Gauss-Bonnet Quintessence: Background Evolution, Large Scale Structure   and Cosmological Constraints
  We investigate a string-inspired dark energy scenario featuring a scalar field with a coupling to the Gauss-Bonnet invariant. Such coupling can trigger the onset of late dark energy domination after a scaling matter era. The universe may then cross the phantom divide and perhaps also exit from the acceleration. We discuss extensively the cosmological and astrophysical implications of the coupled scalar field. Data from the Solar system, supernovae Ia, cosmic microwave background radiation, large scale structure and big bang nucleosynthesis is used to constrain the parameters of the model. A good Newtonian limit may require to fix the coupling. With all the data combined, there appears to be some tension with the nucleosynthesis bound, and the baryon oscillation scale seems to strongly disfavor the model. These possible problems might be overcome in more elaborate models. In addition, the validity of these constraints in the present context is not strictly established. Evolution of fluctuations in the scalar field and their impact to clustering of matter is studied in detail and more model-independently. Small scale limit is derived for the perturbations and their stability is addressed. A divergence is found and discussed. The general equations for scalar perturbations are also presented and solved numerically, confirming that the Gauss-Bonnet coupling can be compatible with the observed spectrum of cosmic microwave background radiation as well as the matter power spectrum inferred from large scale surveys. 
Tomi Koivisto and David F. Mota