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May 2006
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WMAP data put cosmic inflation to the test

Feature: May 2006

Measurements of the polarization of the cosmic microwave background open up a new window on the universe when it was just 10-35 s old, explains Gary Hinshaw

While gazing upwards at the night sky you could be forgiven for thinking that the universe is a rather complex place. From elaborate constellations of nearby stars to the faint glow of light from the spiral arms of our galaxy, structure is visible in every direction you look. And were you to peer through the world's largest telescopes you would find a hierarchy of galaxies grouped into clusters, superclusters and super-superclusters hundreds of millions of light-years across. But to cosmologists, this clumpy nature of matter is a mere distraction.

Precision cosmology
Precision cosmology

On the largest cosmic scales, the universe is astonishingly dull. We know this courtesy of the cold sea of radiation that permeates the most distant reaches of the universe: the cosmic microwave background. Discovered serendipitously in 1965, this radiation contains unique clues about the nature and content of the cosmos because it came from an epoch when our universe was just a few hundred thousand years old.

A matter of scale
A matter of scale

Its most remarkable feature, however, is its near lack of any features at all! For almost 30 years following its discovery, the only thing we knew about the cosmic microwave background was its temperature - a chilly 2.725 K. And this temperature is the same to better than a part in 10,000 no matter which direction in the sky we measure. So where did the structure in the universe - from which the Sun, the Earth and we ourselves ultimately descended - come from?

Cosmic explorer
Cosmic explorer

Cosmologists are now able to address fundamental questions such as this from precision measurements of the cosmic microwave background. The first such data came courtesy of the COBE satellite in 1992, revealing miniscule fluctuations in the temperature of the microwave background as a function of position in the sky. And in 2003 the Wilkinson Microwave Anisotropy Probe (WMAP) gave cosmologists a crisp new view of this temperature anisotropy. Three years on, after a painstaking analysis that allowed the WMAP team to map the polarization of the cosmic background radiation across the sky, we are now in a position to put the standard model of cosmology through its toughest test to date.

A bold idea

The cosmic microwave background (CMB) was born when the universe was about 380,000 years old. Before this time, space was filled with a hot plasma of electrons and light nuclei, which meant that light could not travel very far without being scattered. But as the universe expanded, the plasma cooled enough to allow neutral atoms to form. This "decoupling" of matter and radiation suddenly enabled photons to travel across space largely unimpeded, their wavelengths being stretched over time to produce a faint glow of radiation in the microwave region that we can detect today.

In the early 1980s, in an attempt to explain the mind-boggling uniformity of the CMB, theorists came up with a bold concept called inflation. The idea was that the universe underwent a period of enormous growth when it was just 10-35 s old, during which it expanded by a factor of at least 1026 in a fraction of a second. Inflation could therefore account for the uniformity of the CMB because it proposes that the portion of the universe we observe today inflated from a tiny region that was presumably in thermal equilibrium. Without inflation, regions in opposite directions of the sky could never have been in contact - let alone thermal equilibrium.

Another consequence of inflation is that any previously existing curvature in space-time would have become immeasurably small after the exponential expansion, thereby accounting for the flat, Euclidean geometry of the present-day universe. Perhaps most remarkably, however, inflation offers an explanation for the clumpiness of matter in the universe: quantum fluctuations in the mysterious substance that powered the expansion would have been inflated to astrophysical scales and therefore served as the seeds of stars and galaxies.

Inflation is a key component of what is known as the standard cosmological model, but so far it has been very difficult to put the idea to the test directly. The tiny temperature anisotropy in the CMB provides a way to do this, since it is linked to the initial quantum fluctuations in the "stuff" that powered inflation. However, before we can extract useful information about these fluctuations, we need to understand other effects that contribute to the observed temperature anisotropy.

The most prominent effect is that of weak, low-frequency sound waves in the primordial plasma. A direct product of the initial quantum fluctuations, these waves "froze out" when matter and radiation decoupled 380,000 years after inflation to leave a distinctive oscillatory signature in the CMB anisotropy. Another important effect is that of secondary scattering, whereby on their journey across the universe some of the CMB photons scattered off free electrons in gases that were heated by the first stars. In addition to reducing the amplitude of the anisotropy signal, these interactions would have polarized the photons. Physicists have therefore been eager to measure the polarization of the CMB across the whole sky, which would give us both a better idea of how much attenuation took place and when the first stars formed.

Fortunately, the physics of these separate contributions to the CMB anisotropy is quite well understood, so it is straightforward to disentangle them from the initial quantum fluctuations. In order to do so, however, we need high-resolution measurements of the temperature and polarization of the CMB over the full sky - something that is now coming to fruition.

Anisotropy observations

In April 1992 a team led by George Smoot at the University of California at Berkeley and Chuck Bennett at NASA's Goddard Space Flight Center announced the first detection of anisotropy in the CMB temperature. Using the COBE satellite, they found variations in the temperature of roughly one part in 100,000 (which equates to about 30 μK) from point to point across the sky. The wonderful map of the fluctuating microwave background - which Smoot famously likened to "seeing the face of God" - had three major implications for cosmology.

First, it showed that nature has been kind to us, since the amplitude of the anisotropy is large enough to stand out above the microwave emission from our own galaxy (provided we look in the direction away from the galactic plane). Second, the measurement fixed the amplitude of the initial quantum fluctuations for the first time. But since inflationary models do not specifically predict the amplitude of the initial fluctuations, this measurement did not directly test inflation as the source of the fluctuations. The third important implication of the COBE data, however, was that they provided a rough test of inflation by constraining a parameter called the scalar spectral index.

The scalar spectral index, ns, measures the relative strength of the temperature anisotropy on small and large angular scales. As such, it corresponds to the slope of the angular power spectrum - which plots the temperature anisotropy as a function of angular scale - once its oscillatory features have been removed (see figure). Before inflation was introduced, theorists argued that the spectral index needed to have a value of unity to produce the correct relative abundance of stars, galaxies and clusters of galaxies. This corresponds to a flat line in the angular power spectrum. Although today's inflationary models predict a range of values for ns, all of which are close to unity, the simplest models predict a value slightly but measurably less than one.

Due to its limited angular resolution, COBE was only able to measure the anisotropy at large angular scales, which made it difficult to measure ns precisely. Throughout the 1990s, however, several sophisticated ground- and balloon-based experiments were carried out to measure the CMB temperature anisotropy with finer angular resolution. While these experiments could only observe relatively small patches of the sky, their results began to refine the measurement of ns, and to test the other major prediction of inflation: the flatness of the universe, which is determined by the position of the first acoustic peak in the angular power spectrum.

Then, in June 2001, NASA launched the WMAP satellite, which was designed to produce full-sky maps of the CMB anisotropy with higher sensitivity and resolution than ever before. Results from the first year of WMAP observations were released in February 2003. Among other things, these allowed researchers to conclude that the universe is 13.7 ± 0.2 billion years old and that its geometry is Euclidean to within 2% (see "The cosmic microwave background" Physics World April 2003 pp27-32). The first-year data also corroborated the standard "cold dark matter" model of the universe, suggesting that the relative abundances of ordinary matter, dark matter and dark energy in the universe are 4.4%, 24% and 72%, respectively.

Three-year WMAP results

In March the WMAP team announced results based on three years' worth of WMAP observations, which includes the most precise measurements of ns to date. One of the key features of the new data is that they have enabled us to measure the polarization of the cosmic microwave background. For an electromagnetic wave propagating along the z-axis, its polarization state is described by the relative amplitude and phase of the x and y components of the oscillating electric field. Specifically, if the line of sight from the observer to a free electron is the z-axis and the CMB photon has an intensity asymmetry in the x-y plane, then the radiation scattered in the z-direction will be polarized - much as sunlight is polarized when viewing the sky at right angles to the Sun.

There are two periods in the history of the universe during which free electrons were available to polarize CMB photons: first at the epoch of decoupling, and then again at the epoch of "reionization" - a few hundred millions years after decoupling - when the first stars ionized the surrounding gas. The polarization signal produced at decoupling only appears at small angular scales less than about 1°, while that produced by the reionized electrons occurs on angular scales of tens of degrees because these electrons are much closer to us.

Thus, by measuring the large-scale polarization of the CMB we can measure the "optical depth", τ, of the reionized gas - which gives the probability that a CMB photon was scattered by a reionized electron on its trip across the universe. A by-product of this scattering is that it suppresses the amplitude of the small-scale temperature anisotropy by a factor of e-2τ, which is important because it gives cosmologists a new handle on disentangling the effects of acoustic oscillations and secondary scattering from the primordial fluctuation signal produced by inflation.

One of the most daunting challenges for the WMAP team has been to measure the temperature anisotropy of the polarized photons, which, at about 0.1 μK, is over 100 times weaker than the unpolarized signal. To reach such exquisite precision, which is 50 times better than the original requirement for the WMAP mission, we had to rewrite the data-processing algorithms twice and construct an elaborate "covariance matrix" in order to measure how the noise in a single sky-map pixel correlates with the noise in every other pixel. The full-resolution sky map contains over three million pixels, but we had to use a lower resolution of 3072 pixels to make the matrix tractable. It was also crucial to have several independent years of data (WMAP repeats a full-sky survey every year) in order to perform vital cross-checks of the results.

The final analysis of the full-sky polarization maps suggests that the optical depth produced by reionized electrons is 9 ± 3%, which implies that the first stars formed roughly 400 million years after decoupling. In contrast, the first-year WMAP data put this event at about 200 million years. The new determination of the optical depth has also allowed us to refine our measurement of the scalar spectral index to be ns = 0.951 ± 0.016, compared with the first-year estimate of 0.99 ± 0.04.

Thus, for the first time we have evidence based solely on CMB data that the spectral index prior to inflation is significantly different from the scale-invariant value of unity, which had been long advocated on the basis of somewhat ad hoc arguments. In contrast, simple models of inflation in which the cosmic expansion is driven by a single "scalar field" predict that the spectral index should be measurably less than one and in the range observed by WMAP.

Grand unification

The era of precision cosmology is well under way, and is now reaching the realm of precision tests of inflation. But there is one more prediction of inflation that remains to be verified. According to Einstein's general theory of relativity, the fluctuations produced by inflation are accompanied by variations in the curvature of space-time, which include gravitational waves. Since CMB photons gain or lose energy as they traverse the associated gravitational potential wells, gravitational waves would also contribute to the temperature anisotropy.

The most compelling test of inflation would therefore be to unambiguously detect these relic ripples in space-time. Crucially, the amplitude of the gravitational-wave signal depends on the energy scale of inflation, so detecting it would significantly constrain models of what actually powered inflation. Since the unpolarized CMB signal arises from both the density- and gravitational-fluctuation sources, we need to somehow determine the ratio of the two contributions.

At present our only handle on this comes from the shape of the unpolarized anisotropy spectrum, but that information does not unambiguously determine the ratio. However, if inflation occurred at the "grand unification" scale (about 1015-1016 GeV), then the gravitational-wave signal could be inferred indirectly from observations of the CMB polarization. Specifically, gravitational waves would instil a unique vortex-like pattern in the polarization that might be detectable with a well-designed polarization experiment. We therefore have the tantalizing possibility of probing physics at energy scales several orders of magnitude higher than are possible with any terrestrial particle accelerator!

A recent study of inflation by Latham Boyle of Princeton University and co-workers shows that if the scalar spectral index ns is indeed greater than 0.95 - i.e. in accord with current measurements - then the ratio of the gravitational-wave and density contributions to the CMB anisotropy is greater than 0.01, otherwise the inflationary model is "unnaturally fine tuned" ( Although very small, Boyle and colleagues say that such a signal should be detectable in proposed CMB polarization experiments and direct gravitational-wave searches. So, there is reason to be optimistic about the prospects for detecting such a signal. To date, inflation has passed a number of very significant tests, and the detection of a gravitational wave background would be another notch in its belt.

About the author

Gary Hinshaw is at NASA's Goddard Flight Center in Maryland, US, where he leads the data analysis for the WMAP science team, e-mail

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