Dilaton-Induced Resonant Production of Ultralight Vector Dark Matter

Abstract

A dilatonic half-mass resonance can produce ultralight vector dark matter only if the Floquet instability becomes efficient before the oscillating spectator scalar dominates the cosmic expansion. We formulate this requirement in terms of the microscopic modulation parameter $\epsilon_i=\Phi_i/M$ and the gravitational onset fraction $r_i=\Phi_i^2/(6\Mpl^2)$. For a background with constant equation-of-state parameter $w_b$, the narrow-band Floquet exponent obeys $\mu/H\propto a^{3w_b/2}$; during radiation domination this ratio grows as $a^{1/2}$, while it remains constant for matter-like expansion. Imposing that the delayed instability occurs before spectator domination yields the amplitude-independent bound $M/\Mpl\lesssim\sqrt6,c_1\simeq0.31$, with $c_1\simeq1/8$ determined by the linear half-mass branch. An explicit expanding-background analysis confirms that $a_\star<a_{\rm dom}$ for sub-Planckian $M$, whereas $M\simeq\Mpl$ postpones efficient growth until after domination. Combining this embedding condition with the efficient-transfer normalization gives $m_{\gamma'}\propto r_i^{-2}$, implying that the ultralight range $m_{\gamma'}\sim10^{-20}$--$10^{-18},{\rm eV}$ corresponds to $r_i\sim10^{-5}$--$10^{-4}$ rather than to early spectator domination. The polarization-resolved canonical analysis shows that longitudinal production is more strongly concentrated in the infrared than transverse production, while derivative terms from canonical normalization modify the leading Floquet exponents at order unity. St\"uckelberg and Higgsed completions impose distinct ultraviolet consistency conditions, including radial decoupling and symmetry-restoration constraints. The viable branch is therefore radiation-era, perturbative, infrared-dominated, and associated with a sub-Planckian kinetic scale.