B-modes and the Nature of Inflation

TL;DR

This work integrates the EFT of inflation with a nontrivial sound speed to connect tensor modes and scalar fluctuations. By deriving a bound on $c_s$ as a function of the tensor-to-scalar ratio $r$ and accounting for the different freeze-out times of scalar and tensor perturbations, the authors show that even modest B-mode detections ($r>0.01$) tighten constraints beyond Planck's non-Gaussianity bounds, and near $r\sim 0.1$ the bound approaches a critical $c_s$ of about 0.47, signaling a threshold between perturbative slow-roll and strongly coupled dynamics. They perform a joint Planck-BICEP2 analysis, demonstrate the bound’s robustness to second-order corrections and data choices, and discuss how future measurements of equilateral non-Gaussianity could probe physics above this threshold. The paper also outlines theoretically motivated scenarios—one-scale strong coupling, stable hierarchies, and additional light degrees of freedom—where observable non-Gaussianity could arise, highlighting the role of $f_{NL}^{equil}$ as a key diagnostic of the inflationary UV completion.

Abstract

Observations of the cosmic microwave background do not yet determine whether inflation was driven by a slowly-rolling scalar field or involved another physical mechanism. In this paper we discuss the prospects of using the power spectra of scalar and tensor modes to probe the nature of inflation. We focus on the leading modification to the slow-roll dynamics, which entails a sound speed $c_s$ for the scalar fluctuations. We derive analytically a lower bound on $c_s$ in terms of a given tensor-to-scalar ratio $r$, taking into account the difference in the freeze-out times between the scalar and tensor modes. We find that any detection of primordial B-modes with $r > 0.01$ implies a lower bound on $c_s$ that is stronger than the bound derived from the absence of non-Gaussianity in the Planck data. For $r \gtrsim 0.1$, the bound would be tantalizingly close to a critical value for the sound speed, $(c_s)_\star = 0.47$ (corresponding to $(f_{\rm NL}^{\rm equil})_\star = -0.93$), which we show serves as a threshold for non-trivial dynamics beyond slow-roll. We also discuss how an order-one level of equilateral non-Gaussianity is a natural observational target for other extensions of the canonical paradigm.

Figures (9)

• Figure 1: Graphical illustration of the threshold value $(c_s)_\star =0.47$.
• Figure 2: For $c_s < 1$, scalars and tensors freeze out at different times.
• Figure 3: Plots of $c_s(r,\varepsilon_1)$ ( left) and $r(c_s,\varepsilon_1)$ ( right) as given by (\ref{['equ:r4']}). The dashed contour in the left plot shows the value of $r$ for $c_s =0.1$. It has a maximum of $r=0.13$ for $\varepsilon_1 = 0.2$. The dashed contour in the right plot illustrates the lower bound on $c_s$ for $r=0.13$.
• Figure 4: Left: plot of $c_s(\varepsilon_1, \varepsilon_2)$, as given by (\ref{['equ:r5']}), for $r = 0.13$. The dashed contour corresponds to the previous bound $c_s=0.1$. The grey shaded area is the region that is consistent with the constraint from the running: $| \varepsilon_1 \varepsilon_2| < 0.01$. Right: plot of $c_s(r,\varepsilon_1,\varepsilon_2)$ as given by (\ref{['equ:r5']}) with $\varepsilon_2 \to -0.01/\varepsilon_1$ (the most negative value consistent with the bound on $\alpha_s$).
• Figure 5: Left: 68% and 95% confidence contours of the marginalized posterior probability distribution for the parameters $c_s$ and $\varepsilon_1$. The red shows shows that case with $\delta_1 = 0$, while the blue allows for $\delta_1 \ne 0$. Right: Marginalized posterior probability distribution for $c_s$, for $\delta_1=0$ (solid red line) and $\delta_1 \ne 0$ (dashed blue line). The Planck exclusion, $c_s >0.02$, is shown in grey.