If inflation is an exponential expansion, is the exponent known? Inflation is often called exponential expansion.
I can't seem to find what that exponent is. Is it 2, or 20, or completely unknown?
 A: In cosmic inflation, the Friedmann scale factor $a(t)$ of the universe doesn’t grow as some power of the time, such as $a\sim t^2$ or $a\sim t^{20}$. These are not exponential expansions at all. Exponential expansion means that time appears in the exponent: $a\sim e^{t/\tau}$ or $a\sim 2^{t/\tau}$ or $a\sim 10^{t/\tau}$ or whatever you prefer to use as the base to be exponentiated. Physicists normally use $e$, the base of the natural logarithms, so let’s go with $e^{t/\tau}$. Using a different base just changes $\tau$ a bit.
In inflation, the characteristic time $\tau$ for the scale factor to increase by a factor of $e$ (which is about 2.7) is fantastically small: typically around a trillionth of a trillionth of a trillionth of a second! That’s $10^{-36}$ seconds. In various inflation models it might be bigger or smaller by a few orders of magnitude, but it is always fantastically small.
So in just $10^{-36}$ seconds everything in the universe got 2.7 times further apart. In another $10^{-36}$ seconds it grew by another factor of 2.7. In another $10^{-36}$ seconds it grew by another factor of 2.7. After 60 $e$-foldings the scale factor is 100,000,000,000,000,000,000,000,000 times larger, and this took just, say, 60 trillionths of a trillionth of a trillionth of a second.
It is truly one of the most astounding ideas in the history of physics.
