exponential expansion (3 facts) - Extremely rapid expansion. "Exponential" is a mathematical term that precisely defines the rate of expansion. For example, a balloon that doubles its size every second is expanding exponentially. By contrast, a balloon whose radius is one inch after one second, two inches after two seconds, three inches after three seconds, and so on, is expanding linearly with time, rather than exponentially. According to the inflationary universe model, the early universe went through a brief period of exponential expansion, during which its size increased enormously., An expansion described by a fixed doubling time. The size doubles after one doubling time, quadruples after two doubling times, octuples after three doubling times, etc.