  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 $k=1$.
