Dilaton-Induced Resonant Production of Ultralight Vector Dark Matter

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 $ε_i=Φ_i/M$ and the gravitational onset fraction $r_i=Φ_i^2/(6\Mpl^2)$. For a background with constant equation-of-state parameter $w_b$, the narrow-band Floquet exponent obeys $μ/H\propto a^{3w_b/2}$; 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

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