The recent robust and homogeneous analysis of the worlds supernova distance-redshift data, together with cosmic microwave background and baryon acoustic oscillation data, provides a powerful tool for constraining cosmological models. Here we examine particular classes of scalar field, modified gravity, and phenomenological models to assess whether they are consistent with observations even when their behavior deviates from the cosmological constant Lambda. Some models have tension with the data, while others survive only by approaching the cosmological constant, and a couple are statistically favored over LCDM. Dark energy described by two equation of state parameters has considerable phase space to avoid Lambda and next generation data will be required to constrain such physics.
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