  I present a theory of quantum gravity based on the principle of gravitational
energy fluctuations. Gravitational energy fluctuations -- gravitons -- are
responsible for elastic scattering of subatomic particles. Such scattering
corresponds to complimentary force -- graviton scattering force -- arising in
gravitational interaction in addition to Newtonian gravity. The strength of the
graviton scattering force is proportional to the graviton scattering
probability. Unlike Newtonian gravity the graviton scattering force follows the
1/r law and dominates the former on cosmological scale in the limit of low
orbital accelerations. Similarly to Modified Newtonian Dynamics the quantum
gravity accounts for variations in observed M/L ratios of diverse stellar
systems ranging from dwarf spheroid galaxies to X-ray galaxy clusters without
requiring an invisible matter (which is still required by MOND in X-Ray cluster
cores). Unlike MOND the presented theory neither violates cornerstone Newton
Laws nor suffers from the ambiguity of acceleration frames while enjoying vast
experimental evidence usually cited in favor of MOND. To ascertain the validity
of the presented theory I have examined the predictions of quantum gravity for
dwarf spheroid, ordinary and giant elliptic galaxies, and X-ray clusters. In
all cases quantum gravity yields M/L ratios and scaling relations consistent
with observations. Quantum gravity accounts for the tilt of the Fundamental
Plane of elliptical galaxies erasing the differences in M/L vs. luminosity
relations for faint and bright ellipticals, which cannot be easily explained by
CDM model. Lastly, by analyzing the behavior of the gravitational energy
fluctuations in the limit of high matter density expected in the early Universe
I show that primordial inflation and dark energy (i.e. non-zero cosmological
constant) arise as natural effects of quantum gravity in the expanding
Universe.

General Relativity and Quantum Cosmology