AMPLIFICATION OF GRAVITATIONAL-WAVES IN SCALAR-TENSOR THEORIES OF GRAVITY

The gravitational wave equation for a spatially flat Friedmann-Roberts on-Walker universe is derived in the context of scalar-tensor theories of gravity, which have the Brans-Dicke theory as a particular case. T his equation is solved for several cosmological scenarios, including t he expansions governed by the Nariai as well as the Gurevich-Finkelste in-Ruban solutions of Brans-Dicke theory and for a new set of exact so lutions of other scalar-tensor theories. The amplification of gravitat ional waves is studied in comparison to what happens in the general re lativistic case. It is shown how the coupling with the scalar field ch anges the scales defining very large and very small wave numbers, and consequently the value of the amplification coefficient. It is found t hat very small values for the coupling parameter could lead to amplifi cation of subhorizon waves. The creation of the corresponding high-fre quency gravitons is explained as a response to the rapid time variatio n of the gravitational ''constant,'' which can occur near the singular ity in some models. It is also shown that there could be amplification of waves even in a radiation-dominated universe in some cases, becaus e the wave equation is not conformally invariant, except for the case of Nariai's solution in the Brans-Dicke theory.