that it leaves me enough time to continue doing my readings on the way to it. When it moves on too fast, I feel like it's a lost opportunity. Much as it gives you a good feeling to have one more paper written, what's the point of it, really, if it didn't get me to learn enough stuff along the way. Paraphrasing the old Tao, it's the path and not the goal that matters, and the path that is a true path is never a straight path. So I am taking my good time with this cosmology thoughts. Meanwhile I got hold of a few books, which appear to be very good stuff. Since I have not done all my reading yet, I'll be rather short in reviewing them here. I'll just take a short promenade through my little cosmological collection.

A couple of good books I got hold of last year, while I was spending time in Cambridge, are both (not surprisingly) recently published by Cambridge University Press. One is Liddle and Lyth, "Cosmological inflation and large-scale structure",
published in 2000, and the other, more recent, is Mukhanov's "Physical foundations of cosmology", which came out in 2004.

Liddle and Lyth provide a very readable and highly informative overview of inflationary cosmology. The main idea is that a phase of cosmological inflation in the early universe should provide an explanation for the formation of large scale structures in the cosmos. On the experimental (that is observational) side, this type of models are closely related to the study of irregularities in the cosmic microwave background radiation. Inflationary cosmology is tied up to particle astrophysics, in the sense that different models of particle physics (with or without supersymmetry, grand unified, stringy, etc) determine different shapes for the potential of the scalar field that is responsible for inflation in the cosmological models. This book, however, does not get into the particle physics aspects. The authors take different particle physics models as black boxes that produce different potential for the scalar field and concentrate on the behavior of these fields, including vacuum fluctuations, spontaneous symmetry breaking, etc. Models with several scalar fields are also considered. The formation of structure is studied in terms of Gaussian perturbations. The evolution of the perturbations via Newtonian gravity is modeled by thinking of the universe as a fluid with certain mass density and pressure functions and considering Euler equations for this fluid. A good part of the book is dedicated to topics like the spectrum of the cosmic microwave background, matter density perturbations, cold dark matter models. The COBE satellite data on the cosmic microwave radiation figure prominently in this pre-WMAP book, but the volume also contains a good deal of information on galaxy clustering and motion, which is by itself a very interesting topic.

For a more detailed analysis of the relation between particle physics and cosmological models, Mukhanov's book has a much more systematic treatment. I am far behind in reading it at this point, but it seems to me that chapter 4 on the early universe combines a good amount of particle physics with its cosmological implication. After reviewing the Standard Model, the book singles out the most important aspects for the purpose of cosmological applications, such as quark-gluon transitions, electroweak symmetry, and violation of lepton number conservation.
I am still in the process of getting through this book, so I won't give a detailed review here.

Another book I picked up more recently is the Springer paperback "Cosmology and particle astrophysics" by Bergstrom and Goobar.

This is at a more introductory level, with not too many technical details. It covers a fair amount of material though, and I've been reading it over lunch and late afternoon aperitif during the few days when the summer looked anything like a summer when one might want to seat outside in the sun and read. Some nice things in the book: a chapter on gravitational lensing (I am quite fond of this topic since I found out that one can model it very efficiently using Morse theory, one of my favorite mathematical topics). Well, this book doesn't go into that, but it gives a nice overview of gravitational lensing and its application, for instance, to galactic dark matter searches. Another nice chapter is the one on phase transitions and their possible relevance to the early universe. This is something I am quite inclined to think about and, while not very detailed, the exposition in this book is a good starting point at least. The relation to cosmic strings and other such models is briefly touched upon. I am into reading the part on the role of neutrinos at this point, another topic I'd like to know more about. Even the chapters that recall well known stuff are nice to read: for example the particle physics chapter contains a few nice examples of calculations of cross sections, a very relevant topic for astrophysical applications as well as for particle physics itself.

A very interesting aspect of cosmology is, of course, the dark matter and dark energy debate. I tried to get hold of an up-to-date view of the subject, and I found in Paris the newly published Springer volume "The invisible universe: dark matter and dark energy" edited by Papantonopoulos. I haven't had a chance yet to read through much of it, but one thing that seems interesting is the discussion of the possible particle candidates for the basic constituents of dark matter. In particular, some of the contributions to the book give arguments against the hypothesis of massive neutrinos as the main constituent of dark matter, in favor of more exotic particles.