Aspects of scalar field dynamics in Gauss-Bonnet brane worlds

Abstract

The Einstein-Gauss-Bonnet equations projected from the bulk to brane lead to a complicated Friedmann equation which simplifies to H²˜~ρ^q in the asymptotic regimes. The Randall-Sundrum (RS) scenario corresponds to q=2 whereas q=2/3 and q=1 give rise to high-energy Gauss-Bonnet (GB) regime and the standard general relativity (GR), respectively. Amazingly, while evolving from RS regime to high-energy GB limit, one passes through a GR-like region which has important implications for brane world inflation. For tachyon GB inflation with potentials V(Φ)˜Φ^ρ investigated in this paper, the scalar to tensor ratio of perturbations R is maximum around the RS region and is generally suppressed in the high-energy regime for the positive values ofρ. The ratio is very low for ρ>0 at all energy scales relative to GB inflation with ordinary scalar field. The models based upon tachyon inflation with polynomial type of potentials with generic positive values of ρ turn out to be in the 1σ observational contour bound at all energy scales varying from GR to high-energy GB limit. The spectral index n_S improves for the lower values of ρand approaches its scale invariant limit for ρ=−2 in the high-energy GB regime. The ratio R also remains small for large negative values of ρ, however, difference arises for models close to scale invariance limit. In this case, the tensor to scale ratio is large in the GB regime whereas it is suppressed in the intermediate region between RS and GB. Within the framework of patch cosmologies governed by H²˜ρ^q, the behavior of ordinary scalar field near cosmological singularity and the nature of scaling solutions are distinguished for the values of q<1 and q>1. The tachyon dynamics, on the other hand, exhibits stable scaling solutions ∀q if the adiabatic index of barotropic fluid γ<1.