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We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation-of-state of x-matter which can express a wide range of matter from the pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component in addition to the equation-of-state w₀=pₗ₀/\ₗ₀. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.
Chiba et al. (Sun,) studied this question.