Addressing Dipole Tension via Clustering in $\Lambda$CDM and beyond

The dipole in the angular distribution of the cosmic microwave background (CMB) is attributed to the Doppler effect and our motion relative to the CMB rest frame. It is expected that observations of large-scale structures (LSSs) would also exhibit a related kinematic dipole. However, numerous studies of the LSS dipole have shown significant discrepancies with predictions based on the CMB. In this work, we investigate how considering the clustering dipole affects the LSSs distribution dipole using the National Radio Astronomy Observatory (NRAO) Very Large Array (VLA) Sky Survey (NVSS) and the Wide-field Infrared Survey Explorer (WISE), and examine the nonlinear regime to calculate the correlation between the clustering and the kinematic dipole. Our results show up to $\lesssim28\%$ enhancement in the clustering dipole amplitude compared to previous studies, with increases of up to $\lesssim 22\%$ in $\Lambda$CDM and $\lesssim 28\%$ in modified gravity scenarios. Additionally, we explore a model in which the distribution of matter on LSS could be intrinsically anisotropic by a long-mode modulation. Using the remnant discrepancy between the observed and predicted dipole, we derive an upper limit for the amplitude of intrinsic dimensionless anisotropy $\lesssim 0.22$. Furthermore, we investigate these results within the framework of the $f(R)$ modified gravity model. We conclude that nonlinear clustering and local structure correlations partially alleviate the dipole tension within $\Lambda$CDM, yet, this anomaly remains a challenge. Two alternative models are in the direction of relaxing the tension. However, further investigation and more accurate data are needed to support a stronger argument.