Narrow Results

We study a minimally coupled tachyon field rolling down to its ground state on the FRW brane. We construct tachyonic potential which can implement power law inflation in the brane world cosmology. The potential turns out to be V₀ϕ^-1 on the brane and reduces to inverse square potential at late times when brane corrections to the Friedmann equation become negligible. We also do similar exercise with a normal scalar field and discover that the inverse square potential on the brane leads to power law inflation.

We find exact rolling tachyon solutions in DBI type noncommutative field theory with constant open string metric and noncommutative parameter on an unstable Dp-brane. Their functional shapes span all possible homogeneous rolling tachyon solutions, i.e. they are hyperbolic-cosine, hyperbolic-sine, and exponential under 1/cosh runaway NC tachyon potential. Even if general DBI type NC electric field is turned on, only constant electric field satisfies equations of motion and again exact homogeneous rolling tachyon solutions are obtained.

The property and gravitational field of global monopole of tachyon are investigated in a four-dimensional static space–time. We give an exact solution of the tachyon field in the flat space–time background. Using the linearized approximation of gravity, we get the approximate solution of the metric. We also solve analytically the coupled Einstein and tachyon field equations which is beyond the linearized approximation to determine the gravitational properties of the monopole solution. We find that the metric of tachyon monopole represents an asymptotically AdS space–time with a small effective mass at the origin. We show that this relatively tiny mass is actually negative, as it is in the case of ordinary scalar field.