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 the 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, 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)violation of strong energy condition at present for $w_0 < -1/3$;2)locallystable(i\mathrm{.}e\mathrm{.}$c_s^2\geq 0$); 3)causality is guaranteed ($c_s\le 1$). Considering the case that $w_0$ and $c_s^2$ are constants, we find that there is a large parameter space of $(w_0,c_s^2,{\mathrm{\Omega }}_{x0})$ in which the model universe is consistent with the age of the universe and the observations of distant Type I supernovae.