Propagation Constraints and Classical Solutions in K-essence Like Theories

TL;DR

This paper investigates the constraints on scalar field theories with higher derivatives, focusing on cosmological and static solutions, ensuring hyperbolicity and causality, and analyzing their physical properties and implications.

Contribution

It provides new constraints on interactions and boundary conditions in higher-derivative scalar theories, ensuring hyperbolicity and causality, with applications to cosmology and static solutions.

Findings

Identifies classes of models where tachyon matter behaves like dust at large times.

Shows causality constrains boundary conditions for static solutions.

Finds static solutions with negative energy density at the origin.

Abstract

We consider two examples of solutions of the equations of motion of scalar field theories with higher derivatives. These are the cosmology of the rolling tachyon and static spherically symmetric solutions of the scalar field in flat space. By requiring that the field equations always be hyperbolic and that the speed of propagation of the small fluctuations are not superluminal, we find constraints on the form of the allowed interactions in the first case and on the choice of boundary conditions in the latter. For the rolling tachyon we find a general class of models which have the property that at large times the tachyon matter behaves essentially like a non-relativistic gas of dust. For the spherically symmetric solutions we show how causality influences the choice of boundary conditions and those which are finite at the origin are shown to have negative energy density there.