Inflation in Mimetic f(G) Gravity

Mimetic gravity is analysed in the framework of some extensions of general relativity (GR), whereby a function of the Gauss–Bonnet invariant in four dimensions is considered. By assuming the mimetic condition, the conformal degree of freedom is isolated, and a pressureless fluid naturally arises. Then, the complete set of field equations for mimetic Gauss–Bonnet gravity is established, and some inflationary models are analysed, for which the corresponding gravitational action is reconstructed. The spectral index and tensor-to-scalar ratio are obtained and compared with observational bounds from Planck and BICEP2/Keck array data. Full agreement with the above data is achieved for several versions of the mimetic Gauss–Bonnet gravity. Finally, some extensions of Gauss–Bonnet mimetic gravity are considered, and the possibility of reproducing inflation is also explored