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I understand the basics of the inflationary period. However, there are a couple of things that I would like to better understand.

How could minute quantum fluctuation in the slowing of inflation be enough to cause the galactic structure we see today? From a nonmathematical perspective, shouldn't inflation have completely smoothed out the primordial plasma to the point where it was completely homogenous throughout the expanded universe?

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While any particular inflationary region indeed becomes exponentially smoother and diluted; quantum fluctuations, meanwhile, result in many, many such patchwork regions each with slightly different energy densities (because inflation ends at slightly different times in each of these regions; energy density in each is replenished through reheating.) Those regions that are over-dense with respect to their neighbors will grow in density via gravitational instability.

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Inflation doesn't completely smooth out density perturbations. It smooths perturbations out to a large extent, but a small number is still not zero.

As for how these minute fluctuations can cause galactic structure, it's because of gravity. The dense get denser. If one works through the math it does look like the minute fluctuations are too minute, which is one of the strands of evidence for dark matter. Dark matter is affected only by gravity, so while ordinary matter is still unable to collapse because of radiation, dark matter can collapse first. These gravitational wells then attract ordinary matter afterwards, and the result is galactic structure.

For more on this see the Wikipedia article and sources therein.

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