We use the framework of a recently proposed model of reduced relativistic gas (RRG) to obtain the bounds for $Omega$s of Dark Matter and Dark Energy (in the present case, a cosmological constant), taking into consideration an arbitrary warmness of Da
rk Matter. An equivalent equation of state has been used by Sakharov to predict the oscillations in the matter power spectrum. Two kind of tests are accounted for in what follows, namely the ones coming from the dynamics of the conformal factor of the homogeneous and isotropic metric and also the ones based on linear cosmic perturbations. The RRG model demonstrated its high effectiveness, permitting to explore a large volume in the space of mentioned parameters in a rather economic way. Taking together the results of such tests as Supernova type Ia (Union2 sample), $H(z)$, CMB ($R$ factor), BAO and LSS (2dfGRS data), we confirm that $La$CDM is the most favored model. At the same time, for the 2dfGRS data alone we found that an alternative model with a very small quantity of a Dark Matter is also viable. This output is potentially relevant in view of the fact that the LSS is the only test which can not be affected by the possible quantum contributions to the low-energy gravitational action.
We study the matter density fluctuations in the running cosmological constant (RCC) model using linear perturbations in the longitudinal gauge. Using this observable we calculate the growth rate of structures and the matter power spectrum, and compar
e them with the $SDSS$ data and other available data of the linear growth rate. The distribution of collapsed structures may also constraints models of dark energy. It is shown that RCC model enhances departures from the $Lambda CDM$ model for both cluster number and cumulative cluster number predicted. In general increasing the characteristic parameter $ u$ leads to significant growth of the cluster number. In general, we found that the theory of perturbations provides a good tool to distinguish the new model $RCC$ of the standard cosmological model $Lambda CDM$.
