What Was the Initial Size of the Big Bang?

[rogerl]

How big is the initial size of the Big Bang... inside a Planck length? Can it fit inside? Or as big as an egg? Or a kilometer?

 

[bcrowell]

There are two kinds of cosmological models. One is spatially infinite and always has been spatially infinite. The other is spatially finite and always has been. Current measurements of curvature are statistically consistent with flatness, which puts us on the fence between these two cases.

In either case, it's not valid to imagine the Big Bang as an explosion with a certain size that happened against a backdrop of empty space. In all cosmological models, the Big Bang is a process in which space itself stretches out. Every region of space on a cosmological scale increases its own volume over time. In the early universe, all regions of space were uniformly filled with hot matter and radiation.

In the spatially infinite case, the universe has been spatially infinite at all times, so there is no way to measure the diameter or volume of the Big Bang with a real number.

In the spatially finite case, the universe wraps around on itself spatially, like a sphere. There is no edge. It does have a well-defined volume at any given time. According to general relativity, this volume approaches zero in the limit as time approaches zero. GR does not describe t=0 itself as a moment in time.

The above picture of the finite case would presumably be modified by quantum effects at early times. We don't have a theory of quantum gravity, but there is only one length scale that you can make by combining Planck's constant with c and G, and that's the Planck scale.

So in summary, there are three possible answers to the question: infinity, approaching zero, or the Planck scale.

A somewhat different question is the initial size of the *observable* universe. The current radius of the observable universe (i.e., the region of space from which light has had time to reach us since the Big Bang) is about 46 billion light years. (This is greater than the result you get by naively multiplying the age of the universe by c, because space has been expanding.) Yesterday the observable universe was smaller, and tomorrow it will be bigger. In all cosmological models (in GR), the radius of the observable universe for an observer at time t approaches zero as t approaches zero (although of course there were no actual observers present in the very early universe). A hypothetical theory of quantum gravity might change this answer to the Planck length.

[EDIT] Fixed a mistake in my original answer, then rewrote it from scratch.