Cosmological effects of radion oscillations

We show that the redshift of pressureless matter density due to the expansion of the universe generically induces small oscillations in the stabilized radius of extra dimensions (the radion field). The frequency of these oscillations is proportional to the mass of the radion and can have interesting cosmological consequences. For very low radion masses $m_b\left[m_b\sim \right(10\mathrm{}–{100)H}_0\simeq {10}^{-32}\mathrm{eV}]$ these low frequency oscillations lead to oscillations in the expansion rate of the universe. The occurrence of acceleration periods could naturally lead to a resolution of the coincidence problem, without need of dark energy. Even though this scenario for low radion mass is consistent with several observational tests it has difficulty meeting fifth force constraints. If viewed as an effective Brans-Dicke theory it predicts $\omega =-1+1/D$ $(D$ is the number of extra dimensions), while experiments on scales larger than 1 mm imply $\omega >2500.\mathrm{}$ By deriving the generalized Newtonian potential corresponding to a massive toroidally compact radion we demonstrate that Newtonian gravity is modified only on scales smaller than $m_b^{-1}.$ Thus, these constraints do not apply for $m_b>{10}^{-3}\mathrm{eV}$ (high frequency oscillations) corresponding to scales less than the current experiments (0.3 mm). Even though these high frequency oscillations cannot resolve the coincidence problem they provide a natural mechanism for dark matter generation. This type of dark matter has many similarities with the axion.