Cosmology with x-matter

Motivated by the possibility of H(0)t(0) > 1 (where H-0 and t(0) are the Hubble parameter and the age of the Universe, respectively), we investigate cosmology including x-matter. x-matter is expressed by the equation of state p(x) = w(0) rho(x0) + c(s)(2)(rho(x) - rho(x0)), where p(x), rho(x) and rho(x0) are the pressure and the density of x-matter and the density at present, respectively. w(0) and c(s)(2) are functions of rho(x) in general. x-matter has the most general form of the equation of state which is characterized by (1) the violation of the strong energy condition at present for w(0) < - 1/3; (2) being locally stable (i.e. c(s)(2) greater than or equal to 0); and (3) having a guaranteed causality (c(s) less than or equal to 1) Considering the case in w(0) and C-s(2) are constants, we find that there is a large parameter space of (omega(0), c(s)(2), Omega(x0)) in which the model universe is consistent with the age of the Universe and the observations of distant Type I supernovae.