Geometric approach to modulus stabilization

Modulus stabilization, a must for explaining the hierarchy problem in the context of Randall-Sundrum-like scenarios, is traditionally achieved through the introduction of an extra field with ad hoc couplings. We point out that the stabilization can, instead, be achieved in a purely geometrodynamical way, with plausible quantum corrections in the gravity sector playing the key role. The size of the corrections that lead to acceptable phenomenology is also delineated.

Figure 1

The solid line denotes the potential for $a=0.01,b=0.01,\lambda =-0.6$, while the dashed line denotes a typical approximation for ${\varphi }_a=5.05M^{3/2}$.

Figure 2

Isohierarchy ($k{r}_c$) contours in the $(b,\lambda )$ plane for $a=0$ (top) and $a=0.1$ (bottom).

Figure 3

Isohierarchy ($k{r}_c$) contours in the $(a,\lambda )$ plane for $b=0.1$ (top) and $b=0.5$ (bottom).

Figure 4

The mass of the radion as a function of $b$ for fixed values of the parameter $a$ and the hierarchy $k{r}_c$. (The value of $\lambda$ is automatically determined vide Figs. 2.) The figures have been made for $V_1=0$ and $m_{\mathrm{rad}}$ calculated to $\mathcal{O}({\epsilon }^{1/2})$. Relaxing these would lead to thickening of the curves into bands.