  In order to resolve the cosmological constant problem, the notion of
reference frame is re-examined at the quantum level. By using a quantum
non-linear sigma model (Q-NLSM), a theory of quantum spacetime reference frame
(QSRF) is proposed. The underlying mathematical structure is a new geometry
endowed with intrinsic 2nd central moment (variance) or even higher moments of
its coordinates, which generalizes the classical Riemannian geometry based on
only 1st moment (mean) of its coordinates. The 2nd central moment of the
coordinates directly modifies the quadratic form distance which is the
foundation of the Riemannian geometry. At semi-classical level, the 2nd central
moment introduces a flow which continuously deforms the Riemannian geometry
driven by its classical Ricci curvature, which is known as the Ricci flow. A
generalized equivalence principle of quantum version is also proposed to
interpret the new geometry endowed with at least 2nd moment. As a consequence,
the spacetime is stabilized against quantum fluctuation, and the cosmological
constant problem is resolved within the framework. With an isotropic positive
curvature initial condition, the long flow time solution of the Ricci flow
exists, the accelerating expansion universe at cosmic scale is an observable
effect of the spacetime deformation of the normalized Ricci flow. A
deceleration parameter -0.67 consistent with measurement is obtained by using
the reduced volume method introduced by Perelman. Effective theory of gravity
within the framework is also discussed.
