Analysis of Gravitational Waves from Inflation Model with Minimal, Non-minimal, and Non-Minimal Derivative Coupling of Scalar Field from Horndeski Theory
M Zhahir Djogama (a*), Getbogi Hikmawan (a), Freddy P Zen (a,b)

a) Theoretical Physics Laboratory, THEPI Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132, West Java, Indonesia
*zhahirdjo[at]gmail.com
b) Indonesia Center for Theoritecal and Mathematical Physics (ICTMP), Jl. Ganesha 10 Bandung 40132, West Java, Indonesia

Abstract

Inflation theory provides solutions for problems in cosmology, such as horizon problem and flatness problem. Gravitational waves production in cosmic inflation era is caused by tensor perturbation in that era. The study of observational signatures of this gravitational waves provide not only a way to probe the general inflation theory, but also to discriminate in detail among specific models. In this paper, 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 indices for each perturbation mode and tensor-to-scalar ratio. Spectral indices and tensor-to-scalar ratio nearly scale-invariant and agree with observational data for some \(H_0\), \(\zeta\), and \(\xi\). Gravitational waves remain constant during inflation and start oscillates when its modes re-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.

Keywords: Inflation- Gravitational waves- Modified gravity- Horndeski theory

Topic: Theoretical High Energy Physics