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Revisiting the holographic dark energy in a non-flat universe: alternative model and cosmological parameter constraints

We propose an alternative model for the holographic dark energy in a non-flat universe. This new model differs from the previous one in that the IR length cutoff $L$ is taken to be exactly the event horizon size in a non-flat universe, which is more natural and theoretically/conceptually concordant with the model of holographic dark energy in a flat universe. We constrain the model using the recent observational data including the type Ia supernova data from SNLS3, the baryon acoustic oscillation data from 6dF, SDSS-DR7, BOSS-DR11, and WiggleZ, the cosmic microwave background data from Planck, and the Hubble constant measurement from HST. In particular, since some previous studies have shown that the color-luminosity parameter $β$ of supernovae is likely to vary during the cosmic evolution, we also consider such a case that $β$ in SNLS3 is time-varying in our data fitting. Compared to the constant $β$ case, the time-varying $β$ case reduces the value of $χ^2$ by about 35 and results in that $β$ deviates from a constant at about 5$σ$ level, well consistent with the previous studies. For the parameter $c$ of the holographic dark energy, the constant $β$ fit gives $c=0.65\pm 0.05$ and the time-varying $β$ fit yields $c=0.72\pm 0.06$. In addition, an open universe is favored (at about 2$σ$) for the model by the current data.