Abstract
Recent observations of high-redshift type Ia supernovae have placed stringent constraints on the cosmological constant \ensuremath{\Lambda}. We explore the implications of these SNe observations for cosmological models in which a classically evolving scalar field currently dominates the energy density of the Universe. Such models have been shown to share the advantages of \ensuremath{\Lambda} models: compatibility with the spatial flatness predicted by inflation; a Universe older than the standard Einstein--de Sitter model; and, combined with cold dark matter, predictions for large-scale structure formation in good agreement with data from galaxy surveys. Compared to the cosmological constant, these scalar field models are consistent with the SNe observations for a lower matter density, ${\ensuremath{\Omega}}_{m0}\ensuremath{\sim}0.2,$ and a higher age, ${H}_{0}{t}_{0}\ensuremath{\gtrsim}1.$ Combined with the fact that scalar field models imprint a distinctive signature on the cosmic microwave background anisotropy, they remain currently viable and should be testable in the near future.
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