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Reconstructing large running index inflaton potentials

Recent fits of cosmological parameters by first-year Wilkinson Microwave Anisotropy Probe (WMAP) measurements seem to favour a primordial scalar spectrum with a large varying index from blue to red. We use the inflationary flow equations to reconstruct large running index inflaton potentials and comment on the current status of the inflationary flow. We find that previous negligence of higher order slow-rolling contributions when using the flow equations would lead to unprecise results.