  Reduced Relativistic Gas (RRG) is a useful approach to describe the warm dark
matter (WDM) or the warmness of baryonic matter in the approximation when the
interaction between the particles is irrelevant. The use of Maxwell
distribution leads to the complicated equation of state of the J\"{u}ttner
model of relativistic ideal gas. The RRG enables one to reproduce the same
physical situation but in a much simpler form. For this reason RRG can be a
useful tool for the theories with some sort of a "new Physics". On the other
hand, even without the qualitatively new physical implementations, the RRG can
be useful to describe the general features of WDM in a model-independent way.
In this sense one can see, in particular, to which extent the cosmological
manifestations of WDM may be dependent on its Particle Physics background. In
the present work RRG is used as a complementary approach to derive the main
observational exponents for the WDM in a model-independent way. The only
assumption concerns a non-negligible velocity $v$ for dark matter particles
which is parameterized by the warmness parameter $b$. The relatively high
values of $b$ ( $b^2\gtrsim 10^{-6}$) erase the radiation (photons and
neutrinos) dominated epoch and cause an early warm matter domination after
inflation. Furthermore, RRG approach enables one to quantify the lack of power
in linear matter spectrum at small scales and in particular, reproduces the
relative transfer function commonly used in context of WDM with accuracy of
$\lesssim 1\%$. A warmness with $b^2\lesssim 10^{-6}$ (equivalent to $v\lesssim
300 km/s$) does not alter significantly the CMB power spectrum and is in
agreement with the background observational tests.
