Consistency relation in power law G-inflation

Abstract

In the standard inflationary scenario based on a minimally coupled scalar field, canonical or non-canonical, the subluminal propagation of speed of scalar perturbations ensures the following consistency relation: $r \leq - 8n_{_T}$, where $r$ is the tensor-to-scalar-ratio and $n_{_T}$ is the spectral index for tensor perturbations. However, recently, it has been demonstrated that this consistency relation could be violated in Galilean inflation models even in the absence of superluminal propagation of scalar perturbations. It is therefore interesting to investigate whether the subluminal propagation of scalar field perturbations impose any bound on the ratio $r/|n_{_T}|$ in G-inflation models. In this paper, we derive the consistency relation for a class of G-inflation models that lead to power law inflation. Within these class of models, it turns out that one can have $r > - 8n_{_T}$ or $r \leq - 8n_{_T}$ depending on the model parameters. However, the subluminal propagation of speed of scalar field perturbations, as required by causality, restricts $r \leq -(32/3)\,n_{_T}$.