Sunday, November 05, 2006

Inflation and the cosmic microwave background

About three weeks ago I wrote a little about the cosmic microwave background (CMB), and talked about writing more. So here's a little more. The CMB is microwave radiation we can (almost) literally "see" even though it originated only about 350,000 years after the big bang. (I'll explain more in a minute about what "originated" means in this context.)

There are a number of things very wonderful and remarkable about the CMB. Not only is it one of the major pieces of evidence supporting the big bang theory in general, but it also gives us much information about things as diverse as the relative proportions of ordinary matter and dark matter in the universe, the overall curvature of the universe ("flat", "convex", or "concave"), and the ratio of the number of baryons (protons and neutrons) to photons in the universe.

Further, of particular concern here, the CMB provides a means of testing a theory – the theory of cosmic inflation – that describes a much different period of time than that of the CMB itself, a period of time that began only about 10-35 seconds after the big bang itself. The theory of inflation comprises a range of models describing what may have happened at that time. If there is any truth at all to the theory, the CMB can help narrow the range of acceptable models.

I have a couple of older articles on this from back in March/April here and here. These deal with the announcement back then of analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP) that, among several other things, gave the first reasonable evidence for inflation.

Rather than dive right away into further explanation of that, I'm going to refer you first to this excellent recent article on the subject by Sean Carroll: Reconstructing Inflation.

What's that, you say? It sounds impressive, but you don't quite follow the details? OK, let's step back for a moment and review the basics. The picture below is a graphical representation of the main data obtained from WMAP:

This picture shows slight variations in temperature across the entire sky, at microwave frequencies, where blue represents coolest and red represents warmest. The variations are actually very small: the whole range is ± 200 microKelvins (millionths of a degree K).

Temperature differences correspond directly to differences in matter density – because a gas under higher pressure is warmer and denser than the same gas under lower pressure (the "combined gas law"). So what we see here are minute ripples of higher and lower pressure in the matter of the universe at roughly 350,000 years after the big bang. What has caused these pressure waves? Carroll's article explains

The same basic mechanism works in both cases — quantum fluctuations (due ultimately to Heisenberg’s uncertainty principle) at very small wavelengths are amplified by the process of inflation to macroscopic scales, where they are temporarily frozen-in until the expansion of the universe relaxes sufficiently to allow them to dynamically evolve.

The spots and blotches you see in this picture are shadows on the wall, as it were, of quantum fluctuations that actually occurred 10-35 seconds after the big bang. At first, in a period that lasted perhaps only 10-33 seconds, these fluctuations were inflated at an incredible rate. Thereafter, they continued to expand along with the rest of spacetime itself, until we see them projected on the CMB wall 350,000 years later.

To be more precise, we should note that this metaphorical CMB "wall" did not form at some single precise time. Instead, the CMB itself is a result of most of the hydrogen and helium matter in the early universe making the transition from an ionised plasma to an ordinary gas of neutral atoms, as free electrons were "captured" by the hydrogen and helium ions. Consider, for simplicity, just the hydrogen. It takes 13.6 eV (electron volts) of energy to separate an electron from a hydrogen atom. In the early universe when the typical photon had much more than this energy, atomic hydrogen could not exist for long, as most passing photons could "liberate" the electrons. But when the energy of the typical photon dropped, as the universe expanded, to the equivalent of around 13.6 eV, hydrogen atoms became stable for longer periods of time. This is known as the period of "recombination" (even though prior to this, protons and electrons had never been in a "combined" state). Once there was a lot of atomic hydrogen, photons of the most common energy levels "scattered" from the atomic hydrogen, and the universe was somewhat opaque to those photons.

But as the temperature dropped further, most photons did not have enough energy to liberate electrons from hydrogen atoms. So most photons ceased to scatter from atomic hydrogen, and the universe effectively became transparent again. Although this happened over a relatively short period of time, it was not instantaneous. By the time that most hydrogen was in an unionized state, a typical photon never again scattered off a hydrogen atom. So around any present observer, there is a "surface of last scattering". Assuming what are currently considered the most likely cosmological parameters, this corresponds to a time about 13.3 billion years ago (equivalent to a red shift of about 1100), about 350,000 years after the big bang. This surface of last scattering is what we see today as the CMB. The temperature of the universe at this time of last scattering was about 3000° Kelvin, but due to the subsequent expansion of the universe, the CMB photons now have an energy that peaks around 2.725° K, in the microwave part of the spectrum.

There is another way to represent the WMAP data for the CMB. You've probably seen it in some form. (It's in Carroll's article, if you read that.)

The vertical scale on the left is a measure of the amplitude of temperature fluctuations. The top and bottom scales are measures of angular size. 90°, for instance, is one fourth of the whole sky. The "multipole moment" (l) is an integer that corresponds to an angular measure of 180°/l. So, for instance, the peak on the above graph occurs around l=200, which is slightly less than 1°. For comparison, the angular size of the full moon viewed from earth is about .5°. What the graph is saying, roughly, is that strongest temperature fluctuations (spots in the picture above the graph), if you could see them with your naked eyes, are almost twice the angular size of a full moon. (Astrophysicists use multipole moments, since they are the relevant identifiers of "spherical harmonic" functions that are used to construct a series representation of the function which describes theoretical temperature variations, similar to the way that a Fourier series can represent a function of one real variable.)

The small dots on the graph are WMAP measurements for various values of l. They come with error bars, which are mostly too small to see, because the WMAP measurements were mostly pretty precise. The red line through the measured values is the theoretically predicted values, assuming that the temperature variations are actually the result of quantum fluctuations that occurred in the inflationary period. The locations of the two peaks to the right of the main peak are especially important, and they correspond fairly well to theoretical predictions.

Carroll's article explains how there are actually two kinds of perturbations we might potentially observe in measured quantities: "scalar" and "tensor", reflecting the fact that Einstein's equation describing gravity waves (which result from the inflation-era quantum fluctuations) is a tensor differential equation. Further, all that we can readily measure from the WMAP data are scalar perturbations:

To date, we are quite sure that we have detected the influence of scalar perturbations; they are responsible for most, if not all, of the temperature fluctuations we observe in the Cosmic Microwave Background. We’re still looking for the gravity-wave/tensor perturbations. It may someday be possible to detect them directly as gravitational waves, with an ultra-sensitive dedicated satellite; at the moment, though, that’s still pie-in-the-sky (as it were). More optimistically, the stretching caused by the gravity waves can leave a distinctive imprint on the polarization of the CMB — in particular, in the type of polarization known as the B-modes. These haven’t been detected yet, but we’re trying.

Problem is, even if the tensor modes are there, they are probably quite tiny. Whether or not they are substantial enough to produce observable B-mode polarization in the CMB is a huge question, and one that theorists are presently unable to answer with any confidence.

The WMAP experiment was capable of studying polarization of CMB microwaves only rather crudely. But a new experiment is due for launch very soon (early 2007) in the form of the European Space Agency's Planck mission. Considering that it took several years to analyze WMAP data, we may not have better information right away – but it won't be too long, if everything goes reasonably well.


Further information about CMB:

Wilkinson Microwave Anisotropy Probe
NASA web site of WMAP, containing background information, images, and graphs.
Wayne Hu's Home Page
One of the best collections of CMB information, including an introduction, explanation of the physics, and discussion of CMB polarization.


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