Parametric resonance production of ultralight vector dark matter

Vector bosons heavier than ${10}^{-22}\mathrm{eV}$ can be viable dark matter candidates with distinctive experimental signatures. Ultralight dark matter generally requires a nonthermal origin to achieve the observed density, while still behaving like a pressureless fluid at late times. We show that such a production mechanism naturally occurs for vectors whose mass originates from a dark Higgs. If the dark Higgs has a large field value after inflation, the energy in the Higgs field can be efficiently transferred to vectors through parametric resonance. Computing the resulting abundance and spectra requires careful treatment of the transverse and longitudinal components, whose dynamics are governed by distinct equations of motion. We study these in detail and find that the mass of the vector may be as low as ${10}^{-18}\mathrm{eV}$, while making up the majority of the dark matter abundance. This opens up a wide mass range of vector dark matter as cosmologically viable, and further motivates the experimental searches for such particles.

Figure 1

Instability charts of transverse (red) and longitudinal (blue) modes. The dashed lines represent different values of $\kappa$, and resonance bands above $\kappa =e/\lambda$ correspond to relativistic production. In the inset we show the $e/\lambda \ll 1$ limit in which the enhancement of longitudinal mode production over transverse modes is seen explicitly.

Figure 2

Viable parameter space for parametric resonance production of vectors in the limit $\lambda \gg e$. We fix the initial condensate amplitude ${\varphi }_0$ such that the dark sector saturates the DM relic abundance ${\mathrm{\Omega }}_X+{\mathrm{\Omega }}_{\varphi }\simeq {\mathrm{\Omega }}_{\mathrm{DM}}$. Shown are constraints from coldness (yellow), cosmic strings (red), isocurvature (purple), late-time dark Higgs decays (brown) and sufficiently long PR (blue) as described in the text. Left: At every point in parameter space we fix $m_{\varphi }\simeq 100m_X$. We do not incorporate any additional interactions, and the dark Higgs makes up nearly all the DM, i.e., ${\mathrm{\Omega }}_X\simeq {10}^{-2}{\mathrm{\Omega }}_{\varphi }$. Right: Vectors make up all of the DM, and the dark Higgs is eliminated at late times. At every point in parameter space we fix $m_{\varphi }=10\mathrm{GeV}$ and show the corresponding constraint from thermalization requirements (green) as described in the Appendix.

Figure 3

Viable parameter space for parametric resonance production of vectors in the limit $e\gg \lambda$. We fix the initial condensate amplitude ${\varphi }_0$ such that the dark sector saturates the DM relic abundance ${\mathrm{\Omega }}_X+{\mathrm{\Omega }}_{\varphi }\simeq {\mathrm{\Omega }}_{\mathrm{DM}}$. Shown are constraints from coldness (yellow), cosmic strings (red), and sufficiently long PR (blue) as described in the text. Both plots have the vector making up nearly all the DM. Left: At every point in parameter space we fix $m_X\simeq 10m_X$ and thus ${\mathrm{\Omega }}_{\varphi }\simeq {10}^{-1}{\mathrm{\Omega }}_X$. Right: At every point in parameter space we fix $m_X\simeq 1000m_{\varphi }$ and thus ${\mathrm{\Omega }}_{\varphi }\simeq {10}^{-3}{\mathrm{\Omega }}_X$.