Signature flipping of isotropic homogeneous space-time with holographic dark energy in [formula omitted]gravity.

• The piece of the work is achieved towards power and exponential inflation cosmologies. • The perceived cosmologies are singular and singularity observed at an initial epoch. • The Gauss-Bonnet energy density is unity while Gauss-Bonnet matter-energy density is null i.e. not observed in the model. • The equation of state parameter of both the models are affected by the value of constant n. • Gauss-Bonnet term in linear and quadratic model is just like as cosmological constant which described Λ CDM model. Present investigation devoted to the dynamical study of isotropic and homogeneous FRW space-time filled with a Holographic dark energy fluid with cosmic string in the framework of numerous form of f (G) gravity models say linear, quadratic and inverse model. We determine the aspects of the model by considering the hybrid expansion law for the average scale factor that yields power and exponential inflation cosmologies, in its special cases. As per the observation, the model is singular and singularity observed at an initial epoch. The contribution of Gauss-Bonnet term in linear and quadratic model is just like as cosmological constant hence for whole expansion it is Λ CDM model which supports and resembles with the observational fact that the usual matter is about 4% and the dark energy occupies near about 73% of the energy also the results with several high precision observational experiments, especially the Wilkinson Microwave Anisotropic Probe (WMAP) satellite experiment. [ABSTRACT FROM AUTHOR]