Our universe seems to be dominated by radiation at early times, and
positive vacuum energy at late times.  Taking the symmetry and
analyticity properties of such a spacetime seriously leads to a new
formula for the gravitational entropy of our universe, and a picture
in which the Big Bang may be regarded as a kind of mirror.

I will explain how this line of thought suggests new explanations for
a number of observed properties of the universe, including: its
homogeneity, isotropy and flatness; the arrow of time (i.e. the fact
that entropy increases *away* from the bang); several properties of
the primordial perturbations; the nature of dark matter (which, in
this picture, is a right-handed neutrino, radiated from the early
universe like Hawking radiation from a black hole); the origin of the
primordial perturbations; and even the existence of three generations
of standard model fermions.  I will discuss some observational
predictions that will be tested in the coming decade, and some key
open questions.