Gauss-Bonnet quintessence: Background evolution, large scale structure, and cosmological constraints

Abstract

We investigate a string-inspired dark energy scenario featuring a scalar field with a coupling to the Gauss-Bonnet invariant. We discuss extensively the cosmological and astrophysical implications of the coupled scalar field. 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. The evolution of fluctuations in the scalar field and their impact on the clustering of matter are studied in detail and model independently. The small-scale limit is derived for the perturbations and their stability is addressed. 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. Data from the solar system, supernovae Ia, cosmic microwave background radiation, large-scale structure, and big bang nucleosynthesis are used to constrain the parameters of the model. The geometric constraints from background expansion favor exponential potentials with a shallow slope, which is in tension with the nucleosynthesis bound on early quintessence. Also, high values for the present matter density are required. Including the baryon oscillation scale, one could rule out the model at about 99% confidence level. A discussion of how to overcome such possible problems in more elaborate models is included, together with considerations of the validity of these constraints in the present context. Interestingly, one also finds that a good Newtonian limit may require fixing the coupling.