A Low-Density Closed Universe

Matter with an equation of state $p=-\rho /3\mathrm{}$ may arise in certain scalar field theories, and the energy density of this matter decreases as $a^{-2\mathrm{}}$ with the scale factor $a$ of the Universe. In this case, the Universe could be closed but still have a nonrelativistic-matter density ${\Omega }_0<1\mathrm{}$. Furthermore, the cosmic microwave background could come from a causally connected region at the other side of the Universe. This model is currently viable and might be tested by a host of forthcoming observations.