Blue Tensor Spectrum from Particle Production during Inflation

TL;DR

The paper introduces a mechanism where a rolling pseudo-scalar ψ coupled to a hidden U(1) gauge field sources abundant gauge quanta during inflation, producing a GW background that can be blue, chiral, and non-Gaussian while leaving inflaton perturbations standard. By allowing ξ to vary in time, the tensor tilt n_T can be driven positive, enabling scale-dependent tensor spectra that may alleviate tension between Planck and BICEP2 data. The authors derive a reconstruction method to infer the pseudo-scalar potential U(ψ) from the GW spectrum and demonstrate two illustrative examples (constant δξ and Gaussian ξ(N)) that yield explicit U(ψ) forms. They also highlight distinctive observational signatures, including parity violation and tensor non-Gaussianity, offering a pathway to test hidden axion-gauge sectors during inflation.

Abstract

We discuss a mechanism of particle production during inflation that can result in a blue gravitational wave (GW) spectrum, compatible with the BICEP2 result and with the r < 0.11 limit on the tensor-to-scalar ratio at the Planck pivot scale. The mechanism is based on the production of vector quanta from a rolling pseudo-scalar field. Both the vector and the pseudo-scalar are only gravitationally coupled to the inflaton, to keep the production of inflaton quanta at an unobservable level (the overproduction of non-gaussian scalar perturbations is a generic difficulty for mechanisms that aim to generate a visible GW signal from particle production during inflation). This mechanism can produce a detectable amount of GWs for any inflationary energy scale. The produced GWs are chiral and non-gaussian; both these aspects can be tested with large-scale polarization data (starting from Planck). We study how to reconstruct the pseudo-scalar potential from the GW spectrum.

Figures (6)

• Figure 1: Slow roll parameter $\epsilon$ vs particle production parameter $\xi$, when $P_\zeta$ is fixed to the measured amplitude, and for three different values of $r$. At the smallest $\xi$ shown, particle production is negligible, and $\epsilon = r/16$. As $\xi$ increases the sourced GWs become dominant, and $\epsilon$ needs to decrease to keep $r$ at the given value.
• Figure 2: Parameter $X$, defined in (\ref{['X-def']}), controlling the amount of non-gaussianity as a function of the particle production parameter $\xi$, when $P_\zeta$ is fixed to the measured amplitude, and for three different values of $r$. See the main text for discussion.
• Figure 3: Chirality of the observed GWs $\Delta \chi$, defined in (\ref{['dchi']}), as a function of the particle production parameter $\xi$, when $P_\zeta$ is fixed to the measured amplitude, and for three different values of $r$. The value of $\Delta \chi$ interpolates from $0$ at small $\xi$ (negligible sourced GWs) to $1$ at large $\xi$ (dominant sourced GWs).
• Figure 4: Two illustrative spectra of the tensor-to-scalar ratio. The blue curve corresponds to the case in Example I, and the red dashed curve to the case in Example II. See the corresponding subsections for the details. The Planck upper bound $r < 0.11$ at $k = 0.002 \; {\rm Mpc}^{-1}$ and the BICEP2 measurement $r = 0.20_{-0.05}^{+0.07}$ at $k = 0.0057 \; {\rm Mpc}^{-1}$ ($\ell \approx 80$) are also shown.
• Figure 5: Reconstructed pseudo-scalar potential for constant $\epsilon = 10^{-5}$ and $\delta_\xi = 0.012$ in Example I, corresponding to the blue solid curve in Figure \ref{['fig:r-vs-k']}. The horizontal axis is $(\bar{\psi}-\psi_c)/\Delta\psi_c$ and the vertical axis is $(U-U_c)/\Delta U_c$.