Constraining slow-roll inflation with WMAP and 2dF

TL;DR

This study uses WMAP together with VSA, CBI, ACBAR and 2dF to constrain slow-roll inflation via horizon-flow parameters $ε_1$ and $ε_2$, employing MCMC within CAMB/CosmoMC frameworks. It yields tight bounds such as $0<ε_1<0.032$ and $ε_2+5ε_1=0.036±0.025$, and translates these into limits on inflationary potentials; monomial models with $V∝ φ^α$ face strong pressure on $λφ^4$ ($α≈4$) while $m^2 φ^2$ remains viable for a finite range of $N_{ m hor}$. The authors also introduce a convergence criterion for the power-spectrum expansion to determine when including a running or higher-order terms is meaningful, finding current data do not reliably measure running. Overall, the work significantly narrows the slow-roll inflation parameter space and provides fiducial parameter sets for future analyses, highlighting how current data prefer a nearly scale-invariant spectrum with limited tensor contribution.

Abstract

We constrain slow-roll inflationary models using the recent WMAP data combined with data from the VSA, CBI, ACBAR and 2dF experiments. We find the slow-roll parameters to be $0 < ε_1 < 0.032$ and $ε_2 + 5.0 ε_1 = 0.036 \pm 0.025$. For inflation models $V \propto φ^α$ we find that $α< 3.9, 4.3$ at the 2$σ$ and $3σ$ levels, indicating that the $λφ^4$ model is under very strong pressure from observations. We define a convergence criterion to judge the necessity of introducing further power spectrum parameters such as the spectral index and running of the spectral index. This criterion is typically violated by models with large negative running that fit the data, indicating that the running cannot be reliably measured with present data.

Figures (6)

• Figure 1: 1D posterior constraints for the basic cosmological parameters assuming slow-roll inflation.
• Figure 2: 2D posterior constraints in the $\epsilon_1$--$\epsilon_2$ plane. The contours are the $1\sigma$ and $2\sigma$ bounds.
• Figure 3: 2D posterior constraints in the $(n_{{\rm s}}-1)$--$R_{10}$ plane, again at $1\sigma$ and $2\sigma$. Models with a tensor spectrum on large scales require a bluer scalar spectrum in order to increase CMB power to short scales.
• Figure 4: 1D posterior constraints on inflationary parameters. The solid line corresponds to a power-law fit to the data using $\epsilon_1$ and $\epsilon_2$. The dashed line corresponds to a fit where weak running of the spectral index is included in the fit via the slow-roll parameter $\epsilon_3$, which is unconstrained by the data.
• Figure 5: 2D posterior constraints in the $\epsilon_1$--$\epsilon_2$ plane, for the region $\epsilon_2>0$. The contours are the $1\sigma$, $2\sigma$ and $3\sigma$ bounds. The hatched region $\epsilon_2<1/60$ is inaccessible to monomial inflation models. The thick lines indicate the available parameter space for two monomial inflation models: the $\lambda \phi^4$ model is under strong pressure from observations.