Observational constraints on braneworld geometry

The low energy regime of 5D braneworld models with a bulk scalar field is studied. The setup is rather general and includes the Randall-Sundrum and dilatonic braneworlds models as particular cases. We discuss the cosmological evolution of the system and conclude that, in a two brane system, the negative tension brane is generally expected to evolve towards a null warp-factor state. This implies, for late time cosmology, that both branes end up interacting weakly. We also analyze the observational constraints imposed by solar-system and binary-pulsar tests on the braneworld configuration. This is done by considering the small deviations produced by the branes on the 4D gravitational interaction between bodies in the same brane. Using these constraints we show that the geometry around the braneworld is strongly warped, and that both branes must be far apart.

Figure 1

Schematic representation of the 5-dimensional brane configuration. In the bulk there is a scalar field $\varphi$ with a bulk potential $U(\varphi )$. Additionally, the bulk space is bounded by branes, ${\Sigma }_1$ and ${\Sigma }_2$, with tensions ${\lambda }_1=+{\sigma }_1({\varphi }^1)$ and ${\lambda }_2=-{\sigma }_2({\varphi }^2)$ respectively.

Figure 2

The figure shows the generic behavior of the warp factor $\omega$ and the scalar field $\varphi$ as functions of $z$. We can always choose $\varphi$ to increase and $\omega$ to decrease in the $z$ direction.

Figure 3

The figure shows the evolution of the second brane for the initial condition ${\dot{\omega }}_2<0$. The second brane is forced to evolve towards the fixed point $({\omega }_2,{\dot{\omega }}_2)=0$ regardless of the evolution of the first brane.

Figure 4

The figure sketches the constrained parameter space spanned by ${\alpha }_1^2$ and $⟨{\alpha }^2⟩$. The Randall-Sundrum model corresponds to the point $({\alpha }_1^2,⟨{\alpha }^2⟩)=0$, while dilatonic braneworlds are represented by the curve $⟨{\alpha }^2⟩={\alpha }_1^2$.

Figure 5

The figure shows a generic potential $\sigma$ as a function of $\omega$. The parameter ${\omega }_0$ can be adjusted to analyze different cases near the first brane (where $\omega ={\omega }_1$).

Figure 6

The figure shows different behaviors for $\sigma (\varphi )$ about the first brane position ${\varphi }^1$. The curves are: Curve 1, ${\alpha }_1^2=⟨{\alpha }^2⟩$ (dilatonic braneworlds); Curve 2, ${\alpha }_1^2<⟨{\alpha }^2⟩$; Curve 3, ${\alpha }_1^2>⟨{\alpha }^2⟩$.