Re: Could the 'Big Bang' have happened more than once?

Well, yes, the Big Bang could certainly have happened more than once, and 
in more than one place; there is a category of inflationary theories in 
which this is true. However, it doesn't solve the problem of the 
acceleration of the expansion of the universe. 

Why not?

Two reasons: First, as the universe expands, it doesn't expand "into" 
anything; it creates spacetime, along with the fields that characterize it 
in our universe (particular values of the fundamental constants and so 
on), as it expands. Other universes, created in the same way as ours, 
would not be causally connected - we would have no way of knowing they 
were there. They are literally not in the same space as we are, and have 
no way of exerting forces on us.
Second, even if another universe could exert a force on us, it would be in 
a particular direction; as far as we can tell, the acceleration of the 
expansion of the universe is uniform in all directions and therefore 
cannot be due to a single (however massive) universe located in a 
particular direction.

Here are some references about the Big Bang:

Frequently Asked Questions in Cosmology
 
http://www.astro.ucla.edu/~wright/cosmology_faq.html

The Accelerating Expansion of the Universe
 
http://www.space.com/scienceastronomy/generalscience/darkenergy_folo_010410.html


Errors in some popular attacks on the Big Bang
 
http://www.astro.ucla.edu/~wright/errors.html

Hope this helps!