Revamped braneworld gravity

Gravity in five-dimensional braneworld backgrounds often exhibits problematic features, including kinetic ghosts, strong coupling, and the van Dam-Veltman-Zakharov (vDVZ) discontinuity. These problems are an obstacle to producing and analyzing braneworld models with interesting and potentially observable modifications of 4d gravity. We examine these problems in a general ${\mathrm{AdS}}_5/{\mathrm{AdS}}_4$ setup with two branes and localized curvature from arbitrary brane kinetic terms. We use the interval approach and an explicit straight gauge-fixing. We compute the complete quadratic gauge-fixed effective 4d action, as well as the leading cubic order corrections. We compute the exact Green’s function for gravity as seen on the brane. In the full parameter space, we exhibit the regions which avoid kinetic ghosts and tachyons. We give a general formula for the strong coupling scale, i.e., the energy scale at which the linearized treatment of gravity breaks down, for relevant regions of the parameter space. We show how the vDVZ discontinuity can be naturally but nontrivially avoided by ultralight graviton modes. We present a direct comparison of warping versus localized curvature in terms of their effects on graviton mode couplings. We exhibit the first example of Dvali-Gabadadze-Porrati (DGP)-like crossover behavior in a general warped setup.

Figure 1

The unshaded area is where $-1<T_i^{+}<1$. On the boundary, the curved lines are described by $w_i=-6v_i-\frac{6}{v_i}$, and the straight lines are $w_i=\pm 12$.

Figure 2

The ${\overline{\mathcal{C}}}_g^{(0)}=0$ on ($v_L$, $w_L$)-plane when $v_0=0.3$ and $w_0=10$, 5, $-5$, $-10$ for the lines from left to right, respectively.

Figure 3

The ${\overline{\mathcal{C}}}_g^{(0)}=0$ on ($v_L$, $w_L$)-plane when $w_0=5$ and $v_0=1.5$, 0.5, $-0.5$, $-1$ for the lines from left to right, respectively.

Figure 4

The ${\overline{\mathcal{C}}}_{\psi }=0$ on ($v_L$, $w_L$)-plane when $v_0=0.3$ and $w_0=10$, 5, $-5$, $-10$ for the lines from left to right, respectively.

Figure 5

The ${\overline{\mathcal{C}}}_{\psi }=0$ on ($v_L$, $w_L$)-plane when $w_0=5$ and $v_0=1.5$, 0.5, $-0.5$, $-1$ for the lines from left to right, respectively.

Figure 6

$\mathfrak{D}{|}_{q=0}\times \mathfrak{D}{|}_{q\to -\infty }>0$ on ($v_L$, $w_L$)-plane when $v_0=2$ and $w_0=1$. The solid curve is where $\mathfrak{D}{|}_{q=0}=0$ and dashed straight lines are $\mathfrak{D}{|}_{q\to -\infty }=0$.

Figure 7

Allowed region (unshaded) on ($v_L$, $w_L$)-plane with $v_0=2$ and $w_0=1$.

Figure 8

Masses (in units of the brane curvature $H$) for the first five massive graviton KK modes as a function of the bulk to brane curvature ratio, $k/H$. The strong warping regime corresponds to the far right region of the figure.

Figure 9

Masses (in units of the brane curvature $H$) for the first five massive graviton KK modes as a function of $v_0$ for fixed $H/k=0.25$ (left panel) and $H/k=0.95$ (right panel).

Figure 10

Coupling of the first five massive graviton KK modes to the brane at $y=0$ (in units of the coupling of the first mode) as a function of the bulk to brane curvature ratio $k/H$. The strong warping regime corresponds to the right of the figure.

Figure 11

Coupling of the $j=2$, 3, 4, 5 massive graviton KK modes to the brane at $y=0$ (in units of the coupling of the first mode) as a function of $v_0$ for fixed $H/k=0.25$ (left panel) and $H/k=0.95$ (right panel).

Figure 12

The dots represent the couplings of the massive graviton KK modes to the brane at $y=0$ (in units of the coupling of the first mode) as a function of their mass (in units of $H$), for $v_0=0.05$, 0.1, 0.15, 0.25, and 0.4, respectively, and fixed $H/k=1$. The lines correspond to the expectation from the DGP model with crossover scale $r_c=v_0/k$.

Figure 13

Coupling of the $j$th graviton KK mode (in units of $H/M^3$) to a probe brane localized at $y$ for $0\le y\le 2y_0$. We have fixed $H/k=0.95$ and $v_0=1$ and $j=1$, 2, 4, 6 from top to bottom in the coupling at the brane at $y=0$. The dots correspond to the couplings to the brane as computed in the Green’s function analysis.