Four Problems for the Standard Model of Cosmology
and Their Resolution by Inflation

The Flatness Problem. It turns out, by examining the details of a Friedmann-Robertson-Walker cosmology, that Ω, which is the ratio of the mass/energy density of the Universe to its critical value, must have been very, very close to 1 during the earliest moments of cosmic history if Ω is roughly near one today. For example, when the Universe was one second old, it must have deviated from one by less than one part in ten-thousand-trillion (1016). This is a fine-tuning problem. It is hard to understand how Ω could have been adjusted to such precision. Another way to view the difficulty is as follows. If, on one hand, Ω had been initially less than one but not precisely tuned to be very, very close to one, the Universe would have expanded and collapsed during its earliest stages of development; in other words, the age of the Universe would have been a tiny fraction of a second. Since the Universe is at least 10 billion years old, there is a contradiction. If, on other hand, Ω had been more than one but not precisely tuned to be very, very close to one, the Universe would have expanded extremely rapidly cooling to a frigid temperature above absolute zero but indiscernibly so. Since the Universe is not that cold today, there is again a contradiction.

The Large-Scale Smoothness Problem. As noted above, the cosmic microwave background radiation is amazingly uniform. Its temperature in different directions only fluctuates to about one part per 100,000. What is unusual about this is that the two distant regions on opposite sides of our visible Universe were never in physical contact or communication if the world is governed by a Friedmann-Robertson-Walker cosmology. Systems achieve thermal uniformity through conduction, convection or radiation transfer. All these mechanics require the constituents of the system to be causally connected. However, in the Friedmann-Robertson-Walker model, source regions of cosmic microwave background radiation are not causally connected as soon as they are separated by at least one degree. How could these different regions achieve identical temperatures to within one part in 100,000? This is the smoothness dilemma.

The Small-Scale Inhomogeneity Problem. The fluctuations in the cosmic microwave background radiation led to the structures seen by astronomers. The large-scale structure of the Universe consists of regions in which few galaxies exists and regions in which many galaxies are present. The former are called giant voids and the latter are called galaxy clusters. The size across these regions is roughly 50 million light-years.
     The origin of these large-scale structures is readily understood. Those volumes of space in the early Universe with slightly greater mass/energy attracted the matter in surrounding volumes and became denser. The matter in these volumes then collapsed under the influence of gravity thereby forming galaxy clusters. Likewise, those volumes with slightly less mass/energy lost matter to denser surrounding regions and became less dense, eventually ending up as the giant voids. The Universe also has other kinds of lumpiness or inhomogeneities: Galaxy clusters consist of dozens and dozens of galaxies, and galaxies consist of tens of billions of stars, all of which have mostly empty space between them. These finer structures were produced in the same manner as the large-scale structures, that is, in terms of smaller fluctuations in the mass/energy density of the early Universe. Because the visible Universe consists of many causally distinct regions in a Friedmann-Robertson-Walker cosmology, it is impossible to account for the character of the structures at all scales: One would expect huge fluctuations at distances larger than those associated with a single causally distinct volume, medium fluctuations at a size associated with the boundary of such a volume, and much smaller fluctuations at scales smaller than the size of such a volume. However, observations indicate that the size of the fluctuations at all these various scales need to be roughly of the same order of magnitude.

The Magnetic Monopole Problem. Certain grand unified gauge theories predict the existence of magnetic monopoles. Other unification models suggest the existence of exotic heavy particles. None of these particles has been detected. Actually, the magnetic monopole issue may not be a problem because the lack of observation of proton decay disfavors grand unified gauge theories and string theory provides a unification mechanism not requiring a unifying gauge group.

How Inflation Eliminates the Problems. It is straightforward to see why inflation solves the magnetic monopole problem if these particles are generated before inflation. The rapid stretching of space will greatly diminish the density of any early-Universe particle relics. In other words, if inflation and grand unified gauge theories are features of nature then monopoles exist but are spread apart so far that it is quite unlikely that they will be detected by scientists on Earth.
     Inflation resolves the flatness problem because when a geometry is scaled up by a great factor then locally it appears quite flat: Compare a beach ball to the planet Earth; it is obvious that a beach ball is a sphere but the surface of the Earth appears flat to beings the size of a few meters.
     Next consider the large-scale smoothness problem. It is eliminated because a small causally connected volume, which would be in thermal equilibrium, of the early Universe is blown up into an enormous volume. Not only would the current visible Universe be causally connected but it would actually also be a small part of the volume, all whose contents of which would be almost smoothly distributed. Inflation predicts that the visible part of the Universe is much smaller than the entire Universe. The small-scale inhomogeneity problem is solved because the minute fluctuations that exist in the original causally connected volume are stretched out over a wide range of distance scales.

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