Noether Symmetries and Inflationary Scenarios in Ghost-Free f(R,G) Gravity

Despite the well-known problem of the appearance of ghost degrees of freedom in gravitational models containing the Gauss–Bonnet invariant, there are special modifications in which this disadvantage can be eliminated. Such models include ghost-free generalizations of the Einstein–Gauss–Bonnet theory. Despite the mathematical attractiveness and theoretical validity of ghost-free f(R, G) models, their cosmological viability is often investigated using external reconstructive approaches that do not rely on the internal structure of the theory. In this paper, we propose an alternative method based on the use of internal model relationships defined by Noether symmetries. This approach makes it possible to significantly narrow down the class of acceptable theories and obtain explicit functional forms of scalar field potentials consistent with both the symmetric requirements and the ghost-free nature of the model. By applying the Noether symmetry method to a homogeneous and isotropic cosmological background, it is possible to obtain a set of allowable potentials with a nontrivial dynamic structure. These potentials are considered as physically motivated candidates for describing the early Universe. Based on them, a study of the inflationary dynamics of the model is conducted, based on the slow-roll parameters and spectral indices. The values obtained are compared with observations from the Planck mission and the Atacama Cosmology Telescope.