TURNING VERY LONG TENSOR PERTURBATIONS INTO EFFECTIVE GRAVITATIONAL-WAVES - AN ESTIMATE OF THE GRAVITONS BACK-REACTION

The inequivalence of vacua at different instants of time leads to the production of tensor perturbations (''gravitational waves'') in scales larger than the Hubble radius. During noninflationary periods of expa nsion, the very long tensor perturbations become effective gravitation al waves as they enter the Hubble length, thus adding new contribution s to the energy density associated with the subhorizon waves rho(g). I t is shown that this phenomenom can be described as a process of produ ction of effective gravitons by using the macroscopic formalism to mat ter creation based on the thermodynamics of open systems. A creation p ressure term is introduced in the continuity equation obeyed by rho(g) in order to deal with this process. This allows the derivation of a d ynamical equation for the scale factor a(t) that takes into account th e effective gravitons back reaction. This equation is numerically solv ed for a model in which the universe suffers a transition from an arbi trary initial phase to a radiation-dominated period. If the barotropic index of the equation of state in the first epoch is close to 2/3, th e back reaction of the effective gravitational waves makes a(t) deviat e noticeably from the standard behavior a(t)proportional to t(1/2). Th e same phenomenom may happen during the matter-dominated era, which co uld affect theoretical calculations involving the age of the universe. [S0556-2821(97)07222-6].