Tomographic Alcock-Paczynski method with redshift errors

The tomographic Alcock-Paczynski (AP) method is a promising method that uses the redshift evolution of anisotropic clustering in redshift space to calibrate cosmology. It extends the applicable range of the AP method to substantially nonlinear scales, yielding very tight cosmological constraints. For future stage-IV slitless spectroscopic surveys, non-negligible redshift errors might reduce the advantage of the tomographic AP method by suppressing the resolution of the nonlinear structure along the line of sight. The present work studies how redshift errors propagate to cosmological parameters in tomographic AP analysis. We use a formula sigma(z) = sigma(1 + z)(alpha) to model the redshift errors, with sigma varying from 0.001 to 0.006 and alpha varying from 0.5 to 1.5. The redshift errors produce a signal of anisotropic clustering that is similar to a strong Finger-of-God effect, which smears out both the AP signal and the contamination caused by redshift-space distortions (RSD). For the target precision of the Chinese Space Station Telescope optical survey (sigma less than or similar to 0.002), the decrement of constraining power on the dark energy equation of state is mild (less than or similar to 50 per cent), and the suppression of RSD contamination leads to a smaller bias-to-signal ratio. Our results indicate that the tomographic AP method will remain a useful and complementary tool for analyses of future slitless spectroscopic surveys.