Gravitational portals with nonminimal couplings
- Clery, Simon et al
- arXiv:2203.02004UMN--TH--4116/22FTPI--MINN--22/07CERN-TH-2022-025
 | \em \small Feynman diagram for the 4-point interactions between the inflaton $\phi$, the dark matter scalar candidate $X$, and the Higgs boson $h$, given by the Lagrangian~(\ref{lag4point}). |
 | \em \small Feynman diagram for the (dark) matter production through the gravitational scattering of the inflaton or the Higgs boson from the thermal bath. |
 | \em \small Contours of the ratio of the dark matter production rates from the thermal bath based on non-minimal gravitational interactions to those based on minimal interactions. The ratio is displayed in the $(\xi_h,\xi_X)$ plane. Note that as discussed in the Introduction, negative values of $\xi_h$ may require new physics (such as supersymmetry) to stabilize the Higgs vacuum. |
 | \em \small Contours of the ratio of the dark matter production rates from oscillations in the inflaton condensate based on non-minimal gravitational interactions to those based on minimal interactions. The ratio is displayed in the $(\xi_\phi,\xi_X)$ plane. |
 | \em \small The maximum temperature during reheating generated separately by minimal and non-minimal gravitational scattering of Higgs bosons in the thermal bath. |
 | \em \small Evolution of the inflaton density (blue) and the total radiation density (red), with radiation density produced from inflaton decays (dashed orange) and $\phi~\phi \rightarrow h~h$ scattering processes $\rho_R^{\sigma, \, \xi}$ (dotted green) and $\rho_R^{\sigma}$ (dash-dotted purple) with $\sigma_{\phi h}^{\xi}/\sigma_{\phi h} = 100$ (or $\xi_{\phi} = \xi_h = \xi \simeq -2.3~{or}~1.8$), as a function of $a/\ae$ for a Yukawa-like coupling $y = 10^{-8}$ and $\rhoe \simeq 0.175 \, m_{\phi}^2 M_P^2$ $\simeq 9 \times 10^{62} \, \rm{GeV}^4$. The black dashed lines corresponds to the ratios $a_{\rm{int}}/a_{\rm{end}} \simeq 150$ and $6500$, which agrees with Eq.~(\ref{aint}). The numerical solutions are obtained from Eqs.~(\ref{eq:diffrhophi}), (\ref{eq:diffrhor}), and (\ref{eq:rhorad1}). |
 | \em \small Region of parameter space respecting the relic density constraint $\Omega_X h^2=0.12$ in the plane ($m_X$,$\trh$) for different values of $\xi=\xi_h=\xi_X$ and $\rhoe \simeq 0.175 \, m_{\phi}^2 M_P^2$ in the case of gravitational production from the thermal bath $h~h \rightarrow X~X$. Both minimal and non-minimal contributions are taken into account. |
 | \em \small Region of parameter space respecting the relic density constraint $\Omega_X h^2=0.12$ in the plane ($m_X$,$\trh$) for different values of $\xi_\phi=\xi_h=\xi_X=\xi$ and $\rhoe \simeq 0.175 \, m_{\phi}^2 M_P^2$ in the case of production from gravitational inflaton scattering $\phi~\phi \rightarrow X~X$. Both minimal and non-minimal contributions are taken into account. |