On what scale should inflationary observables be constrained?

TL;DR

The paper addresses how the scale at which inflationary observables are constrained affects the interpretation of parameters, especially when scalar running is allowed. It implements the full hierarchy of inflationary consistency equations to enforce cross-scale relations and uses MCMC (CosmoMC) on WMAP3 data to identify an optimal presentation scale, found to be $k_{\rm dec} = 0.017\,{\rm Mpc}^{-1}$. At this scale, the marginalized constraints on $n_S$ and $dn_S/d\ln k$ are tighter and the $n_S$–$r$ plane shows a minimized 95% contour area, compared to scales like $k=0.002\,{\rm Mpc}^{-1}$. Extending the analysis with additional data preserves the decorrelation scale near $0.016$–$0.017\,{\rm Mpc}^{-1}$ and yields similar conclusions, while models without running exhibit reduced scale sensitivity. The work provides a practical guideline for presenting inflationary constraints that mitigates artificial degradation due to running and improves cross-scale comparison of models.

Abstract

We examine the choice of scale at which constraints on inflationary observables are presented. We describe an implementation of the hierarchy of inflationary consistency equations which ensures that they remain enforced on different scales, and then seek to optimize the scale for presentation of constraints on marginalized inflationary parameters from WMAP3 data. For models with spectral index running, we find a strong variation of the constraints through the range of observational scales available, and optimize by finding the scale which decorrelates constraints on the spectral index n_S and the running. This scale is k=0.017 Mpc^{-1}, and gives a reduction by a factor of more than four in the allowed parameter area in the n_S-r plane (r being the tensor-to-scalar ratio) relative to k=0.002 Mpc^{-1}. These optimized constraints are similar to those obtained in the no-running case. We also extend the analysis to a larger compilation of data, finding essentially the same conclusions.

Figures (9)

• Figure 1: Constraints in the $n_{\rm S}$--$\alpha$ plane (where $\alpha = dn_{\rm S}/d\ln k$) at several scales. $k = 0.017 \, {\rm Mpc}^{-1}$ is the decorrelation scale for these parameters.
• Figure 2: Constraints on $n_{\rm S}$ versus $r$ at several scales.
• Figure 3: Variation of parameter plane area with scale. For the $\epsilon$--$\eta$ case both lowest (black, full) and next order (red, dashed) are shown. For $n_{\rm S}$ versus running the area should be independent of scale, and the variations indicate the noise level in the area estimation.
• Figure 4: Constraints on $\epsilon$ versus $\eta$, at lowest order, evaluated at several scales.
• Figure 5: Constraints on $\epsilon$ versus $\eta$, to next order, at several scales.