Cosmology and Astrophysical Constraints of Gauss-Bonnet Dark Energy

Abstract

Cosmological consequences of a string-motivated dark energy scenario featuring a scalar field coupled to the Gauss-Bonnet invariant are investigated. We study the evolution of the universe in such a model, identifying its key properties. The evolution of the homogeneous background and cosmological perturbations, both at large and small scales, are calculated. The impact of the coupling on galaxy distributions and the cosmic microwave background is examined. We find the coupling provides a mechanism to viably onset the late acceleration, to alleviate the coincidence problem, and furthermore to effectively cross the phantom divide at the present while avoiding a Big Rip in the future. We show the model could explain the present cosmological observations, and discuss how various astrophysical and cosmological data, from the Solar system, supernovae Ia, cosmic microwave background radiation and large scale structure constrain it.

Figures (3)

• Figure 1: Background evolution when $\lambda=4$ and $\alpha=20$. In general, the evolution in the model consists of 1) the scaling attractor and 2) the potential-dominated (de Sitter) solution. Existence of 1) requires $\lambda > \sqrt{6}$, and the transition to 2) then occurs if $\alpha>\lambda$. Here we plot fractional energy densities for matter, $\Omega_m$ (dash-dotted line), scalar field $\Omega_\phi = (x^2+y)/3$ (dashed line) and the GB term, $\Omega_f = \mu$ (dotted line). Solid line is the total equation of state $w_{eff} = -2\epsilon/3 - 1$.
• Figure 2: Top two figures: The effect of the potential slope on the CMB and matter power spectra. Here $\alpha=20$. Dotted lines are for $\lambda=4.5$, dashed line for $\lambda=6.0$, and dash-dotted for $\lambda=8.0$. Bottom two figures: The effect of the coupling slope on the CMB and matter power spectra. Here $\lambda=6.0$. Dotted lines are for $\alpha=10$, dashed line for $\alpha=20$, and dash-dotted for $\alpha=30$. The solid line is $\Lambda$CDM model. $\Omega_m^0=0.4$ for all figures. The CMB and matter power spectra error bars are from the WMAP data Spergel:2006hy and SDSSsloan respectively.
• Figure 3: The 68, 90 and 99 percent confidence limits for the model in the $\Omega_m$ - $\lambda$ plane when $\alpha$ is marginalized over in the range $1.5\lambda < \alpha <10\lambda$. Dotted lines are constraints from the SNeIa data and the solid lines from the combined SNeIa and CMBR shift parameter data. In the gray area the scaling solution is unstable regardless of $\alpha$. If the scalar field is tracking already in the nucleosynthesis epoch, there is a tension with the amount of early quintessence and the nucleosynthesis limit. Conservatively, this limit would translate to $\lambda>6.3$Copeland:2006wr.