Direct Reconstruction of the Dark Energy Scalar-Field Potential

Abstract

While the accelerated expansion of the Universe is by now well established, an underlying scalar field potential possibly responsible for this acceleration remains unconstrained. We present an attempt to reconstruct this potential using recent SN data, under the assumption that the acceleration is driven by a single scalar field. Current approaches to such reconstructions are based upon simple parametric descriptions of either the luminosity distance or the dark energy equation of state. We find that these various approximations lead to a range of derived evolutionary histories of the dark energy equation of state (although there is considerable overlap between the different potential shapes allowed by the data). Instead of these indirect reconstruction schemes, we discuss a technique to determine the potential directly from the data by expressing it in terms of a binned scalar field. We apply this technique to a recent SN dataset, and compare the results with model-dependent approaches. In a similar fashion to direct estimates of the dark energy equation of state, we advocate direct reconstruction of the scalar field potential as a way to minimize prior assumptions on the shape, and thus minimize the introduction of bias in the derived potential.