The Inflationary Universe

Now and then, I mention perplexing facts about the Universe. I will now go into some of them in more detail and offer an explanation (perhaps) for why the Universe is the way it is. You can decide later if you believe this stuff.

• Horizon problem
• Flatness problem

The above mysteries can be explained by what is known as the Inflation Theory . Results from the detailed studies of the CMBR starting with COBE followed by Boomerang and WMAP have lent strong support to the Inflation theory. To get a handle on the inflation recall that the nature of the four forces of nature changes as the Universe evolves:

At earlier and earlier times, the way matter, radiation, and the Universe interact gets simpler. The times when the forces of the Universe get more complicated are referred to as Symmetry Breakings. Symmetry breakings are analogous to phase transitions (e.g., liquid water ---> solid water (ice), liquid water ---> vapor, etc.).

The GUTs era is when symmetry was broken for the nuclear (strong) and electro-weak forces. Inflation occurred at this time. During inflation, the scale factor R(t) and the temperature of the Universe evolved as:

Inflation causes the Universe to increase rapidly in size and to cool. At the end of Inflation, the Universe re-heats and then continues on its normal evolution. Inflation does not affect the late-term evolution of the Universe; it is causes a rapid blow-up in size of the Universe at early time after which it evolves more or less as it would have without the inflationary epoch (see above and below).

What are some consequences of this blow-up?

• For typical models, the Universe roughly doubles in size every ~ 10^-34 seconds This is a phenomenal rate, e.g.,
  • t = 0 sec ---> 10^-24 cm
  • t = 10^-34 sec ---> 2 x 10^-24 cm
  • t = 2 x 10^-34 sec ---> 4 x 10^-24 cm
  • t = 3 x 10^-34 sec ---> 9 x 10^-24 cm
  • ...
  • t = 100 x 10^-34 sec ---> ~ 13 km

  In the example, the Universe grows by a factor of more than 10³⁰ in 10^-32 sec.

  • Horizon Problem
    Suppose that we start with a large universe and consider a small causally connected chunk say, of size 10^-23 cm. Suppose the Universe inflates and that inflation lasts for 10^-32 sec, The causally connected chunk of the Universe expands to a size 10⁷ cm. This inflated patch easily encompasses our Universe which, at this time, is only ~ 30 cm in size. Our Universe was embedded in this huge region which was causally connected before inflation,
    

    This explains the horizon problem.

  • Flatness Problem
    The Earth is known to be spherical, however, for us small (short people) living on the surface of the Earth, the Earth appears flat. It appears flat because we are not tall enough to see over the edge of the Earth. Due to inflation, we have
    

    Inflation predicts that the Universe should appear flat (that is, Omega = 1, identically). This resolves the flatness problem.