Analysis of gravitational waves from inflation model with minimal, non-minimal, and non-minimal derivative coupling of scalar field from Horndeski theory

Abstract

Inflation theory provides solutions for problems in cosmology, such as horizon problem and flatness problem. The study of Gravitational waves production in cosmic inflation era not prove the general inflation theory, but also to differentiate in detail among specific models. In this research, we use inflation model with minimal, non-minimal, and non-minimal derivative coupling of scalar field without potential from Horndeski Theory. From this model, we calculate scalar and tensor perturbation equations and then obtain its equation of gravitational waves, spectral index for each perturbation mode and tensor-to-scalar ratio. Spectral index and tensor-to-scalar ratio nearly scale-invariant and agree with observational data for some Ho, ζ, and ξ. Gravitational waves remain constant during inflation and start oscillates when its modes enter the horizon. Energy of this gravitational waves is scale-invariant for modes that re-enter horizon during radiation dominated era and rises toward lower frequencies.