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In this paper, we reconstruct the holographic dark energy in the framework of the f (G) modified theory of gravity, where G is the Gauss-Bonnet invariant. In this context, we choose the infrared cut-off as the Granda-Oliveros cut-off, which is proportional to the Hubble parameter H and its first derivative with respect to the cosmic time t . We reconstruct the f (G) model with the inclusion of HDE and the three well-known forms of the scale factor a(t) , i.e. the emergent, the logamediate and the intermediate scale factors. The reconstructed model as well as equation of state parameter are discussed numerically with the help of graphical representations to explore the accelerated expansion of the universe. Moreover, the stability of the models incorporating all the scale factors is checked through squared speed of sound v s 2.

Holographic reconstruction of f(G) gravity for scale factors pertaining to emergent, logamediate and intermediate scenarios