Circular Polarization of Primordial Gravitational Waves in String-inspired Inflationary Cosmology

TL;DR

This work investigates whether primordial gravitational waves can carry circular polarization in a string-inspired inflationary framework that includes parity-violating CS and GB terms. The GB term drives a transient super-inflation causing tensor-mode instabilities, while the CS term introduces parity violation, jointly producing a highly polarized GW spectrum with Pi(k) ≈ 1. A single-field realization clashes with CMB constraints, so the authors propose a two-field model in which the polarization is generated in the deci-Hz band, compatible with BBO/DECIGO, and the observed CMB fluctuations arise from the first slow-roll phase. The results offer a potential observational probe of string-inspired parity-violating gravity, predicting a detectable polarization signal in future GW interferometers and a blue-tilted spectrum in the relevant frequency range (n ≈ 2.66).

Abstract

We study a mechanism to produce the circular polarization of primordial gravitational waves. The circular polarization is generated during the super-inflation driven by the Gauss-Bonnet term in the string-inspired cosmology. The instability in the tensor mode caused by the Gauss-Bonnet term and the parity violation due to the gravitational Chern-Simons term are the essential ingredients of the mechanism. We also discuss detectability of the produced circular polarization of gravitational waves. It turns out that the simple model of single-field inflation contradicts CMB observations. To circumvent this difficulty, we propose a two-field inflation model. In this two-field model, the circular polarization of gravitational waves is created in the frequency range designed by the Big-Bang Observer (BBO) or the deci-hertz gravitational-wave observatory (DECIGO).

Figures (7)

• Figure 1: A typical evolution of the background spacetime is numerically calculated and displayed. A short period of the super-inflationary phase is followed by a long period of the slow-roll inflationary phase.
• Figure 2: Phase diagram around $\phi\simeq 0$ is drawn. The thick line in the diagram denotes the trajectory corresponding to Fig. \ref{['evol']}. This tells that the asymptotic solution breaks down before reaching $\phi=0$, and thus the singularity is avoided.
• Figure 3: The degree of the polarization $\Pi (k)$ as a function of wave numbers $k$ is shown. As expected, the gravitational waves are almost 100% circularly polarized.
• Figure 4: The numerical result of the spectral index $n$ for the power spectrum of primordial gravitational waves as a function of wavenumbers $k$ is shown. In the relevant frequency range, we have obtained the spectral index $n = 2.66$ numerically.
• Figure 5: Potential function for the two field model is depicted. Initially, the scalar field $\phi$ is sticked to the point $\phi=-3000$ and the other scalar field $\chi$ slowly rolls down to give rise to the inflation. At some point, $\phi$ starts to roll down toward $\phi=0$. Then, the coupling to the Gauss-Bonnet term induces the super-inflation where the circular polarization of gravitational waves is created. Subsequently, the standard slow-roll inflation follows.