  We consider the problem of matching two spacetimes, the previous and present
aeons, in the Conformal Cyclic Cosmology model. The common boundary between
them inherits two sets of constraints -- one for each solution of the Einstein
field equations extended to the conformal boundaries. The previous aeon is
assumed to be an asymptotically de Sitter spacetime, so the standard conformal
formulation of the Einstein field equations suffice to derive the constraints
on the future null infinity. For the future aeon, which is supposed to evolve
from an initial singularity, they are obtained with the use of the Bach
equation. This equation is regular at the past conformal infinity for
conformally flat and conformally Einstein spacetimes, so we will mostly focus
on them here. An example of the electrovacuum spacetime which does not fall
into this class and has regular conformal Bach tensor will be discussed in the
appendix.
