  Our universe seems to be radiation dominated at early times, and vacuum
energy dominated at late times. When we consider the maximal analytic extension
of this spacetime, its symmetries and complex analytic properties suggest a
picture in which spacetime has two sheets, exchanged by an isometry which, in
turn, picks a preferred (CPT-symmetric) vacuum state for quantum fields on the
spacetime. Previously (arXiv:1803.08928, arXiv:1803.08930), we showed how this
line of thought provides new explanations for dark matter, the
matter-antimatter asymmetry, the absence of primordial vector and tensor
perturbations, and the {\it phase} of the primordial scalar perturbations; and
additional testable predictions. In this paper, we develop this picture in
several respects and, in particular, point out that it also provides a new
explanation for why the thermodynamic arrow of time points away from the bang.
