Steps to Reconcile Inflationary Tensor and Scalar Spectra

TL;DR

The paper tackles the tension between the BICEP2-inferred tensor-to-scalar ratio and Planck constraints by proposing a sharp, recombination-scale transition in the scalar power spectrum, implemented as a step in the tensor-scalar ratio parameter $ε_H c_s$. Using generalized slow-roll calculations and a DBI-inspired Lagrangian, the authors show that such a step can suppress large-scale scalar power without altering the tensor spectrum, substantially improving the joint fit to Planck, WMAP9, and BICEP2 data; for $r=0.2$ they report $2Δ ln L_P ≈ -14.2$ and $2Δ ln L_{tot} ≈ -13.7$, with weaker but still notable improvements at $r=0.1$, and even at $r=0$ a step is favored. The model predicts distinctive changes in the $EE$ polarization and a small but testable $E$-mode signature, making precision polarization a critical test of this explanation. While illustrated with a DBI-type realization, the approach emphasizes a concrete, testable mechanism to reconcile observations without broad changes to cosmological parameters, and it invites further exploration of explicit model constructions and observational tests.

Abstract

The recent BICEP2 B-mode polarization determination of an inflationary tensor-scalar ratio $r=0.2^{+0.07}_{-0.05}$ is in tension with simple scale-free models of inflation due to a lack of a corresponding low multipole excess in the temperature power spectrum which places a limit of $r_{0.002}<0.11$ (95% CL) on such models. Single-field inflationary models that reconcile these two observations, even those where the tilt runs substantially, introduce a scale into the scalar power spectrum. To cancel the tensor excess, and simultaneously explain the excess already present in $Λ$CDM, ideally the model should introduce this scale as a relatively sharp transition in the tensor-scalar ratio around the horizon at recombination. We consider models which generate such a step in this quantity and find that they can improve the joint fit to the temperature and polarization data by up to $2Δ\ln{\cal L} \approx -14$ without changing cosmological parameters. Precision E-mode polarization measurements should be able to test this explanation.

Figures (3)

• Figure 1: Total temperature power spectra showing the unobserved excess produced by adding tensors of $r=0.2$ to the best fit 6 parameter $\Lambda$CDM model and its removal by adding a step in the tensor-scalar parameter $\epsilon_H c_s$. Planck data in fact favor removing more power than the tensor excess, preferring a step even if $r=0$. Step model parameters are given in Tab. \ref{['tab:fits']}.
• Figure 2: Step in tensor-scalar ratio parameter $\epsilon_H c_s$ relative to no step, from the best fit $r=0.2$ solution centered at the efold $N_s$ at which the inflaton crosses the step. Planck data favor a step that is traversed in about an efold.
• Figure 3: $EE$ power spectrum for the models in Fig. \ref{['plot:cl']} showing the change from the best fit $r=0$$\Lambda$CDM power spectrum. Excess $E$-modes from the tensors at $r=0.2$ are partially compensated by the step at $\ell \gtrsim 30$ while changes at lower $\ell$ can be altered by changing the reionization history. Preference for removing power at substantially smaller $r$ would predict a deficit of power as the $r=0$ model shows.