Primordial Gravitational Waves in Parity-violating Symmetric Teleparallel Gravity

Abstract

In this paper, we investigate the inflationary phenomenology of parity-violating (PV) extensions of symmetric teleparallel gravity by applying this PV gravity theory to axion inflation. The presence of PV terms induces velocity birefringence in the tensor perturbations. During inflation, when the inflaton rapidly traverses the cliff-like region in its potential, the tensor modes at specific scales for one of the two circular polarization states undergo significant amplification due to tachyonic instability. Consequently, the resulting primordial gravitational waves (GWs), characterized by a one-handed polarization and a multi-peak structure in their energy spectrum, exhibit a significant amplitude potentially detectable by LISA and Taiji, and their chirality could be determined by the LISA-Taiji network. The detection of such a chiral GW signal provides an opportunity to probe inflation and PV gravity theory. Moreover, we perform the Fisher matrix analysis to forecast the constraints on the model parameters with the LISA-Taiji network.

Figures (8)

• Figure 1: Schematic diagram of the axion potential \ref{['potential']}.
• Figure 2: The evolution of $\phi$ (upper panel) and $|\dot \phi|/m$ (bottom panel) as a function of e-folding number $N$.
• Figure 3: The evolution of $|{H\dot{\phi}^2 + \dot{\phi}\ddot{\phi}|/(m^2 H)}$ as a function of e-folding number $N$. The dashed line denotes the negative value.
• Figure 4: The time evolution of the power spectra $\mathcal{P}^A_h(k,N)$ for different $k$ modes with a coupling constant $c=12~m^{-2}$.
• Figure 5: The resulting power spectra for the left- and right-handed polarization states with a coupling constant $c=12~m^{-2}$.