  The quantum gravity path integral's measure can be written as the product of
classical backgrounds and quantum fluctuations about each background. After
proving that fluctuations about the background do not diffuse in Hilbert space
and obey the laws of many-body statistics, their probability distributions,
entropy, and expected background are determined. This background obeys
expectation-valued Einstein equations and features an entropy-based positive
cosmological constant. From the fluctuation probability distributions, a finite
temperature, R-squared, quantum gravity path integral is constructed whose
action presents an interaction picture of quantum gravity that `moves with' the
expected background in Hilbert space. Within this interaction picture of
quantum fluctuations about an expected background, the fields required to
describe quantum gravity have been transformed into `ordinary' quantum fields
propagating on this `rigid' or `fixed' expected background. Back-reaction has
been fully accounted for, and the quantum formulation is manifestly background
independent.
