  The continuation of the Liouville conformal field theory to c<=1 is
considered. The viability of an interpretation involving a timelike boson which
is the conformal factor for two-dimensional asymptotically de Sitter geometries
is examined. The conformal bootstrap leads to a three-point function with a
unique analytic factor which is the same as that which appears along with the
fusion coefficients in the minimal models. A corresponding non-analytic factor
produces a well-defined metric on fields only when the central charge is
restricted to those of the topological minimal models, and when the conformal
dimensions satisfy h>(c-1)/24. However, the theories considered here have a
continuous spectrum which excludes the degenerate representations appearing in
the minimal models. The c=1 theory has been investigated previously using
similar techniques, and is identical to a non-rational CFT which arises as a
limit of unitary minimal models. When coupled to unitary matter fields, the
non-unitary theories with c<=-2 produce string amplitudes which are similar to
those of the minimal string.
