Observational constraints of a power spectrum from super-inflation in Loop Quantum Cosmology

Abstract

In loop quantum cosmology there may be a super-inflation phase in the very early universe, in which a single scalar field with a negative power-law potential $V= -M^4(ϕ/M)^β$ plays important roles. Since the effective horizon $\sqrt{SD}/H$ controls the behavior of quantum fluctuation instead of the usual Hubble horizon, we assume the following inflation scenario; the super-inflation 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-year data, we place a constraint on the parameters of the potential ($β$ and $M$) and the energy density at the end of the super-inflation, depending on the volume correction parameter $n$.