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Logarithmic corrected Einstein-Gauss-Bonnet inflation compatible with GW170817

In this paper we investigate the inflationary phenomenology of an Einstein-Gauss-Bonnet theory with the extension of a logarithmic modified $f(R)$ gravity, compatible with the GW170817 event. The main idea of our work is to study different results for an almost linear Ricci scalar through logarithmic corrections and examine whether such model is viable. First of all, the theoretical framework under slow-roll evolution of the scalar field is presented and also developed the formalism of the constant-roll evolution making predictions for the non- Gaussianities of the models is developed , since the constant-roll evolution is known to enhance non-Gaussianities. As shown, the non-Gaussianities are of the order $\mathcal{O}\sim(10^{-1})$. Furthermore, the slow-roll indices and the observational indices of inflation, are calculated for several models of interest. As demonstrated, the phenomenological viability of the models at hand is achieved for a wide range of the free parameters and the logarithmic term has a minor contribution to numerical calculations, as expected.