From inflation to reheating and their dynamical stability analysis in Gauss–Bonnet gravity

Abstract

We investigate the inflation and reheating phenomenology in scalar-Einstein-Gauss–Bonnet theory of gravity where a scalar field non-minimally couples with the Gauss-Bonnet (GB) curvature term. Regarding the inflationary phenomenology, we find – (1) the inflation starts with a quasi de-Sitter phase and has an exit at a finite e-fold, which is indeed consistent with the resolution of horizon and flatness problems, (2) the scalar and tensor perturbations prove to be ghost free and do not suffer from gradient instability, (3) the curvature perturbation amplitude as well as its tilt and the tensor-to-scalar ratio turn out to be simultaneously compatible with the recent Planck data for suitable values of the parameters which also results to the inflationary energy scale ∼1012GeV. After the inflation ends, the scalar field starts to decay to radiation with a constant decay width. For our considered scalar potential and the GB coupling function, the model results to an analytic power law solution of the Hubble parameter and a logarithmic solution of the scalar field during the reheating era, where the exponent of the Hubble parameter determines the effective EoS parameter (weff) during the same. The stability of such reheating dynamics is examined by dynamical analysis which ensures that weff can go beyond unity and reach up-to the maximum value of max(weff)=1.56. The scenario with weff>1 proves to be purely due to the presence of the GB coupling function, which in turn may have important consequences on enhancing the primordial gravitational waves’ amplitude observed today. The inflationary e-fold number (Nf) gets further constrained by the input of the reheating stage, and we critically examine the constraint of Nf coming from both the inflation and reheating phenomenology. We finally construct the complete forms of scalar potential (V(ϕ)) and the GB coupling function (ξ(ϕ)) that smoothly transits from inflation to reheating, and numerically solve the Hubble parameter and the scalar field for such complete forms of V(ϕ) and ξ(ϕ). Such numerical solutions match with analytic ones in the respective regime. After the reheating ends, the GB term gets decouple from the theory and the radiation energy density dominates the energy budget of the universe, which in turn produces the standard radiation era of the universe.