  Some results of author's work in a non-geometrical approach to quantum
gravity are reviewed here, among them: a quantum mechanism of classical gravity
giving a possibility to compute the Newton constant; asymptotic freedom at
short distances; interaction of photons with the graviton background leading to
the important cosmological consequences; the time delay of photons due to
interactions with gravitons; deceleration of massive bodies in the graviton
background which may be connected with the Pioneer anomaly and with the problem
of dark matter.
