Effects of velocity dispersion of dark matter particles on the CMB TT power spectrum and on the matter linear power spectrum are investigated using a modified CAMB code. Cold dark matter originated from thermal equilibrium processes does not produce
appreciable effects but this is not the case if particles have a non-thermal origin. A cut-off in the matter power spectrum at small scales, similar to that produced by warm dark matter or that produced in the late forming dark matter scenario, appears as a consequence of velocity dispersion effects, which act as a pressure perturbation.
We investigate the Tolman-Oppenheimer-Volkoff equations for the generalized Chaplygin gas with the aim of extending the findings of V. Gorini, U. Moschella, A. Y. Kamenshchik, V. Pasquier, and A. A. Starobinsky [Phys. Rev. D {bf 78}, 064064 (2008)].
We study both the standard case, where we reproduce some previous results, and the phantom case. In the phantom case we show that even a superluminal group velocity arising for $alpha > 1$ cannot prevent the divergence of the pressure at a finite radial distance. Finally, we investigate how a modification of the generalized Chaplygin gas equation of state, required by causality arguments at densities very close to $Lambda$, affects the results found so far.
We exploit the gauge-invariant formalism to analyse the perturbative behaviour of two cosmological models based on the generalized Chaplygin gas describing both dark matter and dark energy in the present Universe. In the first model we consider the g
eneralized Chaplygin gas alone, while in the second one we add a baryon component to it. We extend our analysis also into the parameter range $alpha > 1$, where the generalized Chaplygin gas sound velocity can be larger than that of light. In the first model we find that the matter power spectrum is compatible with the observed one only for $alpha < 10^{-5}$, which makes the generalized Chaplygin gas practically indistinguishable from $Lambda$CDM. In the second model we study the evolution of inhomogeneities of the baryon component. The theoretical power spectrum is in good agreement with the observed one for almost all values of $alpha$. However, the growth of inhomogeneities seems to be particularly favoured either for sufficiently small values of $alpha$ or for $alpha gtrsim 3$. Thus, it appears that the viability of the generalized Chaplygin gas as a cosmological model is stronger when its sound velocity is superluminal. We show that in this case the generalized Chaplygin gas equation of state can be changed in an unobservable region in such a way that its equivalent $k$-essence microscopical model has no problems with causality.
