The volume expansion of the universe does display non-linear behavior if one plots its volume increase against time. A typical non-linear curve is produced which is similar in nature to the exponential decay curves that reflect all entropic processes.
If the universe is expanding at a uniform rate (galaxy recession velocity is neither increasing nor decreasing) then the volume of space is increasing as a cubic function rather than exponential. This would mean that the rate of volume expansion is somewhat faster than if following an exponential curve.
For the volume of space to be increasing exponentially would require that the rate of spatial expansion be decelerating slightly relative to a uniform velocity. This is not an impossible occurrence if two conditions are assumed. The first assumption is that our ability to measure the actual rate of expansion is only approximately correct. The universe could be expanding slightly slower or faster than a perfectly uniform rate. It may not be a linear function. The other assumption is that the universe is closed and therefore cyclic, undergoing periodic expansion and contraction. In this situation, depending upon where on the curve we presently find ourselves, the rate of expansion could be either faster or slower than a straight linear function. If one compares a cyclical curve (sine wave) with a straight linear function expression, as illustrated below, the rate of expansion could be faster or slower than that linear rate.
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