Considering graviton as the only messenger that exists between the inflaton, the dark sector and the Standard Model (SM), we show, it is possible to simultaneously generate the observed relic density of dark matter (DM), the baryon asymmetry via leptogenesis, as well as successful reheating after inflation. Assuming the inflaton $\phi$ oscillates in a monomial potential $V(\phi)\propto \phi^k$ at the end of inflation, reheating via minimal gravitational interaction turns out to be excluded due to excessive production of gravitational wave (GW) energy density from inflation. We thus (a) extend the minimal model by considering a non-minimal gravitational contribution to radiation and (b)) propose an explanation for the PeV excess observed by IceCube, when the DM has an explicit Yukawa coupling to the SM leptong and Higgs. We also propose a novel scenario, where the gravitational production is a two-step process, through the production of a pair of scalars, that eventually decay into fermionic final states. Our framework gives rise to detectable primordial GW signal, that falls within the sensitivity of several proposed GW detectors.