Dilaton-Induced Resonant Production of Ultralight Vector Dark Matter

We study the resonant production of ultralight vector dark matter from an oscillating spectator scalar $\phi$ coupled to a massive vector $A_\mu$ through a dilatonic kinetic function $\W(\phi)$. The mechanism contains a narrow branch near $\mA/\mphi\simeq 1/2$. Assuming that the spectator remains subdominant until oscillations begin, we derive the onset fraction $r_i=\Phii^2/(6\Mpl^2)$ and show that, in the linear regime and for a background with constant equation-of-state parameter $w_b$, the growth-to-Hubble ratio scales as $\mu/H\propto a^{3w_b/2}$. Combined with the tuned-branch abundance estimate, this implies $m_{\gamma'}\propto r_i^{-2}$ for the relic dark-photon mass. In particular, the interval $m_{\gamma'}\sim10^{-20}$--$10^{-18}\,\mathrm{eV}$ maps to $r_i\sim10^{-4}$--$10^{-5}$, corresponding to a radiation-dominated onset with a subdominant spectator, while for $M=10^{17}\,\mathrm{GeV}$ the perturbative range $\epsilon_i=0.1$--$1$ gives $m_{\gamma'}\sim10^{-17}$--$10^{-21}\,\mathrm{eV}$. We also derive the polarization-resolved quadratic action in an FLRW background and formulate ultraviolet consistency conditions for both St\"uckelberg and Higgs completions, including perturbative control of the kinetic modulation, dark-Higgs decoupling, and symmetry-restoration bounds from vector backreaction.