  The quantization of circular strings in an anti-de Sitter background
spacetime is performed, obtaining a discrete spectrum for the string mass. A
comparison with a four-dimensional homogeneous and isotropic spacetime coupled
to a conformal scalar field shows that the string radius and the scale factor
have the same classical solutions and that the quantum theories of these two
models are formally equivalent. However, the physically relevant observables of
these two systems have different spectra, although they are related to each
other by a specific one-to-one transformation. We finally obtain a discrete
spectrum for the spacetime size of both systems, which presents a nonvanishing
lower bound.
