2.2. Inflationary Expansion: The Magic of a Shrinking Comoving Event Horizon

Inflation doesn't make the observable universe big. The observable universe is as big as it is. What inflation does is make the region from which the Universe emerged, very small. How small? is unknown (hence the question mark in Fig. 2), but small enough to allow the points in opposite sides of the sky (A and B in Fig. 4) to be in causal contact.

Figure 2. Inflation is a short period of accelerated expansion that probably happened sometime within the first picosecond (10-12 seconds) - during which the size of the Universe grows by more than a factor of ~ 1030. The size of the Universe coming out of the `Trans-Planckian Unknown' is unknown. Compared to its size today, maybe it was 10-60 as shown in one model...or maybe it was 10-165 as shown in the other model... or maybe even smaller (hence the question mark). In the two models shown, inflation starts near the GUT scale, (~ 1016 GeV or ~ 10-35 seconds) and ends at about 10-30 seconds after the bang.

The exponential expansion of inflation produces an event horizon at a constant proper distance which is equivalent to a shrinking comoving horizon. A shrinking comoving horizon is the key to the inflationary solutions of the structure, horizon and flatness problems. So let's look at these concepts carefully in Fig. 1.

The new -CDM cosmology has an event horizon and it is this cosmology that is plotted in Fig. 1 (the old standard CDM cosmology did not have an event horizon). To have an event horizon means that there will be events in the Universe that we will never be able to see no matter how long we wait. This is equivalent to the statement that the expansion of the Universe is so fast that it prevents some distant light rays, that are propagating toward us, from ever reaching us. In the top panel, one can see the rapid expansion of objects away from the central observer. As time goes by, dominates and the event horizon approaches a constant physical distance from an observer. Galaxies do not remain at constant distances in an expanding universe. Therefore distant galaxies keep leaving the horizon, i.e., with time, they move upward and outward along the lines labeled with redshift `1' or `3' or `10'. As time passes, fewer and fewer objects are left within the event horizon. The ones that are left, started out very close to the central observer. Mathematically, the R(t) in the denominator of Eq. 8 increases so fast that the integral converges. As time goes by, the lower limit t of the integral gets bigger, making the integral converge on a smaller number - hence the comoving event horizon shrinks. The middle panel shows clearly that in the future, as increasingly dominates the dynamics of the Universe, the comoving event horizon will shrink. This shrinkage is happening slowly now but during inflation it happened quickly. The shrinking comoving horizon in the middle panel of Fig. 1 is a slow and drawn out version of what happened during inflation - so we can use what is going on now to understand how inflation worked in the early universe. In the middle panel galaxies move on vertical lines upward, while the comoving event horizon shrinks. As time goes by we are able to see a smaller and smaller region of comoving space. Like using a zoom lens, or doing a PhD, we are able to see only a tiny patch of the Universe, but in amazing detail. Inflation gives us tunnel vision. The middle panel shows the narrowing of the tunnel. Galaxies move up vertically and like objects falling into black holes, from our point of view they are redshifted out of existence.

The bottom line is that accelerated expansion produces an event horizon at a given physical size and that any particular size scale, including quantum scales, expands with the Universe and quickly becomes larger than the given physical size of the event horizon.

Figure 3. Friedmann Oscillations: The rise and fall of the dominant components of the Universe. The inflationary period can be described by a universe dominated by a large cosmological constant (energy density of a scalar field). During inflation and reheating the potential of the scalar field is turned into massive particles which quickly decay into relativistic particles and the Universe becomes radiation-dominated. Since rel R-4 and matter R-3, as the Universe expands a radiation-dominated epoch gives way to a matter-dominated epoch at z 3230. And then, since Ro, the matter-dominated epoch gives way to a -dominated epoch at z 0.5. Why the initial -dominated epoch became a radiation-dominated epoch is not as easy to understand as these subsequent oscillations governed by the Friedmann Equation (Eq. 11). Given the current values (h, m, , rel) = (0.72, 0.27, 0.73, 0.0) the Friedmann Equation enables us to trace back through time the oscillations in the quantities m, and rel.