Inflationary Potential Reconstruction for a WMAP Running Power Spectrum

TL;DR

WMAP1 data motivate a search for large running of the scalar spectral index and its implications for the inflationary potential. Using a Hamilton-Jacobi reconstruction, the paper shows how a target $P(k)$ can be realized by a family of $V(\phi)$, including a renormalizable quartic form, and demonstrates that a partial running spectrum over a limited $k$ range can fit the data comparably to full running. It argues that large running is viable only with a sizable tensor-to-scalar ratio, which implies a high inflation scale around $V^{1/4} \sim 3.5\times10^{16}$ GeV and potential tensor signatures in the CMB, especially if running is cut off at low $k$ to sustain sufficient inflation. The work provides a practical reconstruction framework and suggests that Planck-scale physics and tensor modes could be probed via the inferred inflaton potential, while maintaining EFT consistency.

Abstract

The first year WMAP measurement of the CMB temperature anisotropy is intriguingly consistent with a larger running of the inflationary scalar spectral index than would be expected for single-field inflation. We revisit the issue of a large running spectral index, first by reexamining the evidence from the data, and then by reconstructing the inflationary potential, using an improved method based upon the Hamilton-Jacobi formulation. We note that a spectrum which runs only over 1.5 decades of k space provides as good a fit to the CMB data as one which runs at all k, that significant evidence for running comes from multipoles l near 40, and that large running gives a better fit than a flat spectrum primarily if the tensor-to-scalar ratio $r$ is large, r ~ 0.5, and the field values are at the Planck scale. This allows one to break the large degeneracy of potentials which would be consistent with the scalar power alone. Large running, should it be confirmed, is thus linked to a high scale of inflation and the possibility of seeing effects of tensor modes in the CMB and Planck-scale physics. Nevertheless, we show that the reconstructed inflaton potential is well-described by a renormalizable potential whose quantum corrections are under control despite the large field values.