Parity violation in the CMB trispectrum from the scalar sector

Under the existence of chiral non-Gaussian sources during inflation, the trispectrum of primordial curvature perturbations can break parity. We examine signatures of the induced trispectrum of the cosmic microwave background (CMB) anisotropies. It is confirmed via a harmonic-space analysis that, as a consequence of parity violation, such a CMB trispectrum has nonvanishing signal in the ${\mathrm{\ell }}_1+{\mathrm{\ell }}_2+{\mathrm{\ell }}_3+{\mathrm{\ell }}_4=\text{odd}$ domain, which is prohibited in the concordance cosmology. When the curvature trispectrum is parametrized with Legendre polynomials, the CMB signal due to the Legendre dipolar term is enhanced at the squeezed configurations in $\mathrm{\ell }$ space, yielding a high signal-to-noise ratio. A Fisher matrix computation results in a minimum detectable size of the dipolar coefficient in a cosmic-variance-limited-level temperature survey as $d_1^{\mathrm{o}\mathrm{d}\mathrm{d}}=640$. In an inflationary model where the inflaton field couples to the gauge field via an $f(\varphi )(F^2+F\tilde{F})$ interaction, the curvature trispectrum contains such a parity-odd dipolar term. We find that, in this model, the CMB trispectrum yields a high signal-to-noise ratio compared with the CMB power spectrum or bispectrum. Therefore, the $\ell_1 + \ell_2 + \ell_3 + \ell_4 = $\text{odd}$$ signal could be a promising observable of cosmological parity violation.