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In this paper we investigate the inflationary phenomenology of an Einstein-Gauss-Bonnet theory compatible with the GW170817 event, by imposing the constant-roll evolution on the scalar field. We develop the constant-roll GW170817-compatible Einstein-Gauss-Bonnet formalism, and we calculate the slow-roll indices and the observational indices of inflation, for several models of interest. As we demonstrate, the phenomenological viability of the models we study is achieved for a wide range of the free parameters. In addition, for the same values of the free parameters that guarantee the inflationary phenomenological viability of the models, we also make predictions for the non-Gaussianities of the models, since the constant-roll evolution is known to enhance non-Gaussianities. As we show the non-Gaussianities are of the same order for the slow-roll and constant-roll case, and in fact in some cases, the amount of the non-Gaussianities is smaller in the constant-roll case.

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 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 $${\mathcal {O}}\sim (10^{-1})$$ O ∼ ( 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.

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An alternative scenario about the phenomenology of primordial universe is [Formula: see text]-inflation. According to this concept, inflation can be achieved by nonstandard kinetic term of scalar field, namely, the inflaton. In this paper, we focus on [Formula: see text]-essence models in the presence of a higher order and a linear kinetic term. Furthermore, the inflationary phenomenology with a Dirac–Born–Infeld scalar field is briefly examined, which arises from quantum theories of gravity such as superstring theory. Our approach about the inflationary era is that it can be described in the context of Einstein’s gravity involving quantum corrections such as the Chern–Simons string inspired parity violating gravitational term. The equations of motion namely, the Friedmann equation, the Raychadhuri equation and the Klein–Gordon equation for an expanding background are extracted from the gravitational action utilizing the variational principle. The consequential system of differential equations with respect to Hubble’s parameter and the inflaton field was quite perplexed in order to be solved with an analytic way. Therefore, the slow-roll conditions during inflationary era were imposed and terms with minor numerically contribution were neglected. From the overall phenomenological analysis, it is proved that models with exotic kinetic terms can generate viable results in consistency with the latest Planck data. Finally, the presence of Chern–Simons quantum corrections shifts the primordial spectral tensor index to blue. Even though blue gravitational waves are yet to be observed, if detected, compatibility with the aforementioned theory can be achieved.