Slow Roll Reconstruction: Constraints on Inflation from the 3 Year WMAP Dataset

TL;DR

This paper applies slow-roll reconstruction to the 3-year WMAP data, embedding the slow-roll parameters ($\epsilon$, $\eta$, $\xi$) directly into MCMC cosmological analyses and evolving them with the inflationary flow equations. It investigates whether a running spectral index is favored and how imposing a minimum number of e-folds $N>30$ reshapes the inflationary parameter space, including the pivotal role of the third slow-roll parameter $\xi$ in driving running. The results show that without the $N>30$ prior, $\xi$ and the running can appear sizable, but enforcing $N>30$ tightly confines $\xi$ near zero and suppresses running, with SDSS data further tightening bounds. The study highlights pivot-dependence and argues that upcoming data will substantially sharpen constraints on single-field slow-roll inflation, potentially ruling out large regions of parameter space.

Abstract

We study the constraints on the inflationary parameter space derived from the 3 year WMAP dataset using ``slow roll reconstruction'', using the SDSS galaxy power spectrum to gain further leverage where appropriate. This approach inserts the inflationary slow roll parameters directly into a Monte Carlo Markov chain estimate of the cosmological parameters, and uses the inflationary flow hierarchy to compute the parameters' scale-dependence. We work with the first three parameters (epsilon, eta and xi) and pay close attention to the possibility that the 3 year WMAP dataset contains evidence for a ``running'' spectral index, which is dominated by the xi term. Mirroring the WMAP team's analysis we find that the permitted distribution of xi is broad, and centered away from zero. However, when we require that inflationary parameters yield at least 30 additional e-folds of inflation after the largest observable scales leave the horizon, the bounds on xi tighten dramatically. We make use of the absence of an explicit pivot scale in the slow roll reconstruction formalism to determine the dependence of the computed parameter distributions on the pivot. We show that the choice of pivot has a significant effect on the inferred constraints on the inflationary variables, and the spectral index and running derived from them. Finally, we argue that the next round of cosmological data can be expected to place very stringent constraints on the region of parameter space open to single field models of slow roll inflation.