Recovering the Inflationary Potential and Primordial Power Spectrum With a Slow Roll Prior: Methodology and Application to WMAP 3 Year Data

TL;DR

This work introduces a flow-based, MCMC framework that incorporates the Hubble slow-roll (HSR) hierarchy to apply an inflationary prior directly in cosmological parameter estimation. By solving the flow equations for $H(\phi)$ and using second-order slow-roll expressions for the scalar and tensor spectra, the authors reconstruct the inflationary potential $V(\phi)$ and quantify constraints on the slow-roll parameters from heterogeneous data, including WMAPI+All and WMAPII/WMAPII+SDSS. They show that the prior tightens the allowed region in $(\epsilon,\eta)$ space, reveals a correlation between running $dn_s/d\ln k$ and higher-order slow-roll terms, and demonstrates that current data still permit all basic single-field inflationary classes at 1–2$\sigma$, with WMAPII+SDSS providing the strongest constraints and disfavoring some large-field models. The methodology is particularly suited to future, high-quality, heterogeneous datasets and can accommodate direct tensor detections, enabling a more direct reconstruction of the inflationary potential from observations.

Abstract

We introduce a new method for applying an inflationary prior to a cosmological dataset that includes relations between observables at arbitrary order in the slow roll expansion. The process is based on the inflationary flow equations, and the slow roll parameters appear explicitly in the cosmological parameter set. We contrast our method to other ways of imposing an inflationary prior on a cosmological dataset, and argue that this method is ideal for use with heterogeneous datasets. In particular, it would be well suited to exploiting any direct detection of fundamental tensor modes by a BBO-style mission. To demonstrate the practical use of this method we apply it to the WMAPI+All dataset, and the newly released WMAPII dataset on its own and together with the SDSS data. We find that all basic classes of single field inflationary models are still allowed at the 1-2sigma level, but the overall parameter space is sharply constrained. In particular, we find evidence that the combination of WMAPII+SDSS is sensitive to effects arising from terms that are quadratic in the two leading-order slow roll parameters.