Caustics in Tachyon Matter and Other Born-Infeld Scalars

By Gary N. Felder, Lev Kofman, A. Starobinsky. 2002

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We consider scalar Born-Infeld 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 Hamilton-Jacobi equation that describes free streaming wave front propagation. The analytic solution for this wave propagation shows the formation of caustics with multi-valued regions beyond them. We verified that these caustics appear in numerical solutions of the original scalar BI non-linear 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 high-order 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1d93b426fc22153b96ab894180b9558e8094127e

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Citations in the corpus

DBI in the sky (2004, background): “…dynamical processes to be worked out in our model, such as reheating, formation of cosmic strings, isocurvature perturbations in the case with light KK and χ modes, and the effects of our strongly nonlinear evolution at very late times (which may be similar to “tachyon matter” [38][39]).”
k-Essence, superluminal propagation, causality and emergent geometry (2007, background): “Finally let us note that even well-posed Cauchy problem cannot guarantee the global existence of the unique solution for nonlinear system of the equations of motion: for example, the solution can develop caustics [58] or can become multi-valued [61].”
Tachyon effective actins in open string theory (2003, background): “1) encode non-trivial information about the decay of higher dimensional branes into lower dimensional ones; in particular, they contain information about the relative velocities of the lower dimensional branes created in the process of tachyon condensation [24,25].”
Haloes of k-essence (2005, methodology): “In this work, we extend the analysis of structure formation in k-essence models beyond the perturbative regime [22, 23]; in partic-”
Dust of dark energy (2010, background): “[15] on caustics in Sen’s string-theoretical tachyon matter [16, 17] and Ref.”
Comments on Cosmological Singularities in String Theory (2002, methodology): “All this is consistent with the general picture presented in [48] and in equation (6.”
On the extra mode and inconsistency of Hořava gravity (2009, unknown): “there are space-time regions where the fluid velocity is ill-defined (see [17] for discussion of this topic in the context of field theory models of dark matter).”