So exactly how do astronomers know that the universe’s expansion is accelerating? The two teams looked at Type Ia supernovae at very large distances (that is, high redshifts). The tremendous explosions from Type Ia supernovae are catastrophic thermonuclear explosions of white dwarf stars that occur when the stars reach their maximum possible mass—the so-called Chandrasekhar limit of 1.4 solar masses. Two characteristics of these explosions make Type Ia supernovae excellent gauges of distance, or “standard candles.” First, the brightness of these explosions is nearly constant. Second, even the small deviations from constancy are well calibrated—the brighter the supernova, the slower it declines in brightness. Thus astronomers can use them to determine cosmic distances. The 1998 observations showed that very distant supernovae, those with redshifts of about 0.5, appeared some 0.3 magnitude dimmer than expected at their distances. In other words, these supernovae were farther away than expected and, therefore, the universe’s expansion rate had to be speeding up for the supernovae to reach the larger distances.

The first skeptics wondered whether the 1998 observations might be tainted. For example, was it possible that the supernovae appeared so faint because of obscuring dust lying between us and them? After all, as the saying goes, extraordinary claims require extraordinary proof. In 2001, however, Riess and his colleagues took a big step toward showing that alternative explanations like dust absorption do not explain the faintness. Using Hubble Space Telescope observations of the Hubble Deep Field, the deepest exposure made to that date in visible or ultraviolet wavelengths, the group showed that Supernova 1997ff, which lies in the field, is the most distant Type Ia supernova known. Its amazingly high redshift of 1.7, which corresponds to a whopping 10.2 billion years ago, offers astronomers a unique opportunity to test the idea that dust is obscuring the observations.


Distant Supernovae (PRC04-12)
http://hubblsite.org/newscenter/newsdesk/archive/releases/2004/12/image/a


The idea behind the test is simple. Even in a universe that’s currently accelerating, if you look into the distant past, you’re bound to find an era when the universe was decelerating. When the universe was very small, gravity dominated the dynamics of the cosmos, and the expansion was slowed down by gravity’s pull. Only in the last few billion years did the matter density of the universe dip below the density associated with dark energy, causing the expansion of the universe to speed up. Because of this, observations of supernovae with redshifts greater than about 0.7 can distinguish between obscuration by dust and the real thing—acceleration. If supernovae are dimmed by dust, then more distant ones should appear fainter and fainter, as their light needs to pass through ever-increasing amounts of dust.

The accelerating universe

If, on the other hand, we live in an accelerating universe, then supernovae at very high redshifts (seen when the universe was still decelerating) should look brighter than expected for their distance. Indeed, the observations of supernova 1997ff show it to be brighter than anticipated, which is consistent with a cosmic acceleration scenario rather than a dust obscuration one. Supernova observations also suggest we live in a universe in which matter of all forms, including dark matter, provides only about 27 percent of the density that makes the universe geometrically flat. The other 73 percent of the density comes from dark energy, whatever that is. Astronomers use the Greek letter omega, Ω, to denote the cosmic density: An Ω of 1.0 implies a geometrically flat universe. If Ω is greater than 1.0, the universe would be closed, corresponding to a geometry like that of a sphere. If Ω is smaller than 1.0, then the universe is open with a geometry like that of a saddle. A flat universe with a dark energy contribution of 73 percent is expected to expand forever, at an ever-increasing rate.

Another bit of evidence strongly suggests that the universe is speeding up. For years, astronomers have studied the Cosmic Microwave Background (CMB) radiation. Measurements of the anisotropy (or unevenness) of the CMB radiation show the temperature difference between two points on the sky is greatest when those points are about 0.7° apart. Why is this important? It’s a reflection of the geometry of the universe. The CMB radiation is coming from the “surface” on which radiation particles, or photons, last interacted with matter in the early universe, before the universe became transparent. As baryons and leptons—ions and electrons—fell into the gravitational “wells” generated by dark matter, photons pushed against them, which produced acoustic oscillations. The waves generated by this process caused undulations in the surface from which the CMB radiation was emitted, creating fluctuations in the temperature of the universe.


In the same way that sounds produced on the head of a drum depend on the drum’s size and geometry, the longest wavelength that had time to oscillate in the CMB depended on the geometry of the universe, which depended in turn on the value of Ω. In particular, the maximum temperature difference for points on the sky 0.7° apart corresponds to a flat universe and an Ω of 1.0. If Ω is smaller than 1.0, the differences in temperatures are largest between points separated by less than 0.7°. It’s similar to the experiment you can perform by holding a penny close to your eye, where it covers a wider angle in your field of view than if you hold it farther away. A number of experiments analyzing the CMB—the Wilkinson Microwave Anisotropy Probe in particular—suggest the density of matter in all forms is about 27 percent of the critical value, and that dark energy represents 73 percent.

Astronomers know the dark energy component of the energy density did not interfere with the formation of the structures we observe today in the universe, meaning it was less important in the past. Based on this, one can show that dark energy has a negative pressure. However, in general relativity, gravity acts proportionally to the sum of the matter density and three times the pressure. For a sufficiently negative pressure, therefore, gravity becomes a repulsive force, leading to the acceleration of the universe’s expansion.

Beauty in distress?

Observations of both distant supernovae and the CMB strongly suggest that we live in an accelerating universe whose energy density is dominated by some mysterious form of dark energy. There’s a problem with this finding, however. The model of the universe it implies is preposterously complex. Physicists normally assume fundamental theories of the universe must be “beautiful.” Successful theories, in other words, are based on symmetry and simplicity (see the “Is there beauty in nature?” sidebar). A physicist’s aesthetic sensibility is really an important research tool that can guide him or her to a correct hypothesis. The best example of this is Einstein’s general relativity, which in his own words was “beautiful beyond comparison.”

In general relativity, the underlying symmetry comes from the idea that all frames of reference are equal. Regardless of whether we live on a rocket moving through space at a constant speed, on a clump of matter accelerating from an exploding supernova, or on the surface of a rapidly spinning star, the laws of nature look the same.

How does general relativity fit into this theme of symmetry and simplicity? Isn’t it notoriously complicated? After all, in 1915, Einstein himself said that “only one colleague [mathematician David Hilbert] has really been able to understand it.” Although the equations describing general relativity and their solutions are more complex than Newton’s theory of gravitation, the central idea is actually much simpler. Instead of being a mysterious force that acts across the vast expanses of space, gravity merely reflects the geometry of space-time. In the same way a heavy bowling ball resting on a tight rubber mat would cause it to sag, every mass warps space-time in its vicinity. The planets move along curved orbits because they follow the most natural paths in the curved space-time produced by the Sun. Similarly, an airplane flying from the United States to Europe follows a great circle along Earth’s surface.

So where’s the symmetry and simplicity in the new model of the cosmos? The values of the different energy densities appear to be anything but simple. In fact, the inferred value for dark energy, 73 percent, is bizarre, to say the least. The most “natural” value for the energy density should have come from the so-called Planck Era, when the universe was 10-43 seconds old. But that value is some 123 orders of magnitude larger than the one that astronomers observe—a huge discrepancy even by astronomical standards! When adjustments are made to accommodate the principle of supersymmetry, for example, the energy density value is still 55 orders of magnitude too large. Attempts to reconcile this difference by making dark energy evolve over time still require some fine-tuning. It’s difficult to accept the notion that somehow the influence of dark energy changed in the recent past. Theories of the universe are usually Copernican—they assume that humans are ordinary observers; they are not graced with some special time or place to make things feasible.

Does this mean we are facing a breakdown of some of our most cherished theories of the universe? Has the centuries-old assumption of a simple, symmetric, Copernican view of the universe reached its limits? I don’t think so. We are probably in the same situation that the famous physicist Isidor Rabi found himself in when he heard about the discovery of the muon. “Who ordered that?” he asked indignantly. Assuming that recent indications of the value of Ω are fully confirmed, I believe that in time we’ll find that the current confusion relates to what is really fundamental and what isn’t. Galileo was upset by elliptical orbits because he didn’t realize the shape and symmetry of the orbits were not fundamental—the symmetry of gravity was. Kepler wrote an entire, outrageously wrong treatise trying to explain the number of planets and sizes of their orbits because he thought those numbers and sizes were fundamental. Before the standard model of particle physics emerged, accelerators were finding scores of so-called elementary particles, most of which are now known to be simply excited states of collections of two or three bound quarks.

It’s quite possible that astronomers that will eventually realize that the only truly fundamental value is Ω, and that Ω = 1.0 and the universe is flat. This is a direct result of inflation, which has all the hallmarks of a simple, symmetric, and Copernican theory. The existence of a cosmological constant is not inconsistent with the symmetry principle of general relativity, which states the laws of nature should be the same in all frames of reference in space and time.

But other possibilities exist. Alternative theories of gravity have been proposed that rely on extra dimensions to suggest, for instance, that what we see as dark matter halos may, in fact, reflect the gravitational influence of matter in other, unseen universes. The idea is that while all other interactions are confined to our (four-dimensional) universe, gravity may be free to travel in a fifth dimension, and thus migrate from one universe to another or weaken in a given universe. While these ideas are highly speculative, perhaps they could be tested by measuring the strength of gravity on very small (submillimeter) scales, or by lunar ranging experiments.

No fewer than five experiments are in the works to test this idea. Experiments at the Large Hadron Collector in Geneva, Switzerland, later this decade also may be able to test these ideas by documenting instances of missing energy—gravitons escaping into a fifth dimension, for example. If these alternative ideas about gravity are confirmed—or if we realize that the value of the current density of dark energy is accidental rather than fundamental—it would mean that the beauty of the universe may not be in jeopardy at all. Our understanding of it simply needs to play catch-up.

IS THERE BEAUTY IN NATURE? What do physicists mean when they label a certain theory as beautiful? As defined by Webster, beauty is the quality that “makes an object seem pleasing or satisfying in a certain way.” While this may be a suitable definition for a work of art, physicists don’t quite mean the same thing. Sombrero Galaxy (PRC03-28) http://hubblesite.org/newscenter/newsdesk/archive/releases/2003/28/image/a The two main elements of beautiful theories are symmetry and simplicity. By “symmetry” I don’t mean the symmetry of shapes or objects, like the left-right symmetry of the human face. I mean symmetry in the laws of physics themselves, such as the fact that they don’t change from place to place in the universe. This is what makes astronomy and astrophysics possible. We can use the laws of electromagnetism deduced from laboratory experiments on Earth to study a galaxy a billion light-years away. The laws of physics are also symmetrical under rotation, meaning that physics has no preferred direction in space. Separating the symmetry of shapes from that of laws is best exemplified by looking at planetary orbits. From ancient Greece to Galileo’s time, astronomers had assumed planetary orbits must be circular because of a circle’s inherent symmetry. Consequently, when Kepler discovered that orbits were elliptical, even Galileo refused to accept the finding. Not having Newton’s law of gravitation at his disposal, Galileo didn’t recognize that symmetry under rotation is a property of that law and not of the shape of the orbit. In other words, the orbits can be, and indeed are, ellipses, but the symmetry of the law of gravitation under rotation implies that the ellipses are allowed to have any orientation in space. When I speak of simplicity, I really mean reductionism. The goal of physics has always been to explain the wealth of phenomena we observe in nature by a relatively small number of fundamental laws. Consider star birth in gas clouds, the deaths of stars like the Sun, and the collision of two galaxies. All these processes involve four basic interactions: gravity, electromagnetism, and the two nuclear forces.