Braneworld models of dark energy

Abstract

We explore a new class of braneworld models in which the scalar curvature of the (induced) brane metric contributes to the brane action. The scalar curvature term arises generically on account of one-loop effects induced by matter fields residing on the brane. Spatially flat braneworld models can enter into a regime of accelerated expansion at late times. This is true even if the brane tension and the bulk cosmological constant are tuned to satisfy the Randall--Sundrum constraint on the brane. Braneworld models admit a wider range of possibilities for dark energy than standard LCDM. In these models the luminosity distance can be both smaller and larger than the luminosity distance in LCDM. Whereas models with $d_L \leq d_L(\rm LCDM)$ imply $w = p/ρ\geq -1$ and have frequently been discussed in the literature, models with $d_L > d_L(\rm LCDM)$ have traditionally been ignored, perhaps because within the general-relativistic framework, the luminosity distance has this property {\em only if} the equation of state of matter is strongly negative ($w < -1$). Matter with $w < -1$ is beset with a host of undesirable properties, which makes this model of dark energy unattractive within the conventional framework. Braneworld models, on the other hand, have the capacity to endow dark energy with exciting new possibilities without suffering from the problems faced by models with $w < -1$. For a subclass of parameter values, braneworld dark energy and the acceleration of the universe are {\em transient} phenomena. In these models, the universe, after the current period of acceleration, re-enters the matter dominated regime so that the deceleration parameter $q(t) \to 0.5$ when $t \gg t_0$, where $t_0$ is the present epoch. Such models could help reconcile an accelerating universe with the requirements of string/M-theory.

Figures (8)

• Figure 1: The Hubble parameter in units of $H_{\rm LCDM}(z)$ is plotted as a function of redshift for the two braneworld models BRANE1 and BRANE2. Whereas $H(z)$ in BRANE2 is larger than $H(z)$ in LCDM, in the case of BRANE1 the value of $H(z)$ is smaller than its value in LCDM. Parameter values are: $\Omega_\kappa = 0, ~\Omega_\ell = 1.0$, $\Omega_{\rm m} = 0.3$, and $\Omega_{\Lambda_{\rm b}} = 1, 10, 10^2, 10^3$ (top to bottom for BRANE2 and bottom to top for BRANE1). The value of $\Omega_\sigma$ is determined from (\ref{['omega-r1']}) & (\ref{['omega-r2']}). Parameter values for the LCDM model are $\Omega_{\rm m} = 0.3, ~\Omega_\Lambda = 0.7$. For large values of the bulk cosmological constant $\Omega_{\Lambda_{\rm b}}$, BRANE1 and BRANE2 become indistinguishable from LCDM.
• Figure 2: The luminosity distance is shown as a function of redshift for the two braneworld models BRANE1 & BRANE2, LCDM, SCDM, and 'phantom energy'. All models, with the exception of SCDM, have $\Omega_{\rm m} = 0.3$. SCDM has $\Omega_{\rm m} = 1$. The BRANE1 & BRANE2 models have $\Omega_\ell = 0.3$ and vanishing cosmological constant in the bulk. LCDM and the phantom model have the same dark energy density $\Omega_\Lambda = \Omega_X = 0.7$. The equation of state for dark energy is $w_\Lambda = -1$ for LCDM and $w = p_X/\rho_X = -1.5$ for phantom. The luminosity distance is greatest for BRANE1 & phantom, and least for SCDM. BRANE1 & BRANE2 lie on either side of LCDM.
• Figure 3: The distance modulus ($m-M$) of Type Ia supernovae (the primary fit of the Supernova cosmology project) is shown relative to an empty $\Omega_{\rm m} \to 0$ Milne universe (dashed line). The solid line refers to the distance modulus in BRANE1 with $\Omega_\ell = \Omega_{\rm m} = 0.3$, and vanishing cosmological constant in the bulk. The dotted line (below the solid) is LCDM with $(\Omega_\Lambda, \Omega_{\rm m}) = (0.7,0.3)$. The uppermost and lowermost (dot-dashed) lines correspond to de Sitter space $(\Omega_\Lambda, \Omega_{\rm m}) = (1,0)$ and SCDM $(\Omega_\Lambda, \Omega_{\rm m}) = (0,1)$, respectively.
• Figure 4: The age of the universe (in units of the inverse Hubble parameter) is plotted as a function of the cosmological redshift for the models discussed in Fig. \ref{['fig:lum']}. (The phantom model is not shown.) BRANE1 models have the oldest age while SCDM is youngest.
• Figure 5: The deceleration parameter $q(z)$ is shown for BRANE1, BRANE2 and LCDM. The model parameters are as in Fig. \ref{['fig:lum']}. For reference it should be noted that $q = 0.5$ for SCDM while de Sitter space has $q = -1$.