The Reduced Relativistic Gas (RRG) model was introduced by A. Sakharov in 1965 for deriving the cosmic microwave background (CMB) spectrum. It was recently reinvented by some of us to achieve an interpolation between the radiation and dust epochs in
the evolution of the Universe. This model circumvents the complicated structure of the Boltzmann-Einstein system of equations and admits a transparent description of warm-dark-matter effects. It is extended here to include, on a phenomenological basis, an out-of-equilibrium interaction between radiation and baryons which is supposed to account for relevant aspects of pre-recombination physics in a simplified manner. Furthermore, we use the tight-coupling approximation to explore the influence of both this interaction and of the RRG warmness parameter on the anisotropy spectrum of the CMB. The predictions of the model are very similar to those of the {Lambda}CDM model if both the interaction and the dark-matter warmness parameters are of the order of $10^{-4}$ or smaller. As far as the warmness parameter is concerned, this is in good agreement with previous estimations on the basis of results from structure formation.
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 $Lambda CDM$.
