We investigate the stochastic gravitational wave background (SGWB) from cosmic domain walls (DWs) caused by quantum fluctuations of a light scalar field ϕ during inflation. Large-scale perturbations of ϕ lead to large-scale perturbations of DW energy density and anisotropies in the SGWB. We find that the angular power spectrum of this SGWB is scale invariant and at least of the order of 10^{-2}, which is a distinctive feature of observational interest. Since we have not detected primordial gravitational waves yet, anisotropies of the SGWB provide a nontrivial opportunity to verify the rationality of inflation and detect the energy scale of inflation, especially for low-scale inflationary models. Square kilometer array has the opportunity to detect the anisotropies of such SGWBs. The common-spectrum process observed recently by NANOGrav could also be interpreted by the SGWB from cosmic DWs.
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