Revisiting the Chern-Simons interaction during inflation with a non-canonical pseudo-scalar

Abstract

A Chern-Simons interaction between a pseudo-scalar field and a U(1) gauge field results in the generation of a chiral gravitational wave background. The detection of this signal is contrasted by the fact that this coupling also generates primordial scalar perturbations, on which strong limits exist, particularly at CMB scales. In this study, we propose a new extension of this mechanism characterized by a non-canonical kinetic term for the pseudo-scalar. We find that a decrease of the sound speed of the pseudo-scalar field highly suppresses the sourced scalar with respect to the sourced tensor modes, thus effectively allowing for the production of a greater tensor signal. Contrary to the case of a canonical axion inflaton, it is in this case possible for the sourced tensor modes to dominate over the vacuum ones without violating the non-Gaussianity constraints from the scalar sector, which results in a nearly totally polarized tensor signal at CMB scales. We also study the extension of this mechanisms to the multiple field case, in which the axion is not the inflaton.

Figures (4)

• Figure 1: Maximum allowed value for $\xi$ as a function of $c_s$ compatible with the non-Gaussianity limits. We consider three different values of $\epsilon_{\sigma}$. Deviation from a straight line in the figure are due to the gravitational contributions ($J_{1,2}$) that interfere more significantly with the direct one ($J_3$) at increasing $\epsilon_{\sigma}$.
• Figure 2: Total tensor-to-scalar-ratio $r$ as a function of $\xi$ and $\epsilon_\sigma$. The three panels correspond to three different values of the sound speed, specified on the top of the panel. The value indicated next to each line indicates the value of $r$ along that line. Values of $\xi$ on the right of the vertical green dot-dashed line lead to a too large non-Gaussianity. The area above the red line $r = 0.03$ leads to a too large tensor-to-scalar-ratio Tristram:2021tvhGalloni:2022mok. Left panel: in all the area shown the vacuum GW signal is greater than the sourced one. Central panel: in the area to the left (resp. right) of the blue dashed line the vacuum (resp. sourced) GW signal is dominant. Right panel: the area where the sourced GW signal is dominant and where the limits on non-Gaussianity and $r$ are respected, becomes larger.
• Figure 3: Analogous plot as Fig. \ref{['fig:rtot']} but for the two-field scenario. The left (respectively, right) panel assumes a sound speed equal to $1$ (respectively, to $0.1$). In both panels, we assume that the spectator field rolls for $\Delta N_k = 10$$e$-folds after the mode at which the ratio is evaluated leaves the horizon. As in the previous figure: the red solid contour marks the current upper limit $r \simeq 0.03$; parameters above the dot-dashed green line lead to a too large scalar non-Gaussianity; the sourced tensor mode dominates over the vacuum one above the blue dashed line.
• Figure 4: The contribution of gravitational coupling and that of interference to $f_{2,\zeta}$, relative to that of direct coupling, in the single field model. The left and right panel correspond to $c_{s,\sigma} = 1 ,\, 0.1$, respectively, and we set the same highest value of $\epsilon_\sigma$ as the one considered in Fig. \ref{['fig:rtot']}. As expected from Eq. \ref{['eq:f2_full']}, one can see the parametric dependence as $\epsilon_{\sigma}c_{s,\sigma}^{-2}$ and $\epsilon_{\sigma}^2 c_{s,\sigma}^{-4}$ at the leading order, respectively for the interference and the gravitational one.