The Inflationary Universe

Now and then, I mention perplexing facts about the Universe. I will now go into two of them in more detail and offer an explanation (perhaps).

Flatness Problem
The Universe has total Omega = 1. Is this a problem? Yes.

To understand this point, recall that the Universe is fairly old, 13.7 billion years and that Omega = 1 is for a critical Universe.
Analogy: Try and balance a pencil on its pointed end. If you are far from vertical, the pencil falls to the ground very quickly. The closer you can place the pencil to vertical the longer it stands-up before it falls over. If you could place it at precisely vertical then (classically) it could stand-up forever. It is hard to place the pencil at its critcal position.
Universe: If the Universe started off far from critical, then it would have either quickly collapsed (not lasted for 13.7 billion years) or it would have expanded so quickly that it would have passed through the nucleosynthesis and galaxy formation epochs so fast that we would not be here. The only way for the Universe to have lasted this long and to have passed through the nucleosynthesis era at leisurely enough rates requires that the Universe started off very close to critical. How close?
Amazingly,

Omega must be 1 during the Planck Era to within 60 digits or so

to make Omega(t) ~ 1 today. This is Flatness Problem.

Horizon Problem
The horizon problem arises because light moves with a finite speed. As a result, certain events which occur in the Universe are completely independent of each other,
The current Universe has a horizon distance of

horizon ~ age x speed of light ===> the older the Universe is, the larger the horizon and therefore the larger the size of the region which can communicate.

A simple calculation indicates that at the time of recombination, material which was in causal contact (able to communicate) are currently separated by around 0.8 angular degrees on the sky. this means that the sky could only mix over separations of 0.8 degrees and so, there is no rational reason to believe that the sky should look the same everywhere! This is the Horizon Problem.

The above mysteries may be explained by what is known as the Inflation Theory . Recently results from the Wilkinson Microwave Anisotropy Probe (WMAP) offered strong support for the Inflation theory. To get a handle on 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 and conversely, as the Universe evolves, the way matter, radiation, and the Universe interact get more complicated. Where the forces of the Universe get more complicated are referred to as

Symmetry Breaking

The symmetry breakings are analogous to phase transitions (e.g., liquid water ---> solid water (ice), liquid water ---> vapor, etc.).
The GUTs era, when the symmetry breaking for the nuclear (strong) and electro-weak forces happened. This is when inflation occurred.
Inflation may be driven by a nonzero Cosmological Constant ; ah ha, there might be one even in the early Universe, but the Cosmological Constant must be reasonably small (fine-tuning) and it must essentially disappear or decay (or become very small) as the Universe evolves. During inflation, the scale factor of the Universe R(t) evolves as:

Inflation causes the Universe to increase in size greatly and to cool rapidly. At the end of the rapid expansion which occurs after the Universe transits from the false vacuum to the true vacuum, the Universe re-heats and continues on in its normal evolution . Inflation does not affect the long-term evolution of the Universe in this sense; it only produces a rapid blow-up in size of the Universe at an early time.
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. The exact rate at which the Universe grows depends on the particular model. The point is that the expansion rate is humongous! (Note that in this example, the Universe expands with speed >> c!)

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.

Eternal Inflation
As the Universe inflates, the false vacuum material starts to decay. The part that decays settles into the true vacuum and normal matter which forms Pocket Universes. The remaining false vacuum continues to grow rapidly (creating more false vacuum --dark energy?); inflation continues indefinitely. This suggests that during inflation, part of the false vacuum keeps growing and inflating while part of the false vacuum decays spawning infinite numbers of Pocket Universes.

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