The model of low-energy quantum gravity by the author is based on
the conjecture about an existence of the graviton background. An
interaction of photons and moving bodies with this background
leads to small additional effects having essential cosmological
consequences. In the model, redshifts of remote objects and the
dimming of supernovae 1a may be interpreted without any expansion
of the Universe and without dark energy. Some of these
consequences are discussed and confronted with supernovae 1a, long
GRBs, and QSOs observations in this paper. It is shown that the
two-parametric theoretical luminosity distance of the model fits
observations with high confidence levels (100% for the SCP Union
2.1, 43% for JLA compilations, 99.81% for long GRBs, and 13.73% for
quasars), if all data sets are corrected for no time dilation.
These two parameters are computable in the model.