Can we have bubbles of the tenth dimension in our universe? If the gap between the branes in the Big Bounce theory is the 10th dimension, and branes have wrinkles as they collide, can our universe have 'bubbles' in the 10th dimension? This is in reference to the Ekpyrotic theory or Big Bounce theory formulated by Dr Neil Turok and Dr Paul Steinhardt. 
 A: According to higher dimensional theories, like String Theory, our universe IS ten dimensional (actually 11, considering M-theory). The missing dimensions are compact and very small, therefore we cannot see them unless we probe the universe at very high energy scale, like inside a black hole or in Big Bang-like event.
A: Our universe is considered a bubble, or subset, of a higher dimensional space, which includes 'parallel' worlds and different universes https://phys.org/news/2014-12-universe-dimensions.html
So, what the question comes to mean is can such 'other places' influence 'our place'. And the answer is, at the energies and scales string theory is needed. Which is, at or before the big bang, in black holes, and around the Planck scale. Higher dimensions may also be responsible for dark energy https://www.newscientist.com/article/dn12261-is-dark-energy-lurking-in-hidden-spatial-dimensions/
It seems to me it is better to think of an 'intrusion' from a more fundamental reality, than a bubble within our universe. Of neccesity to be 'in' our universe, they could only be lower dimensional effects of higher dimensional phenomena. 
