Galaxy number-count dipole and superhorizon fluctuations

The following paper will present the problem of the discrepancy between the number-count dipole of far away sources and the Cosmic Microwave Background (CMB) dipole. We will derive calculations up to linear order for the observed galaxy number-count over-density while taking into account the relativistic effects on the past light cone, specifically using the cosmic ruler notation. We will also apply the adiabatic and isocurvature initial conditions on the calculated observed overdensity, testing if superhorizon fluctuations are the cause behind the cosmological dipole tension. We find that neither adiabatic or isocurvature fluctuations impact the number-count dipole. However, we find that isocurvature fluctuations can indeed induce a dipole contribution into the CMB.