Quantum creation of very massive particles in the gravitational background of anisotropically perturbed Minkowski space-time is discussed. In this framework of semiclassical gravity the quantum mechanically produced heavy particles which made the initial space-time unstable and ushered into the FRW expansion phase at the Planck order epoch of the universe can account for the energy density at that epoch. Also, both the conformal and nonconformal particle-creations in the FRW era of the early universe after the Planck order epoch are investigated. In this consideration the total particle number of the observable universe as well as the present value of photon-to-baryon ratio are obtained in agreement with their accepted values from the observational facts. The existence of very massive particles at the very early period of the universe is also discussed here with the suggestion of an observational test. © 2001 Plenum Publishing Corporation.