Inflation with Einstein-Gauss-Bonnet, non-minimal, and non-minimal derivative couplings: the constant-roll condition

Abstract

In our research, we consider and study the inflation theories of Einstein-Gauss-Bonnet, minimal, non-minimal, and non-minimal derivative coupling with the constant-roll condition. Given the gravitational wave event, GW170817, which produces the speed of gravitational waves that was almost equal to the speed of light in vacuum, we constrain that the speed of the tensor perturbation was nearly equal to unity, . We involve a scalar field potential whose function can be obtained from an equation of motion by choosing the Gauss-Bonnet coupling functions. We use the linear and quadratic coupling functions, which are their simplest functions. The one result obtained are able to produce observed quantities such as the spectral index for scalar perturbation, ns = 0.9642, the spectral index for tensor perturbation, nT = −5.2471 × 10−4, and tensor-scalar ratio, r = 0.0041, which are compatible with the newest Planck data using the slow-roll parameters obtained analytically.