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Inflation is a theorized expansion of the universe enlarging 78 orders-of-magnitude within its first 10-32 seconds of existence, a brief yet sizeable expansion immediately after the Big Bang, after which followed the familiar, much slower Hubble expansion. This theoretical rapid early expansion explains both the homogeneity observed in the universe as well as characteristics of its large scale structure. The theorized driver is negative-pressure vacuum energy density. The inflation concept was theorized by physicist Alan Guth in 1980.
One homogeneity-issue that the concept of such inflation addresses is termed the horizon problem: that without some such mechanism, different regions of the early universe would not be casually connected given the speed of light was insufficient to get from some point in the earlier universe to each of the different parts, within the age of the universe (at the time). The smoothness of the cosmic microwave background from every direction must result from some common origin that couldn't exist, given a Big Bang without something like inflation. The theory is it that such rapid inflation distributed the common "seeds" of later events that wee see happening everywhere uniformly.
Another issue inflation addresses is the flatness problem: the question of why the universe shows so little curvature.