A new rolling tachyon solution of cubic string field theory

We present a new analytic time dependent solution of cubic string fieldtheory at the lowest order in the level truncation scheme. The tachyon profilewe have found is a bounce in time, a $C^{\infty}$ function which represents analmost exact solution, with an extremely good degree of accuracy, of theclassical equations of motion of the truncated string field theory. Such afinite energy solution describes a tachyon which at $x^0=-\infty$ is at themaximum of the potential, at later times rolls toward the stable minimum andthen up to the other side of the potential toward the inversion point andthenback to the unstable maximum for $x^0\to+\infty$. The energy-momentumtensor associated with this rolling tachyon solution can be explicitlycomputed. The energy density is constant, the pressure is an even function oftime which can change sign while the tachyon rolls toward the minimum of itspotential. A new form of tachyon matter is realized which might be relevant forcosmological applications.Comment: 18 pages, 4 figure