Reconstruction of modified Gauss–Bonnet gravity for emergent universe

We present a flat emergent universe model in modified Gauss–Bonnet gravity in four dimensions. The emergent universe model is free from a big-bang singularity and also describes the observed universe fairly well. It is assumed that the present universe emerged from a static Einstein universe phase that exists in the infinite past. To obtain the flat emergent universe model, we reconstruct mimetic modified f(G)-gravity (G representing Gauss–Bonnet terms). The functional form of f(G)-gravity is determined with or without matter, and can accommodate the early inflation and late accelerating phases satisfactorily. In contrast, in Einstein’s general theory of relativity, a flat emergent universe was obtained within the modified matter sector.