Exploring extra dimensions through observational tests of dark energy and varying Newton's constant

We recently presented a series of dark energy theorems that place constraints on the equation of state of dark energy ($\text{wdark}$), the ime-variation of Newton’s constant ($\dot{G}$), and the violation of energy conditions in theories with extra dimensions. In this paper, we explore how current and future measurements of $\text{wdark}$ and $\dot{G}$ can be used to place tight limits on large classes of these theories (including some of the most well-motivated examples) independent of the size of the extra dimensions. As an example, we show that models with conformally Ricci-flat metrics obeying the null energy condition (a common ansatz for Kaluza-Klein and string constructions) are highly constrained by current ata and may be ruled out entirely by future dark energy and pulsar observations.