Critical analysis of modulus stabilization in a higher dimensional $F(R)$ gravity

An exact solution for the bulk five-dimensional geometry is derived for $F(R)$ gravity with nonflat de Sitter 3-branes located at the $M_4\times Z_2$ orbifold boundaries. The corresponding form of $F(R)$ that leads to such an exact solution of the bulk metric is derived, which turns out to have all positive integer powers of $R$. In such a scenario, the stability issue of the modulus (radion field) is analyzed critically for different curvature epochs in both Einstein and Jordan frames. The radion in the effective 4D theory exhibits a phantom epoch, making this model viable for a nonsingular bounce. Simultaneous resolution of the gauge-hierarchy problem is exhibited through the resulting stable value of the radion field in the effective $3+1$-dimensional theory.

Figure 1

The above figure depicts the variation of $P(\xi )$ with $\xi$ for $\omega ={10}^{-3}=\gamma$. The noncanonical coupling to the kinetic term has a zero crossing at $\xi ={\xi }_c$ denoted by the green dashed line. The magenta dashed line represents the value of $\xi$ where the potential has an inflection point. For more details, see the text.

Figure 2

The above figure illustrates the behavior of the radion potential $V(\xi )$ for $\omega ={10}^{-3}$ with (a) $\gamma =0.99$, (b) $\gamma ={10}^{-3}$, and (c) $\gamma ={10}^{-6}$. We note that $V(\xi )$ has an inflection point at $\xi ={\xi }_1=\frac{{\omega }_m}{c_2}$ (marked by the magenta dashed line). The green dashed line denotes the value of $\xi$ where the noncanonical kinetic coupling $P(\xi )$ has a zero crossing. The parameter $\gamma$ is directly related to the strength of the scalar field whose presence gives rise to a maxima in $V(\xi )$ which vanishes with smaller and smaller values of $\gamma$ (a)–(c).