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The Sciences

Evolving Potentials

Cosmic VarianceBy Mark TroddenJune 15, 2008 4:58 PM


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An important event of the early summer was the graduation of my most senior graduate student - Alessandra Silvestri - who successfully defended her thesis on May 15th, and who is leaving the nest at the end of the summer to take up a postdoc in the Physics Department and the Kavli Institute for Astrophysics and Space Research at MIT. Congratulations to Alessandra! Alessandra's thesis - Modified Gravity: Cosmic Acceleration and the Large Scale Structure of the Universe - contains, among other things, results obtained in a series of papers in which she, with collaborators, studied how one might search for an observational signature of modified gravity as the origin of cosmic acceleration, as compared to dark energy, or a cosmological constant. While it is relatively easy to obtain the correct expansion history of the universe - how its size changes over the course of time - from all kinds of cosmic acceleration models, differences typically manifest themselves in the details of how structure grows, and how that structure influences the cosmic microwave background radiation (CMB). There are a number of different important effects, but one that is particularly interesting, and unusually easy to explain, is the Integrated Sachs-Wolfe (ISW) effect. Here's how it works. In the early universe, expansion ultimately stretches the wavelengths of photons enough that their energies are too low to ionize hydrogen atoms. This is called decoupling, and after this point the universe is electrically neutral, light essentially ceases to interact with matter, and the leftover photons stream through the universe. Today they form the CMB. During the photons' journey across the universe (ultimately to our detectors) they pass through overdense regions of matter that are in the process of becoming more dense, due to the attractive nature of gravity. In passing through such a growing overdensity, the photons gain energy as they fall into the associated potential well, and lose energy as they climb out of it (this is general relativity after all, and gravity affects light just as it would affect massive particles). For a static potential well, these effects would, of course, cancel, just as a ball rolling from one side of a symmetrical bowl to the other will reach precisely the same height that it started at. However, in reality two competing effects occur - the well is growing due to gravitational attraction, and is becoming shallower due to the expanding background. Thus, there is the possibility of an overall change in the photon energy, depending on how the universe is expanding. The collapse of an overdensity can be thought of as the evolution of a small matter dominated portion of the universe. If the background evolution is matter dominated, this is cancelled by the expansion rate and the overall effect is zero, as for a static potential. However, if the background evolution differs from matter domination then there is a net effect. This adds up as the photon traverses multiple wells, and is known as the ISW effect. Since we now know that the late time evolution of the universe is not matter dominated, but rather is accelerating, the ISW effect provides one possible insight into the nature of this phenomenon. And since cosmic acceleration is occurring in the most recent epoch (and to distinguish the effect from a related one occurring at early times, during radiation domination), we refer to this incarnation of the effect as the late-time ISW effect (or Rees-Sciama effect). Because acceleration is so dominant, the net effect is that the potential decays while the photon traverses the well, meaning that the photon emerges with a slight net blueshift, compared to how it entered. Now, because the details of how structure forms depend not only on the background evolution, but also on how the different energy components of the universe cluster, and on the equations obeyed by the overdensities themselves, the size and sign of the late-time ISW effect depends on the origin of cosmic acceleration. For example, modified gravity theories typically introduce a scale-dependence into the growth function that may be used to distinguish such models from dark energy or the cosmological constant model. Thus, in principle, the late-time ISW effect is a powerful tool. In practice this is very difficult to carry out, since the dominant effect is on large scales in the universe, where cosmic variance (the statistical effect, not us) gets in the way of interpreting any possible signal. Nevertheless, by cross-correlating the microwave background measurements with data from large scale structure surveys, one can make progress. Cosmic acceleration is a huge mystery, but modern cosmology also provides us with a remarkable set of tools with which to probe it, and to constrain our theoretical approaches. The late-time ISW effect is one of these tools, and is a nice example of how the CMB - an amazing discovery in its own right - is now being put to use in many different ways to explore the details of our cosmological models.

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