  In this paper, we explore an idea of having Newton's constant change its
value depending on the curvature scale involved. Such modification leads to a
particular scalar-tensor gravity theory, with the Lagrangian derived from
renormalization group (RG) flow arguments. Several of the well-known f(R)
modified gravity models have remarkably simple description in terms of the
infrared renormalization group, but not the "designer" types in general. We
find that de Sitter-like accelerated expansion can be generated even in the
absence of cosmological constant term, entirely due to running of the Newton's
constant. In hopes of tackling the problem of cosmological constant's
smallness, we explore the flows which are capable of generating exponential
hierarchy between infrared and ultraviolet scales, and investigate cosmological
evolution in the models thus derived.
