Compatibility of Einstein-Gauss-Bonnet inflation theory with non-minimal derivative coupling in the constant-roll

Inflation is a theory in cosmology that explains that the early universe experienceda very fast expansion in a very short time and is able to explain some cosmological problemsand the presence of gravitational waves generated during the inflation period. Based on theevent GW170817, it was found that c2t = 1, which indicates that the speed of gravitationalwaves is nearly equal to the speed of light. This contradicts several modified theories of gravity,one of which is the Einstein-Gauss-Bonnet theory. This paper examines the compatibility ofEinstein-Gauss-Bonnet inflation theory with the GW170817 phenomenon, with the addition ofthe Non-minimal derivative coupling term and the constant-roll approach and its characteristics.The formulation of observational quantities is carried out using Horndeski theory and EffectiveField Theory with ADM formalism and the calculations are done numerically. The constantvalues are selected in such a way that the spectral index values and tensor-scalar ratios are closeto the 2018 Planck data. The results found that this theory is compatible with GW170817 withthe influence of Gauss-Bonnet term and constant-roll parameter β most dominant.