  The main features of an alternative model of redshifts are described here.
The model is based on conjectures about an existence of the graviton background
with the Planckian spectrum and a super-strong character of quantum
gravitational interaction. This model is connected with the assumed quantum
mechanism of gravity. A behavior of two theoretical functions of a redshift $z$
in this model - the geometrical distance $r(z)$ and the luminosity distance
$D_{L}(z)$ - and an existence of two different cosmological horizons for any
observer are discussed.
