Cosmic Inflation

 

Problems Raised By The Big Bang Picture:

  1. Horizon Problem: How did the separate parts of the universe, which couldnŐt even see one another at t = 380,000 years, come to the same temperature?  Remember, even the tiny 40 parts per million temperature variations were caused by density clumps. The identical temperature of regions that, because of separation, could not be in equilibrium needs explanation.
  2. Smoothness Problem: Although a uniform gas is unstable against gravitational collapse, calculations on a uniform density and only statistical variations in density gas show no significant clumping by t= 380,000 years. Yet the clumps exist. They produce temperature variations, and more importantly, galaxies. What caused the clumps, if statistical variations in density are insufficient?
  3. Flatness Problem: The Big Bang picture should be consistent even to the earliest times. However, if the universe is just a tiny bit denser than the critical density at earliest times, it will expand to a small limit and collapse very early. If a little bit less dense than critical, it will expand so fast that other galaxies are invisible. In other words, very tiny deviations from perfect flatness grow to significant curvature over long times. For the space of the universe to not be very significantly curved now, which it is not, requires that it be incredibly flat at earliest times. In terms of density, for it not to be obviously curved today, the density has to be the critical density to about 50 significant figures!

 

The above problems, separately, were recognized fairly early. They emerged from a definition of Ňearliest timeÓ. That was the ŇPlanck timeÓ, which from the quantum theory uncertainty principle can not be described as a classical time interval. Its calculation is outside our syllabus. No present theory makes sense before that time. The Planck time is 10-43 s.

An illustration of the flatness problem is shown below. It starts at t = 10-9 s, well after the Planck time. The middle density is critical. The scale length is what expands in the universe, The differences in density amount to just 4 ounces in every region as massive as the moon! Much smaller differences are necessary if we start the model earlier. Most scientists would rather accept a principle that forces a near-critical density, rather than accept such a nearly critical density as an initial condition.

 

In 1980, a physicist named Alan Guth proposed an early interval now called the inflationary epoch. It started at t = 10-34 s and ended at t = 10-32  s. The idea was based on a particle physics idea called vacuum energy, which had not previously been applied to cosmology. It predicted that the universe doubled in size 200 times in that brief interval. That sounds like lot, and it sure is! Two hundred doublings is 1060.

 

This rapid early, exponential expansion affected more than particle physics theory. It rationalized the problems identified above.

  1. Horizon Problem: It insured that every part of the visible universe, even 180 degrees apart, were once in thermal contact, and would have the same temperature for this reason.
  2. Smoothness Problem: The density doesnŐt change during inflation, but a given volume increases by 10180. The number of particles in the initial unit that became our visible universe was much smaller, and statistical variations would be larger. We need dark energy to prevent the resulting clumping from being larger than observed, rather than being too smooth.
  3. Flatness Problem: The inflation stretched the radius of curvature of space-time by a factor of 1060. That made it flat. The dark energy, or dark matter, or both are caused by inflation. That doesnŐt simply give the dark energy problem another name, since inflation was based on a physics principle.
  4. Inflation also solved the problem that Guth was trying to solve, called the monopole problem. Most attempts to develop a complete theory of elementary particles produce a lot of things called magnetic monopoles, which donŐt seem to exist in nature. Inflation allows monopoles to be formed before the inflation epoch, and then diluted by the factor of 10180, making them undetectable. The monopole problem was never a perceived problem to cosmologists, only to physicists.
  5. You may remember the cosmological constant (Omega), way back in unit 4 of the syllabus. ItŐs EinsteinŐs Ňgreatest blunderÓ, according to himself. One problem it had was that it had no physical basis, another was that in produced an unstable static universe, one that would expand exponentially or collapse catastrophically, given the tiniest nudge in either direction. Well, with inflation, Omega is back. It now has a physical basis (vacuum energy), and exponential expansion of the universe is its greatest virtue! The difference is that it doesnŐt last long.