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Mimetic gravity is analysed in the framework of some extensions of GeneralRelativity, where a function of the Gauss-Bonnet invariant in four dimensionsis considered. By assuming the so-called mimetic condition, the conformaldegree of freedom is isolated and a pressureless fluid naturally arises. Then,the complete set of field equations for mimetic Gauss-Bonnet gravity isestablished and some inflationary models are analysed, for which thecorresponding gravitational action is reconstructed. The spectral index andtensor-to-scalar ratio are obtained and compared with observational bounds fromPlanck and BICEP2/Keck array data. The full agreement with above data isachieved for several versions of the mimetic Gauss-Bonnet gravity. Finally,some extensions of Gauss-Bonnet mimetic gravity are considered and thepossibility of reproducing inflation is also explored.

Inflation in mimetic f(G) gravity