Parity violation in stochastic gravitational wave background from inflation in Nieh-Yan modified teleparallel gravity

Abstract

We study the inflationary implications of a novel parity-violating gravity model, which modifies the teleparallel equivalent of general relativity by introducing the Nieh-Yan term coupled to an axionlike field. The parity-violating Nieh-Yan term results in the velocity birefringence of gravitational waves (GWs) and triggers the tachyonic instability only for one of the two circular polarization states. We consider that the inflaton is identified as the coupled axionlike field with a wiggly potential characterized by steep cliffs connected by smooth plateaus. During inflation, the temporary fast roll of the axion on the clifflike region leads to the significant enhancement of the tensor perturbations in one polarization state with the wave numbers that exit the horizon around this period. In this setup, the resulting energy spectrum for GWs presents a sizable localized bump involving the contribution of only one polarization state. This chiral GW background is detectable by GW detectors like LISA and Taiji, and its chirality can be determined by correlating two detectors, which provides an opportunity to probe the inflation and test the gravity model.