Einstein-Gauss-Bonnet quintessential inflation: From super-inflation to emergent warm inflation

Abstract: This work presents a unified inflationary and late-time cosmology, developed within Einstein-Gauss-Bonnet gravity coupled to three scalar fields, governed by a single potential and coupling function throughout cosmic history. Permitting the Gauss-Bonnet coupling to depend on the field content, rather than assigning it arbitrarily, produces a two-phase inflationary scenario: the higher-curvature term initially drives expansion and later becomes a subdominant. The initial super-inflationary stage ends dynamically when the geometrically induced stabilization of the waterfall field fails, at a field value determined by the combination $(n-1)Q$. Coherent oscillations of the waterfall condensate serve as the initial radiation source, replacing conventional reheating and establishing the thermal bath necessary for the subsequent warm phase. Utilizing a two-stage dissipation mechanism with $Γ_φ\propto T<sup>3$, the scalar and tensor spectra are derived while retaining Gauss-Bonnet contributions, demonstrating that the growth of inflaton fluctuations is regulated by the shear viscosity of the bath, which is essential for model viability. A quartic potential, previously excluded in the cold scenario, becomes viable, with $n_s$ within the Planck $1σ$ band and $r$ suppressed. Agreement with the spectral index is generic, while internal consistency confines the model to a narrow band in $(n-1)Q$. Finally, the release of the third scalar near matter-radiation equality transforms a very small mass scale into a very large coupling by a logic inverse to the seesaw mechanism. At late times, the inflaton persists as dark energy.