Late-time behavior of primordial gravitational waves in expanding universe

The results of two different approaches to the late-time behavior of primordial gravitational radiation are compared. Using asymptotic expansion in time of the tetrad components of the Riemann tensor one finds that initially chaotic behavior transfers itself into a radiative gravitational field of Petrov typeN ast. On the other hand, to accomplish the physical picture, we study the high-frequency behavior of the field variables in the same formalism. We show that the background spacetime is of general Petrov type I, and then calculate the tetrad components of the stress-energy tensor induced by the disappeared radiation with the help of Newman-Penrose equations.