An interesting notion about inflation.

[zeromodz]

I was thinking about how big the universe got after inflation occurred. Then I thought about Hubble's parameter.

Ho = V / d (At the big bang, the distance between the two edges of the universe were zero)
Ho = V / 0
Ho = ∞ km*mpc / s

Therefore, the rate of the expansion must have been infinite once the universe started to expand. Wouldn't that mean the universe now must be infinite in size?

 

[LURCH]

If the rate of expansion is infinite, then the universe became infinitely large in zero nanoseconds, and has become infinitely larger every zero nanoseconds since.

This is the problem when we try to divide by zero, which is why the current mathematical models can't take us to the first instant of the BB (or the center of a BlackHole).

 

[Chronos]

Infinities are generally regarded as mathematical artifacts - where theory, not reality, has broken down.

 

[twofish-quant]

Therefore, the rate of the expansion must have been infinite once the universe started to expand. Wouldn't that mean the universe now must be infinite in size?

No.

Take a piece of graph paper and draw a step function. The rate of expansion is infinite at the step, but the function is finite.

You see these sorts of infinities all the time, and there are a lot of mathematical tools for detailing with them. There are also infinities that "you can deal with" and infinities that really mess things up.