Matter Dipole and Hubble Tension due to Large Wavelength Perturbations

TL;DR

This work investigates whether large-wavelength perturbations can account for the quasar number-count dipole and the local Hubble tension. Using a covariant galaxy number-count formalism, it analyzes subhorizon adiabatic modes with $k$ in $(10^{-4},4 imes10^{-3})$ Mpc^-1 and superhorizon curvature perturbations with $k \,\lesssim\, 0.3 H_0$, finding that subhorizon modes can contribute but typically fall short of the observed dipole, whereas a single superhorizon mode can produce a substantial monopole shift in $H_0$ consistent with CMB quadrupole bounds. The results suggest a mild violation of the cosmological principle on the largest scales could jointly influence dipole observations and the Hubble tension, inviting future probes (e.g., SKA) to test these scenarios. The analysis emphasizes that the dipole amplitude and its redshift dependence are key discriminants among cosmological explanations for the observed anomalies.

Abstract

We theoretically analyze the dipole anisotropy observed in the quasar distribution from the CatWISE2020 catalog. The catalog data shows a peak around $z\approx 1$, 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 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^{-4} - 4 \times 10^{-3})~\mathrm{Mpc}^{-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 wavenumber $k\lesssim0.3H_0$ 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 $H_0$.

Figures (5)

• Figure 1: The transfer function for $\Phi$ as a function of redshift, normalized to the initial curvature perturbation $\Phi_i$. By redshift $z \sim 0.1$, the initial perturbation has decayed by approximately 25% of its original value, highlighting the impact of cosmic expansion and the influence of dark energy.
• Figure 2: (a) Contributions of various terms in Eq. \ref{['Delta_corr']} to the number count dipole at redshift $z = 1$ for wavenumber $k$ in the range $(10^{-4}, 4 \times 10^{-3})$ Mpc$^{-1}$. (b) Contributions of $D_1^{\delta}$ to the number count dipole as a function of $z$.
• Figure 3: The intrinsic dipole amplitude in the number counts is shown as a function of wavenumber $k$ for sources extending up to redshifts $z_s = 1,2,$ and $3$. The curves are smoothed by interpolating the computed data points.
• Figure 4: Distribution of total dipole amplitude $|\vec{D}_{\rm total}|$ from random Gaussian samples, each combining an isotropic intrinsic dipole $\vec{D}_{\rm int}$ and the kinematic dipole $\vec{D}_{\rm kin}$ due to our motion. Result shown for source population resdshift cut at $z_s=1$.
• Figure 5: Plot of $|\Phi_k \sin\omega|$ versus $k/H_0$ for the observed Hubble tension. The horizontal dashed line satisfies the $H_0$ excess at z=0.0017. The blue-shaded region denotes the region of parameter space that satisfies the CMB quadrupole constraint.