GW170817 Implementation on Einstein-Gauss-Bonnet Theory with Non Minimal and Non Minimal Derivative Coupling
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Abstract
The GW170817 event manifests that gravitational wave velocity is close to the
speed of light. As a result, several theories of gravity are no longer applicable, including EinsteinGauss-Bonnet (EGB) inflation. However, a constraint equation could be applied so that the
theory could produce a viable result. In this study, the EGB inflation is being extended by
adding a non-minimal coupling (NMC) and a non-minimal derivative coupling (NMDC). Free
parameters values were evaluated to obtained viability with observational indices. We use power
law and exponential Gauss-Bonnet coupling functions. Each model provides observational values
of ns and r that are compatible with the observations and has its characteristic. It specifies
the free parameter that controls the alteration of ns and r values. The power-law model is
controlled by the power m of the Gauss-Bonnet coupling function and the potential integration
constant, V2. While the exponential model is controlled by the potential integration constant c
and the power m of the exponential function. Some approximations do not hold true so that the
models need to be rectified. Apparently, the rectified power-law model is violating null energy
condition (NEC), so we also provide the non-violating NEC power-law model.
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