Evolution of tensor perturbations in scalar-tensor theories of gravity

The evolution equations for tensor perturbations in a generic scalar-tensor theory of gravity are presented. Exact solutions are given for a specific class of theories and Friedmann-Lemaître-Robertson-Walker backgrounds. In these cases it is shown that, although the evolution of tensor models depends on the choice of parameters of the theory, no amplification is possible if the gravitational interaction is attractive.

Figure 1

Plot of the solutions of (67) for a scalar-tensor theory of gravity in vacuum with $F(\varphi )=-\xi {\varphi }^2$, $V(\varphi )=\lambda {\varphi }^p$, the background (63), $k=10$, and $r=-1$. The dashed line represents ${\sigma }^{(k)}$, the dotted-dashed curve represents $H^{(k)}$, and the solid curve represents $E^{(k)}$.

Figure 2

Plot of the solutions of (70) for a scalar-tensor theory of gravity in vacuum with $F(\varphi )=-\xi {\varphi }^2$, $V(\varphi )=\lambda {\varphi }^p$, the background (63), $k=10$, and $r=-1$. The solid curve represents ${\sigma }^{(k)}$, the dashed curve represents $H^{(k)}$, and the dotted-dashed curve represents $E^{(k)}$.