  In this population synthesis work we study a variety of possible origin
channels of supernovae type Ia (SNe Ia) Among them mergers of carbon-oxygen
(CO) and oxygen-neon (ONe) white dwarfs (WDs) under the influence of
gravitational waves are considered as the primary channel of SNe Ia formation.
We estimated frequencies of mergers of WDs with different chemical compositions
and distributions of masses of merging WDs. We computed the dependence of the
ratio of merger frequencies of ONe and CO WDs as primaries in corresponding
binaries on time. The scatter of masses of considered sources (up to the factor
$1.5-2$) of SNe Ia is important and should be carefully studied with other
sophisticated methods from theoretical point of view. Our ``game of
parameters'' potentially explains the increased dimming of SNe Ia in the
redshift range $z\approx 0.5-1$ by the changes in the ratio of ONe and CO WDs,
i.e., to describe the observed accelerated expansion of the Universe in terms
of the evolution of properties of SNe Ia instead of cosmological explanations.
This example shows the extreme importance of theoretical studies of problems
concerning SNe Ia, because evolutionary scenario and parameter games in nature
potentially lead to confusions in their empirical standardization and,
therefore, they can influence on cosmological conclusions.
