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In loop quantum cosmology there may be a superinflation phase in the very early universe, in which a single scalar field with a negative power-law potential V=-M^4 (/M) ^ plays an important role. Since the effective horizon SD/H controls the behavior of quantum fluctuation instead of the usual Hubble horizon, we assume the following inflation scenario: the superinflation starts when the quantum state of the scalar field emerges into the classical regime and ends when the effective horizon becomes the Hubble horizon, and the effective horizon scale never gets shorter than the Planck length. From consistency with the WMAP 5 yr data, we place a constraint on the parameters of the potential (and M) and the energy density at the end of the superinflation, depending on the volume correction parameter n.
Shimano et al. (Tue,) studied this question.