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 SGWB, 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 impact of Finslerian inflation and gauge field inflation models on PTAs and the Laser Interferometer Space Antenna 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.