Matter dipole and Hubble tension due to large wavelength perturbations

We theoretically analyze the dipole anisotropy observed in the quasar distribution from the CatWISE2020 catalog. The catalog data shows a peak around $z\ensuremath{\approx}1$, suggesting the presence of a large-scale dipole component. We explore the possibility that this dipole could be driven by primordial density fluctuations from modes that were superhorizon at the time of cosmic microwave background (CMB) decoupling but have since entered the horizon and become subhorizon. In particular, we consider the impact of adiabatic modes with wave numbers $k$ in the range $({10}^{\ensuremath{-}4}\ensuremath{-}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3})\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, corresponding to wavelength scales of several Gpc. Such modes can create large-scale density variations, likely causing anisotropies in the distribution of matter and, as a result, affecting the number density of observed quasars. We find that these can lead to a significant contribution to the dipole for sources up to redshifts of about 1, but are unable to explain the observed dipole. We also demonstrate that a superhorizon curvature perturbations mode, with a comoving wave number $k\ensuremath{\lesssim}0.3{H}_{0}$ can lead to a significant enhancement in the locally inferred Hubble constant. This effect offers a viable explanation for the observed discrepancy between local and CMB inferred measurements of ${H}_{0}$.