Caustics in Tachyon Matter and Other BornInfeld Scalars
Abstract
We consider scalar BornInfeld type theories with arbitrary potentials V(T) of a scalar field T. We find that for models with runaway potentials V(T) the generic inhomogeneous solutions after a short transient stage can be very well approximated by the solutions of a HamiltonJacobi equation that describes free streaming wave front propagation. The analytic solution for this wave propagation shows the formation of caustics with multivalued regions beyond them. We verified that these caustics appear in numerical solutions of the original scalar BI nonlinear equations. Our results include the scalar BI model with an exponential potential, which was recently proposed as an effective action for the string theory tachyon in the approximation where highorder spacetime derivatives of T are truncated. Since the actual string tachyon dynamics contain derivatives of all orders, the tachyon BI model with an exponential potential becomes inadequate when the caustics develop because high order spatial derivatives of T become divergent. BI type tachyon theory with a potential decreasing at large T could have interesting cosmological applications because the tachyon field rolling towards its ground state at infinity acts as pressureless dark matter. We find that inhomogeneous cosmological tachyon fluctuations rapidly grow and develop multiple caustics. Any considerations of the role of the tachyon field in cosmology will have to involve finding a way to predict the behavior of the field at and beyond these caustics.
 Publication:

Journal of High Energy Physics
 Pub Date:
 September 2002
 DOI:
 10.1088/11266708/2002/09/026
 arXiv:
 arXiv:hepth/0208019
 Bibcode:
 2002JHEP...09..026F
 Keywords:

 High Energy Physics  Theory;
 Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 21 pages, 5 figures