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5. How Does Inflation Produce All the Structure in the Universe?

In our Universe quantum fluctuations have been expanded into the largest structures we observe and clouds of hydrogen have collapsed to form kangaroos. The larger end of this hierarchical range of structure - the range controlled by gravity, not chemistry, is what inflation is supposed to explain.

Inflation produces structure because quantum mechanics, not classical mechanics describes the Universe in which we live. The seeds of structure, quantum fluctuations, do not exist in a classical world. If the world were classical, there would be no clumps or balls to populate classical mechanics textbooks. Inflation dilutes everything - all preexisting structure. It empties the Universe of anything that may have existed before, except quantum fluctuations. These it can't dilute. These then become the seeds of who we are.

One of the most important questions in cosmology is: What is the origin of all the galaxies, clusters, great walls, filaments and voids we see around us? The inflationary scenario provides the most popular explanation for the origin of these structures: they used to be quantum fluctuations. During the metamorphosis of quantum fluctuations into CMB anisotropies and then into galaxies, primordial quantum fluctuations of a scalar field get amplified and evolve to become classical seed perturbations and eventually large scale structure. Primordial quantum fluctuations are initial conditions. Like radioactive decay or quantum tunneling, they are not caused by any preceding event.

"Although introduced to resolve problems associated with the initial conditions needed for the Big Bang cosmology, inflation's lasting prominence is owed to a property discovered soon after its introduction: It provides a possible explanation for the initial inhomogeneities in the Universe that are believed to have led to all the structures we see, from the earliest objects formed to the clustering of galaxies to the observed irregularities in the microwave background." - Liddle & Lyth (2000)

In early versions of inflation, it was hoped that the GUT scale Higgs potential could be used to inflate. But the GUT theories had 1st order phase transitions. All the energy was dumped into the bubble walls and the observed structure in the Universe was supposed to come from bubble wall collisions. But the energy had to be spread out evenly. Percolation was a problem and so too was a graceful exit from inflation. New Inflation involves second order phase transitions (slow roll approximations). The whole universe is one bubble and structure cannot come from collisions. It comes from quantum fluctuations of the fields. There is one bubble rather than billions and the energy gets dumped everywhere, not just at the bubble wall.

One way to understand how quantum fluctuations become real fluctuations is this. Quantum fluctuations, i.e., virtual particle pairs of borrowed energy DeltaE, get separated during the interval Deltat ltapprox hbar / DeltaE. The Deltax in Deltax ltapprox hbar / Deltap is a measure of their separation. If during Deltat the physical size Deltax leaves the event horizon, the virtual particles cannot reconnect, they become real and the energy debt must be paid by the driver of inflation, the energy of the false vacuum - the Lambdainf associated with the inflaton potential V(phi) (see Fig. 8).

Figure 8

Figure 8. Model of the Inflaton Potential. A potential V of a scalar field phi with a flat part and a valley. The rate of expansion H during inflation is related to the amplitude of the potential during inflation. In the slow roll approximation H2 = V(phi) / mpl2 (where mpl is the Planck mass). Thus, from Eq. 22 we have Lambdainf = 3 V(phi) / mpl2. Thus, the height of the potential during inflation determines the rate of expansion during inflation. And the rate at which the ball rolls (the star rolls in this case) is determined by how steep the slope is: dot{phi} = V' / 3H. In modern physics, the vacuum is the state of lowest possible energy density. The non-zero value of V(phi) is false vacuum - a temporary state of lowest possible energy density. The only difference between false vacuum and the cosmological constant is the stability of the energy density - how slow the roll is. Inflation lasts for ~ 10-35 seconds while the cosmological constant lasts gtapprox 1017 seconds.

What kind of choices does the false vacuum have when it decays? If there are many pocket universes, what are they like? Do they have the same value for the speed of light? Are their true vacua the same as ours? Do the Higgs fields give the particles and forces the same values that reign in our Universe? Is the baryon asymmetry the same as in our Universe?

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