Inflation with Gauss–Bonnet and Chern–Simons higher-curvature-corrections in the view of GW170817

Abstract

Inflationary era of our Universe can be characterized as semi-classical because it can be described in the context of four-dimensional Einstein’s gravity involving quantum corrections. These string motivated corrections originate from quantum theories of gravity such as superstring theories and include higher gravitational terms as, Gauss–Bonnet and Chern–Simons terms. In this paper we investigated inflationary phenomenology coming from a scalar field, with quadratic curvature terms in the view of GW170817. Firstly, we derived the equations of motion, directly from the gravitational action. As a result, formed a system of differential equations with respect to Hubble’s parameter and the inflaton field which was very complicated and cannot be solved analytically, even in the minimal coupling case. Based on the observations from GW170817 event, which have shown that the speed of the primordial gravitational wave is equal to the speed of light, \(c_{\mathcal {T}}^2=1\) in natural units, our equations of motion where simplified after applying the constraint \(c_{\mathcal {T}}^2=1\), the slow-roll approximations and neglecting the string corrections. We described the dynamics of inflationary phenomenology and proved that theories with Gauss–Bonnet term can be compatible with recent observations. Also, the Chern–Simons term leads to asymmetric generation and evolution of the two circular polarization states of gravitational wave. Finally, viable inflationary models are presented, consistent with the observational constraints. The possibility of a blue tilted tensor spectral index is briefly investigated.