WMAPping inflationary physics

TL;DR

The paper uses WMAP data, alone and with seven additional CMB experiments, to distinguish among single-field inflation models by mapping observables to model classes via a grid likelihood and a Monte Carlo reconstruction of the inflaton potential. It formalizes the slow-roll framework with parameters $\epsilon$ and $\eta$, and connects them to observables $n$, $r$, and $dn/d\ln k$, then exhaustively samples the inflationary model space (large-field, small-field, hybrid, and linear) to predict a spectrum of viable potentials. The main findings are that $n=1$ with zero running remains compatible, the combined data tighten limits on tensor modes and rule out $V(\phi)=\lambda\phi^4$ for $N<66$ (3σ), and that a wide variety of smooth potentials survive, with hybrid models often favored by best fits. Overall, the work demonstrates that first-year WMAP data begin to constrain inflationary physics, while the lack of detected tensors limits the ability to determine the inflationary energy scale, and it provides a robust methodology for future CMB-driven inflationary constraints.

Abstract

We extract parameters relevant for distinguishing among single-field inflation models from the Wilkinson Microwave Anisotropy Probe (WMAP) data set, and from a combination of the WMAP data and seven other Cosmic Microwave Background (CMB) experiments. We use only CMB data and perform a likelihood analysis over a grid of models including the full error covariance matrix. We find that a model with a scale-invariant scalar power spectrum ($n=1$), no tensor contribution, and no running of the spectral index, is within the 1-$σ$ contours of both data sets. We then apply the Monte Carlo reconstruction technique to both data sets to generate an ensemble of inflationary potentials consistent with observations. None of the three basic classes of inflation models (small-field, large-field, and hybrid) are completely ruled out, although hybrid models are favored by the best-fit region. The reconstruction process indicates that a wide variety of smooth potentials for the inflaton are consistent with the data, implying that the first-year WMAP result is still too crude to constrain significantly either the height or the shape of the inflaton potential. In particular, the lack of evidence for tensor fluctuations makes it impossible to constrain the energy scale of inflation. Nonetheless, the data rule out a large portion of the available parameter space for inflation. For instance, we find that potentials of the form $V = λφ^4$ are ruled out to $3σ$ by the combined data set, but not by the WMAP data taken alone.

Figures (13)

• Figure 1: Regions on the $r\,-\,n$ plane. The different types of potentials, small field, large field, and hybrid, occupy different regions of the observable parameter space.
• Figure 2: A "zoo plot" of models in the $r\,-\,n$ plane, plotted to first order in slow roll.
• Figure 3: Models generated by Monte Carlo plotted on the $(r,n)$ plane (black dots). The colored lines are the same models as in Fig. 2. For comparison with the models, points are plotted to first order in slow roll.
• Figure 4: Models generated by Monte Carlo plotted on the $(n,dn/d\ln k)$ plane. Points are plotted to second order in slow roll.
• Figure 5: Models generated by Monte Carlo plotted on the $(r,dn/d\ln k)$ plane. Points are plotted to second order in slow roll.