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We investigate the properties of charge neutral equilibrium cold quark matter within the Nambu Jona-Lasinio model. The calculations are carried out for di erent ratios of coupling constants characterizing the vector and scalar 4 fermion interaction, xi = GV /GS. It is shown that for xi < 0.4 matter is self bound and for xi < 0.65 it has a first order phase transition of the liquid gas type. The Gibbs conditions in the mixed phase are applied for the case of two chemical potentials associated with the baryon number and electric charge. The characteristics of the quark stars are calculated for xi = 0, 0.5 and 1. It is found that the phase transition leads to a strong density variation at the surface of these stars. For xi = 1 the properties of quark stars show behaviors typical for neutron stars. At >< 0.4 the stars near to the maximum mass have a large admixture of strange quarks in their interiors. PACS number: 14.65.-q, 26.60.+c, 97.10.-q
The lightest supersymmetric particle, most likely the neutralino, might account for a large fraction of dark matter in the Universe. We show that the primordial spectrum of density fluctuations in neutralino cold dark matter (CDM) has a sharp cut-off due to two damping mechanisms: collisional damping during the kinetic decoupling of the neutralinos at about 30 MeV (for typical neutralino and sfermion masses) and free streaming after last scattering of neutralinos. The last scattering temperature is lower than the kinetic decoupling temperature by one order of magnitude. The cut-off in the primordial spectrum defines a minimal mass for CDM objects in hierarchical structure formation. For typical neutralino and sfermion masses the first gravitationally bound neutralino clouds have to have masses above 10 7M . PACS numbers: 14.80.Ly, 98.35.Ce, 98.80.-k, 98.80.Cq