  Recently, the variation of the Planck mass in the General Relativistic
Einstein-Hilbert action was proposed as a self-tuning mechanism of the
cosmological constant, preventing Standard Model vacuum energy from freely
gravitating and enabling an estimation of the magnitude of its observed value.
We explore here new aspects of this proposal. We first develop an equivalent
Einstein-frame formalism to the current Jordan-frame formulation of the
mechanism and use this to highlight similarities and differences of self-tuning
to the sequestering mechanism. We then show how with an extension of the local
self-tuning action by a coupled Gauss-Bonnet term and a companion four-form
field strength, graviton loops can be prevented from incapacitating the
degravitation of the Standard Model vacuum energy. For certain cases, we
furthermore find that this extension can be recast as a Horndeski scalar-tensor
theory and be embedded in the conventional local self-tuning formalism. We then
explore the possibility of a unification of inflation with self-tuning. The
resulting equations can alternatively be used to motivate a multiverse
interpretation. In this context, we revisit the coincidence problem and provide
an estimation for the probability of the emergence of intelligent life in our
Universe as a function of cosmic age, inferred from star and terrestrial planet
formation processes. We conclude that we live at a very typical epoch, where we
should expect the energy densities of the cosmological constant and matter to
be of comparable size. For a dimensionless quantity to compare the emergence of
life throughout the cosmic history of different universes in an anthropic
analysis of the multiverse, we choose the order of magnitude difference of the
evolving horizon size of a universe to the size of its proton as the basic
building block of atoms, molecules, and eventually life. (abridged)
