Cosmology of viscous holographic f(G) gravity and consequences in the framework of quintessence scalar field

Work reported in this study demonstrates the reconstruction schemes for the f(G) gravity in the framework of bulk viscosity and holographic background evolution by considering the universe filled by the viscous fluid that is just special class of more general fluids as described in Nojiri and Odintsov [Inhomogeneous equation of state of the universe: Phantom era, future singularity, and crossing the phantom barrier, Phys. Rev. D 72 (2005) 023003]. The bulk viscous pressure has been considered as Pi = -3H xi, with xi = xi(0) + xi(1) H + xi(2)((H)over dot + H-2). Considering the scale factor in power law form and taking holographic dark energy (HDE) with density rho Lambda = 3c(3)M(p)(2)L(-2) and generalized extended holographic dark energy (EGHRDE) with density rho Lambda = 3c(2)(alpha(H)over dot + beta H-2), a specific case of Nojiri-Odintsov holographic DE ([unifying phantom inflation with late-time acceleration: Scalar phantom-non-phantom transition model and generalized holographic dark energy, Gen. Relativ. Gmvit. 38 (2006) 1285]) we have derived solutions for f(G) and the subsequent effective equation of state parameters have been found to behave like quintom irrespective of the choice of c(2). Finally, considering f (G) as quintessence scalar field we have explored the possibility of quasi-exponential expansion and warm inflation.