Avoiding Big Rip singularities in phantom scalar field theory with Gauss–Bonnet term

Abstract

We consider a phantom scalar field coupled to the Gauss–Bonnet scalar within a spatially flat FLRW geometry. Moreover, we assume a nonzero interaction between the scalar field and the matter term. We perform a detailed phase space analysis using two sets of dimensionless variables. Specifically, we introduce dimensionless variables based on the Hubble normalization approach and a new set based on the matter-scalar field normalization. These two sets of variables allow for a comprehensive phase space analysis. This model supports inflationary solutions without the Big Rip or Big Crunch singularities appearing as asymptotic solutions. This outcome is attributed to the presence of the Gauss–Bonnet scalar. The result remains valid even in the absence of the interaction term.