Exact solution of the Einstein–scalar–Gauss–Bonnet model with Noether symmetry constraints

By applying Noether symmetry methods, analytic solutions are obtained for a generalized Einstein–scalar–Gauss–Bonnet model with a [Formula: see text] component. Variation with respect to the metric, supplemented by small perturbations, produces the equations of motion and the terms that determine the propagation speed of tensor perturbations. The resulting Hubble parameter incorporates contributions from stiff matter and dark energy, the last originating from a scalar field non-minimally coupled to the Gauss–Bonnet invariant. The viability of the model is assessed by using Cosmic Chronometers, Baryon Acoustic Oscillations, and type Ia supernovae data. Best model selection based on information criteria indicates a slight preference for this new framework over the [Formula: see text] Cold Dark Matter model. Stability of the model follows from the positive speed of sound and absence of “Ostrogradsky ghosts”. The total equation of state parameter hints toward the presence of a transition from decelerated to accelerated expansion at [Formula: see text], corresponding to the transition from matter to dark energy dominance. Early Universe dynamics, derived from the slow-roll parameters, spectral indices, and the tensor-to-scalar ratio, are found to be perfectly consistent with observations from Planck 2018 and the Atacama Cosmology Telescope.