If that's the case, then wouldn't we have some kind of special background radiation? Penrose stated that some things must be visible through background radiatio

If that's the case, then wouldn't we have some kind of special background radiation? Penrose stated that some things must be visible through background radiation right? (something with black holes of the preveious aeon) If that's the case, then we might be able to observe that state and try to workout, whether we get to that same state.