  A framework of quantum spacetime reference frame is proposed and reviewed, in
which the quantum spacetime at the Gaussian approximation is deformed by the
Ricci flow. At sufficient large scale, the Ricci flow not only smooths out
local small irregularities making the universe a homogeneous and isotropic
Friedmann-Robertson-Walker metric, but also develops a local singularity at the
physical-time origin. Due to the phenomenological suppression of the
non-Gaussian primordial perturbations, we assume the validity of the Ricci flow
applying to the high curvature region near the local singularity of the early
universe. The no-local-collapsing theorem of Perelman ensures the existence of
a canonical neighborhood around the large curvature pinching point, which
resembles a gradient shrinking Ricci soliton (GSRS) solution of the Ricci flow.
Without any inflaton field, the GSRS naturally reproduces an exact inflationary
deSitter universe near the singularity at the leading order. Without any
rolling-down behavior of inflaton, the deviation from exact deSitter described
by the "slow roll parameters" can be calculated by a small deviation from the
singular flow-time via the Ricci flow, and the primordial perturbations can
also be studied on the GSRS background, the power spectrum of the scalar
perturbation agrees with present observations, and the one of the tensor
perturbation is predicted too small to be detectable than the standard
inflation. The previous treatment of the cosmological constant and the
effective gravity are also briefly reviewed in the framework. So we argue that
the Ricci flow provides us a possible unified view and treatment of the late
epoch accelerating expansion and early epoch inflation of the universe without
introducing dark energy or inflaton (dark energy of the second kind).
