Spin-1 Ultralight Dark Matter under Cosmological Scrutiny: Mass Constraints from CMB and Distance Probes

Abstract

We present cosmological constraints on spin-1 ultralight dark matter, described by a vector field (VFDM) with mass $m_{\rm A}$, using Planck CMB data and geometrical probes from BAO and SNIa. A key theoretical result is the derivation of the full CMB temperature covariance matrix, including both diagonal and off-diagonal anisotropic contributions induced by the preferred direction of the background vector field. We first constrain the model using the diagonal part of the covariance, together with CMB lensing; the off-diagonal terms, which couple multipoles with $\Delta\ell\in\{2,4\}$, could bias lensing reconstruction, but only at very low multipoles ($L=\{2,4\}$) not included in the Planck likelihood. We consider both a pure VFDM scenario and a mixed VFDM+CDM scenario, characterized by the fraction $f=\Omega_{\rm A}/(\Omega_{\rm A}+\Omega_{\rm cdm})$, obtaining $\log_{10}(m_{\rm A}/\mathrm{eV})>-24.07$ (95\% C.L.) in the pure case, and a clear correlation between $f$ and $m_{\rm A}$ in the mixed case, with smaller fractions allowing lighter masses; standard cosmological parameters remain fully consistent with $\Lambda$CDM. For the off-diagonal contributions, we derive the corresponding Bipolar Spherical Harmonic (BipoSH) coefficients and predict their amplitude using our best-fit and bounds. While the anisotropic signal is difficult to detect in the pure VFDM scenario with current Planck data, mixed VFDM+CDM models can produce signals at, or above, Planck sensitivity over a range of multipoles, motivating dedicated searches for this characteristic signature.