WIMPs, FIMPs, and Inflaton phenomenology via reheating, CMB and $\Delta N_{eff}$

In this paper, we extensively analyzed the reheating dynamics after inflation and looked into its possible implication on dark matter (DM) and inflaton phenomenology. We studied the reheating through various possible channels of inflaton going into massless scalars (bosonic reheating) and fermions (fermionic reheating) via non-gravitational and gravity-mediated decay processes. We further include the finite temperature effect on the decay process. Along with their precise roles in governing the dynamics, we compared the relative importance of different temperature-corrected decay channels in the gradual process of reheating depending on the reheating equation of state (EoS), which is directly related to inflaton potential. Particularly, the universal gravitational decay of inflaton is observed to play a very crucial role in the reheating process for a large range of inflaton decay parameters. For our study, we consider typical $\alpha$-attractor inflationary models. We further establish the intriguing connection among those different inflaton decay channels and the CMB power spectrum that can have profound implications in building up a unified model of inflation, reheating, and DM. We analyze both fermion and scalar DM with different physical processes being involved, such as gravitational scattering, thermal bath scattering, and direct inflaton decay. Gravitational decay can again be observed to play a crucial role in setting the maximum limit on DM mass that has already been observed earlier in the literature [52]. Depending on the coupling strength, we have analyzed in detail the production of both FIMP and WIMP-like DM during reheating and their detailed phenomenological implications from the perspective of various cosmological and laboratory experiments.