From Big to Little Rip in modified F(R,G) gravity

We discuss the cosmological reconstruction in modified Gauss-Bonnet (GB) gravity. It is demonstrated that the modified GB gravity may describe the most interesting features of late-time cosmology. We derive explicit form of effective phantom cosmological models ending by the finite-time future singularity (Big Rip) and without singularities in the future (Little Rip).Comment: 15 pages, 7 figure