On gravitational waves generated during inflation under the influence of a dynamical cosmological “constant”

Abstract

We study cosmological gravitational waves generated during inflation under the influence of a decaying cosmological “constant”, in the Transverse-Traceless (TT) gauge. In our approach we consider a non-perturbative contribution of the dynamical cosmological “constant” to the tensor modes. As an application of the model we study the well-known cases $\Lambda(t)=\sigma H^2$ and $\Lambda(t)=\vartheta H$ . The spectrum of gravitational waves for the first case results scale invariant at the end of inflation, whereas for the second case scale invariance is not achieved, leaving this to new proposals of the form: $\Lambda(t)=f(H,H^{2})$ , in order to include inflation in some $\Lambda(t)CDM$ models. We also found that the non-perturbative contributions of $\Lambda$(t) , accelerate the decreasing of the amplitude of gravitational waves during a power law inflationary stage, by an exponential factor.