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.