  The three cosmological conjectures to which our work refers are: the
phenomenon called geodesic incompleteness, the physical gravitational
$\theta_G$-term that would characterize the 1-parameter family of inequivalent
vacua of quantum gravidynamics, and the hypothesis of multiversality, more
specifically, a zero-energy multiverse.
  The known cosmological phenomenology leads under plausible assumptions to
theorems which establish that the universe is past incomplete. Here, starting
from Wilczek's definition of multiverse (a larger physical structure of which
the universe forms part) and that spacetime is much larger than the observable
universe, in a new sense suggested by these theorems, we place the observable
universe, labelled by $U_{\theta_G^{(1)}}$, within a multiverse ensemble,
$\{U_{\theta_G}\}$. Its topological $\theta_G^{(1)}$-term would characterize
the observable universe from the Planck epoch until the present time, and it
could have physical effects in, for example, black-hole physics.
  Our proposal is therefore a possible framework for a multiverse quantum
cosmology, in which the temporal parameters (see figures in the main text)
start from a "timeless multiverse big bang" (TLMBB), where all members of the
multiverse ensemble, $\{U_{\theta_G}\}$, disappear, together with their
corresponding classical spacetimes. Since quantum cosmology can be viewed as
one attempt among many to face with the question of finding a gravitational
quantum theory, if the TLMBB were the appropriate ground to define the physical
or mathematical underlying structure of quantum cosmology, then multiversality
could come to have a predictive power within our observable universe.
