A forecast for the detection of the power asymmetry from galaxy surveys

Abstract: We investigate the possibility of detecting in redshift surveys a hemispherical power asymmetry similar to that first reported in CMB observations. We assume the hemispherical asymmetry arises from a linear gradient in comoving coordinates in the perturbation amplitude. We predict the resulting clustering of galaxy or galaxy cluster tracers using an excursion set approach; doing so accounts for the variation of both the underlying clustering and the tracer bias. Based on the predicted variation of the clustering of tracers, we perform a Fisher matrix forecast of the galaxy clustering amplitude and calculate the statistical significance for ideal surveys and planned surveys. The results indicate that the DESI galaxy survey would be able to detect this signal with higher than $3\sigma$ significance if the asymmetry does exist. We also investigate the amplitude and scale dependence of the above result. The DESI galaxy survey can probe the dipole amplitude higher than 0.04, which correspond to a $\pm4\%$ difference of the temperature fluctuation along and opposite the dipole direction, at least at the $2\sigma$ level. Additionally, we investigate a modulation of the power spectrum that exhibits asymmetry only for large scales. This modulation is potentially detectable. For Milky Way galaxy mass tracers, the scale-dependent modulation yields a larger change in the large scale power spectrum than does a scale-independent modulation, because the former does not alter the bias.