Post-inflationary production of particle Dark Matter: non-minimal Natural and Coleman--Weinberg inflationary scenarios

We investigate the production of non-thermal fermionic dark matter particles during the reheating era following slow roll inflation, driven by inflaton $\varphi$ non-minimally coupled to the curvature scalar, $\mathcal{R}$. Two types of non-minimal couplings are considered: $\xi\varphi^2\cal{R}$ for both natural (referred to as NM-N) and for Coleman-Weinberg (referred to as NM-CW) inflation, and $\alpha\left(1+\cos(\frac{\varphi}{f_a})\right)$ only for natural inflation (referred to as NMP-N), where $\alpha$ and $\xi$ are dimensionless parameters and $f_a$ is an energy scale. We determine benchmark values for slow roll inflationary scenarios satisfying current bounds from Cosmic Microwave Background (CMB) radiation measurement and find the mass of inflaton to be $m_\phi\sim {\cal O}\left(10^{12}\right) \text{GeV}$ for all three inflationary scenarios and tensor-to-scalar ratio, $r\sim 0.0177$ (for NM-N), $\sim 0.0097$ (for NMP-N), and $r\sim 0.0157$ (for NM-CW) which fall inside $1-\sigma$ contour on scalar spectral index versus $r$ plane of Planck2018+BICEP3+KeckArray2018 joint analysis, and can be probed by future CMN~observations e.g. Simons Observatory. We then show that dark matter particles produced from the decay of inflaton can fully match the present-day cold dark matter (CDM) yield, as well as other cosmological constraints, if the coupling value between inflaton and dark matter, $y_\chi$, and the dark matter mass, $m_\chi$, are within the range $10^{-1}\gtrsim y_\chi\gtrsim 10^{-20}$ for NM-N and NMP-N ($10^{-4}\gtrsim y_\chi\gtrsim 10^{-20}$ for NM-CW) and ${\cal O}\left(\text{keV}\right)\lesssim m_\chi\lesssim m_\phi/2$ (for NM-N, NMP-N, and NM-CW). The exact range of $y_\chi$ and $m_\chi$ varies with different benchmark values as well as parameters of inflation, like energy scale of inflation and $r$, some of which are within reach of next-generation CMB experiments.