I've been thinking recently (in part inspired by Penrose and other recursive universe theories): what if we can effect the trajectory of this current universe such that the next universe that is created has definable properties. As a highly improbable example I use only to spur imagination, what if we could control the next big bang so precisely that a solar system exactly like ours would exist containing humans just like us.

That would lead me to speculate that if we were looking for messages from the previous universe (in the style of the movie/book Contact) then we should look to the signature of the background radiation (CMB). Imagine a previous universe left us instructions there to help us achieve this, and perhaps therefore to achieve some objective that spans multiple universes (i.e. some objective too large to complete within the lifespan of a single universe).

If that isn't a sci-fi book then it should be. Also maybe an interesting area for legit academic study (e.g. how to imprint instructions in the CMB to pass along to future universes).