Estimation of gravitational production uncertainties

Abstract

Cosmological production of scalar, non-minimally coupled dark matter depends on the specifics of the inflationary model under consideration. We analyze both Starobinsky inflation and a quadratic potential, solve the full background dynamics, study pair production during inflation and reheating, and find that the observed dark matter abundance can be explained solely by this mechanism, regardless of the inflationary model. Qualitative differences between the two cases only appear for dark matter masses close to the inflationary scale. In addition, we identify a large region in parameter space in which cosmological production of dark matter is mostly independent of the chosen inflationary potential, highlighting the robustness of this dark matter production mechanism and its independence of the unknown particular details of inflation. In the region of masses lower than the scale of inflation, and sufficiently away from the conformal limit, the total comoving number density of produced particles becomes a function of the coupling to the geometry alone. This allows us to provide an approximated analytic expression for fitting the resulting abundance.

Figures (8)

• Figure 1: Ricci scalar $R$ as function of cosmological time $t$ during transition from inflation to reheating for the quadratic (red) and Starobinsky potential (blue).
• Figure 2: Spectra of produced particles as function of the wavenumber $k$ for $m=10^{-4}m_{\phi}$ (left) and $m=1.6m_{\phi}$ (right), and different values of the coupling $\xi$. The solid lines correspond to the Starobinsky potential, whereas the dashed lines are the results in the quadratic case.
• Figure 3: Spectra of produced particles as function of the wavenumber $k$ for $m=10^{-4}m_{\phi}$ (left) and $m=1.6m_{\phi}$ (right), and different values of the coupling $\xi$. The solid lines correspond to the Starobinsky potential, whereas the dashed lines are the results in the quadratic case.
• Figure 4: Abundance in the present day of produced particles for each potential as a function of their mass $m$ and coupling $\xi$, for a reheating temperature of $T_{\text{rh}}=10^{13}\ \mathrm{GeV}$. The dashed line corresponds to the observed abundance of dark.
• Figure 5: Abundance of produced particles as a function of reheating temperature $T_{\text{rh}}$ and mass $m$, for each potential and two values of the coupling, $\xi=1$ (top) and $\xi=1/6$ (bottom). The dashed line corresponds to the observed abundance of dark matter.