The Case for an Accelerating Universe from Supernovae

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The unexpected faintness of high-redshift Type Ia supernovae (SNe Ia), as measured by two teams, has been interpreted as evidence that the expansion of the Universe is accelerating. We review the current challenges to this interpretation and seek to answer whether the cosmological implications are compelling. We discuss future observations of SNe Ia which could offer extraordinary evidence to test acceleration.
To appear as an Invited Review for PASP 20 pages, 13 figures

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