"Changing Constants, Dark Energy and the Absorption of 21 cm Radiation" -- By Ben Wandelt
Ben Wandelt [Photo credit: Department of Physics, University of Illinois/Thompson-McClellan Photography]
Rishi Khatri and Ben Wandelt have recently proposed a new technique for testing the constancy of the fine structure constant across cosmic time scales using what may prove to be the ultimate astronomical resource for fundamental physics. In this invited article, Ben Wandelt explains the motivation for this work and the physical origin of this treasure trove of information.
Author: Ben Wandelt
Affiliation: Center for Theoretical Astrophysics, University of Illinois at Urbana-Champaign
What makes Constants of Nature so special? From a theorist's perspective constants are necessary evils that ought to be overcome. The Standard Model has 19 “fundamental constants,” and that is ignoring the non-zero neutrino masses which bring the total count to a whopping 25. That's 25 numbers that need to be measured as input for the theory. A major motivating factor in the search of a fundamental theory beyond the Standard Model is to explain the values of these constants in terms of some underlying but as yet unseen structure.
What's more, not even the constancy of Constants of Nature (CoNs) is guaranteed (Uzan 2003). Maybe the quantities we think of as constants are actually dynamic but vary slowly enough that we haven't noticed. Or even if constant in time, these numbers may be varying across cosmic distances.
Quite contrary to taking the constancy of the CoNs for granted, one can argue that it is actually surprising. String theorists tell us these constants are related to the properties of the space spanned by the additional, small dimensions beyond our observed four (3 space + 1 time). These properties could well be dynamical (after all, we have known since Hubble that the 3 large dimensions are growing) so why aren't the 'constants' changing? This perspective places the onus on us to justify why the small sizes are at least approximately constant. So the modern, 21st century viewpoint is that it would be much more natural if the CoNs were not constant but varying—either spatially or with time.
By way of example consider the cosmic density of dark energy. The 20th century view was in terms of “vacuum energy,” a property of empty space that is predicted by the Standard Model of particle physics. This is qualitatively compelling, but quantitatively catastrophically wrong. More recently three main categories of attempts emerged to explain that particular constant (and ignore the vacuum energy problem). The first category explains dark energy as some new and exotic form of matter. The second category of explanations sees the acceleration of the Universe as evidence that our understanding of Gravity is incomplete.
The third argues that the dark energy density is just another CoN, the “cosmological constant,” which appears as an additive term in Einstein's equations of general relativity and therefore increases the rate of the expansion of the Universe. This possibility was originally suggested by Einstein himself. While this is quite an economical way of modeling all currently observed effects of the universal acceleration it is also hugely unsatisfactory as an actual explanation—somewhat analogous to a boss explaining the size of your salary as “Because that's the number and that's it.” The attempt to turn this into an actual explanation through the pseudo-anthropic reasoning associated with string-theoretic landscape arguments corresponds to your boss adding “Because if you wanted to earn any more than that you wouldn't be here to ask me this question.”
If we consider the cosmic density of dark energy as another CoN that appears in Einstein's equation, it should also somehow arise from the underlying fundamental theory, like the other constants. By the identical argument we went through before we should in fact be surprised by its constancy. Hence most of the theoretical activity takes place within categories one and two, endowing this supposedly constant CoN with dynamical properties that can in principle be tested by observation.
Of course none of these aesthetic or theoretical arguments for what constitutes a satisfying explanation holds any water if it cannot be tested. And in fact, there are two sorts of tests: laboratory tests and astronomical observations. For definiteness, let's focus the discussion on a particular CoN, the most accurately measured CoN, the fine structure constant α. This number tells us the strength of the force that will act on an electric charge when it is placed in an electromagnetic field. If you have heard about the charge of the electron you have already encountered this constant in a slightly different form. Since charge has units (Coulomb), one could always redefine the units to change the value. So the relevant number is a dimensionless combination of the charge of the electron with other CoNs. This gives α ≈ 1/137.
Over the years, the value of α has been measured in laboratory experiments to about 10 digits of accuracy. Using the extreme precision of atomic fountains, the value of α was measured over 5 years and found to have changed by less than 1 part in 1015 per year [Marion et al. 2003].
Laboratory experiments do have their distinct advantages: the setup is under complete control and repeatable. However, they suffer from the very short lever arm of human time scales. Astronomical observations provide a much longer lever arm in time. The best current observations use quasar absorption lines and limit the variation to a similar accuracy when put in terms of yearly variation—but these measurements constrain variation over the last 12 billion years, the time it took the Universe to expand by a factor of 2.
In fact, using such quasar data, one group has claimed a detection of a change in α of 0.001% over the last 12 billion years [Webb et al. 2001]—though this claim is certainly controversial [Chand et al. 2006], but things may become interesting at that level.
My graduate student Rishi Khatri and I have discovered a new astronomical probe of the fine structure constant that is likely the ultimate astronomical resource of information for probing its time variation. Compared to the quasar data our technique probes α at an even earlier epoch, only a few million years after the Big Bang, when the Universe went from 200 times smaller to 30 times smaller than it is today. And in principle, if some technological hurdles can be overcome, there is enough information to measure α to nine digits of accuracy 13.7 billion years in the past! This would be 10,000 more sensitive than the best laboratory measurements.
What is this treasure trove of information? It arrives at the Earth in the form of long wavelength radio waves between 6 meters and 42 meters long. Theses radio waves started out their lives between 0.5 cm and 3 cm long, as part of the cosmic microwave background that was emitted when the hot plasma of the early Universe transformed into neutral hydrogen gas. As the Universe expands, these waves stretch proportionally. After about 7 million years, the ones with the longest initial wavelength first stretch to a magic wavelength: 21 cm. At this wavelength these waves resonate with hydrogen atoms: they have just the right energy to be absorbed by its electron. Waves that are absorbed are removed from the cosmic microwave background and can be seen as an absorption line (similar to the well-known Fraunhofer lines in the solar spectrum). As the Universe expands during the next 120 million years, waves that were initially shorter stretch to 21 cm and are similarly absorbed by hydrogen. After this time, light from the first stars heat the hydrogen to the point that it can no longer absorb these waves [Loeb and Zaldarriaga 2004]
It turns out that the amount of absorption is extremely sensitive to the value of α. Therefore, the spectrum of absorption lines we expect to see in the radio waves is an accurate record of the value of α during this epoch. We could even look for variations of α within this epoch, and check for spatial variations of α and other 'constants.' I argued above that these variations are expected on general grounds, but they are also predicted by specific string-theory inspired models for dark energy such as the chameleon model.
The tests we propose are uniquely promising to constrain fundamental physics models with astronomical observations. Important technological hurdles have to be overcome to realize measurements of the radio wave spectrum at the required level of accuracy. Still, the next time you see snow on your analog TV you might consider that some of what you see is due to long wavelength radio waves have reached you from the early Universe, having traveled to you across the gulf of cosmic time and carry in them the signature that may reveal the fundamental theory of Nature.
Chand H. et al. 2006, Astron. Astrophys. 451, 45.
Khatri, R. and Wandelt, B. D. 2007, Physical Review Letters 98, 111301. Abstract
Loeb, A. and Zaldarriaga, M. 2004, Physical Review Letters 92, 211301. Abstract
Marion, H. et al. 2003, Phys.Rev.Lett. 90, 150801. Abstract
Uzan, J.-P. 2003, Reviews of Modern Physics, vol. 75, 403. Abstract
Webb,J. K. et al. 2001, Physical Review Letters 87, 091301. Abstract