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A model of vector dark matter that communicates with the Standard Model onlythrough gravitational interactions has been investigated. It has been shown indetail how does the canonical quantization of the vector field in varying FLRWgeometry implies a tachyonic enhancement of some of its momentum modes.Approximate solutions of the mode equation have been found and verified againstexact numerical ones. De Sitter geometry has been assumed during inflationwhile after inflation a non-standard cosmological era of reheating with ageneric equation of state has been adopted which is followed by theradiation-dominated universe. It has been shown that the spectrum of darkvectors produced gravitationally is centered around a characteristic comovingmomentum $k_\star$ that is determined in terms of the mass of the vector $m_X$,the Hubble parameter during inflation $H_{\rm I}$, the equation of stateparameter $w$ and the efficiency of reheating $\gamma$. Regions in theparameter space consistent with the observed dark matter relic abundance havebeen determined, justifying the gravitational production as a viable mechanismfor vector dark matter. The results obtained in this paper are applicablewithin various possible models of inflation/reheating with non-standardcosmology parametrized effectively by the corresponding equation of state andefficiency of reheating.

Gravitational production of vector dark matter