The Tachyon in a Linear Expanding Universe

TL;DR

This paper explores the behavior of tachyon fields in a dynamic universe, revealing how their properties depend on background parameters and uncovering conditions for masslessness.

Contribution

It models tachyon and dilaton fields in an expanding universe using conformal field theory techniques, linking their quantization to mathematical structures like Chebyshev polynomials.

Findings

Tachyon can be massless at a specific level k=1.

Spatial tachyon modes are described by Chebyshev polynomials.

Quantization conditions relate the universe's radius, dilaton, and tachyon.

Abstract

We investigate the tachyon coupling in a static Robertson--Walker like metric background. For a tachyon and dilaton field which are only time dependent one can rewrite this model as a SU(2) Wess--Zumino--Witten model and a scalar Feigin--Fuchs theory. In this case the restriction to a real exponential tachyon field fixes the level $k$ of the Wess--Zumino--Witten model. For a spatially dependent tachyon the world radius and the dilaton are quantized in terms of $k$ and the tachyon by two integers, i.e. one has a discrete set of fields. The spatial part of the tachyon is given by Chebyshev polynomials of the second kind. An investigation of the tachyon mass shows that the tachyon is massless for $k=1$.