Were parts of the Universe deflating during Inflation? I was reading about the history of the early universe in Carroll &amp; Ostlie and specifically looking at Inflation, which, as I understand, occurred because our [observable] part of the universe entered a false vacuum state containing negative pressures, thus fueling expansion. (Carroll &amp; Ostlie state the opposite, but as per the discussion below, that appears to be incorrect). 

Does that mean that there are other parts of the Universe (outside of our horizon) that experienced deflation, as inflationary parts pressed against them? Would there be boundaries between separate parts of the larger universe where inflationary parts encounter one another? Any thoughts on what those parts of the Universe are like, such as containing their own CMB that's NOT close to uniform, or where there is a much higher density of matter?
That sounds... confused, or else just wrong. Negative pressure is what causes inflation: something (inflaton field, cosmological constant, or "dark energy" in general) with an energy density that stays approximately constant as space expands has negative pressure and will drive the exponential expansion of space.

The transition to "true" vacuum is what shuts off inflation, after which you get  the standard Big Bang, during which the expansion continues but slows down.

(The cosmological constant -- or "dark energy" -- also has negative pressure, and so the universe is gradually moving towards a state where the space between galaxy groups and galaxy clusters will again be expanding exponentially.)

The "eternal inflation" model has our visible universe -- almost certainly a tiny part of a much larger region of true vacuum -- as one of many such pockets of true vacuum embedded within a vastly larger false vacuum that's still expanding exponentially.