Probing small-scale anisotropic inflation with stochastic gravitational-wave background

Abstract

In June 2023, multiple pulsar timing array (PTA) collaborations provided evidence for the existence of a stochastic gravitational-wave background (SGWB). As a significant source of the SGWBs, scalar-induced gravitational waves (SIGWs) receive extensive attention. We explore the influence of anisotropic primordial power spectra on second-order SIGWs and derive explicit expressions for the energy density spectra. For specific anisotropic inflation models, we analyze the impacts of Finslerian inflation and gauge field inflation models on PTA and the Laser Interferometer Space Antenna (LISA) and generalize the findings to model-independent scenarios. Our results indicate that current PTA observations cannot rule out the existence of small-scale anisotropic primordial perturbations.