  Recently we suggested a reformulation of General Relativity which completely
sequesters from gravity {\it all} of the vacuum energy from a protected matter
sector, assumed to contain the Standard Model. Here we elaborate further on the
mechanism, presenting additional details of how it cancels all loop corrections
and renders all contributions from phase transitions automatically small. We
also consider cosmological consequences in more detail and show that the
mechanism is consistent with a variety of inflationary models that make a
universe big and old. We discuss in detail the underlying assumptions behind
the dynamics of our proposal, and elaborate on the relationship of the physical
interpretation of divergent operators in quantum field theory and the apparent
`acausality' which our mechanism seems to entail, which we argue is completely
harmless. It is merely a reflection of the fact that any UV sensitive quantity
in quantum field theory cannot be calculated from first principles, but is an
input whose numerical value must be measured. We also note that since the
universe should be compact in spacetime, and so will collapse in the future,
the current phase of acceleration with $w_{DE}\approx-1$ is just a transient.
This could be tested by future cosmological observations.
