Finite temperature R-squared quantum gravity

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.