Interesting theory.

There must be, as you say, for there to be a background for a fluctuation to occur in, but because it is only a quantum fluctuation that underwent inflation due to a high negative cosmological constant, there is no way for us to tell what the characteristics of that background might have been or be, other than it being capable of having quantum fluctuations with a high negative cosmological constant.

This was why the BICEP-2 results (that later turned out to be wrong) that appeared to show signatures in the B-mode polarization of the CMB of gravity waves that occurred during inflation was such a big deal: it would have proven not only that this scenario is correct, but also that there were other nearby fluctuations undergoing inflation too. We’re still looking for evidence like this, pawing through the PLANCK data.